Summary on Development Economics (Ray) written in 2012-2013.

Chapter A: Introduction to development

Development Economics is concerned with the economic transformation of the developing countries. The most widely used measurement to determine whether a country can be considered as being developing is the world development Report income per capita. If this is below 9.000 dollar per year the country is a low- or middle-income country, and therefore developing. Above this threshold a country is a high-income country. However, there are several complications with using this estimate, and consequently other measurements will be discussed. Development economics does not only describe the situation of the developing countries, it does also point out ways to close the gap with the developed countries (or at least improve the gap).  
 
It is possible to evaluate the situation of developing countries in two different ways. The first one is from a global context, and concentrates on the environmental differences between developed and developing countries. Part of the current situation can be explained this way. However, a different view is the internal and individual one of each developing country. This way, differences between developing countries can be explained and there may be individual solutions to improve the country’s situation. This analytical perspective will focus on aspects such as: market failure and government intervention. The inequality throughout the world will be described using the historical process, the implications due to market failure, the implications on other aspects and policies and there is a role for new theories and models. New empirical research offers new data, which might show that ‘established’ theories and models do not apply, or definitely need to be adjusted.  
 
Some economics argue that development economics is just a bundle micro-, macro- and international economics, built around specific fields such as: labour market economics, (public) finance, international trade, monetary policies etc. Obviously this is in some sense true. However, the developing countries have a complete different framework to begin with analyzing the specific fields of economics. This is the main reason why development economics is a separate subject.  
 
Among the most important objectives / goals of countries, economic development might be the most crucial. This ‘development’ can be quite vague, so we will need some further investigation in what a country is really aiming at and how we can measure the realized development. One way to measure if a country is developed is to analyze the physical quality of the inhabitants’ life. Do they have proper food, health, housing and clothing? Moreover, we can also add aspects such as: political freedom, technology level, environmental issues and employment level. One widely used measurement of wealth is gross domestic product (GDP) and considering this, the growth in GDP reflects the economic development of a country. However, it is clear that GDP is not a complete measurement, the way income is divided among the inhabitants as well as aspects as clean water, health services and the ability the read and write are very important. We can better view GDP as a yardstick of economic development rather than an exact definition of development. There is a correlation between GDP and social aspects as mentioned above: when additional income is used to increase a nation’s welfare on the most needing aspects it clearly raises a country’s development. When additional income is distributed to a very small group of wealthy
people, the development of the country might be significantly smaller. This results in two different ways to analyze development economics: the first is the level of average income levels and how they can be increased, and the second way focuses on the way the income is distributed among the inhabitants.  
 
Income Measurement
A low per capita income level is the most important sign of economic underdevelopment. To be able to compare this throughout all countries across the world, the local income level (measured in the local currency) is converted to one specific currency, which is usually the U.S. dollar. This amount is than divided by the country’s population. The world development report collects these numbers, which are
now easy to compare. One of the most eye-catching results is that of total world output (24 trillion U.S. dollars) 20% comes from low- and middle income countries. However, of the world’s population 85% lives in these countries. Another result which can be drawn from these numbers is that the richest per capita country is 400 times richer than the poorest one (respectively: Switzerland and Tanzania).  
 
Without any doubt, these results prove the unfair distribution of the world’s income. As the total picture is quite clear, some problems arise with measuring. One of these is the reported level of income: in developing countries the tax collection system is not as waterproof as it is in developed countries. This way the level of income may be underestimated. A second aspect which biases the level of income of developing countries is the problem of non-traded goods. The exchange rate can be expressed as
a price measured in the commodity prices relative to that of the foreign countries. The exchange rate is rather only determined by the prices of traded goods. These are, due to international trade relatively more expensive than non-traded goods. When the domestic data is than converted to U.S. dollars, the real income or purchasing power is again underestimated for developing countries. An income level measured using PPP (purchasing power parity) compared to one using the exchange rate offers a better picture of the real world. A third aspect is that in developing countries, self-consumption is performed more often than in developed countries. The total output contributed through self-consumption is not measured in the per capita income level. Furthermore, there are a number of aspects which also contribute to biased results: market related, such as: monopolies, oligopolies and not fully flexible prices. Also differences in
consumer preferences and input factors available across countries exist. Finally, externalities such as pollution, resource depletion and other environmental damages bias GDP measures.
 
History: 1960 – 1990
Parente and Prescott analyzed the growth rates of the last few decades. They calculated that the average per capita growth rate for 102 countries was around 1.9% per year. However, this rate can, and does, differ greatly across countries.  East Asian economies such as: Japan, South-Korea, Taiwan, Singapore, Hong Kong, Thailand, Malaysia and Indonesia showed an annual growth rate of 5.5% between ’65 – ’90.
China grew even more: at an annual rate of 8.2%! 

As the average rate is not more than 1.9% there must be quite some countries at a zero-rate or even below. Most of them are located in Latin America or Sub-Saharan Africa. Only two countries (Chile & Colombia) ended in 1990 at a higher per capita income level than they had in 1980 of all Latin American countries.  The ‘Doubling Time’ method clearly shows the consequences of these differing growth rates. This method calculates the number of years necessary to double the income level given the current growth rate.  
 
[1 + ( r / 100 ) ] ^ T = 2, r is growth rate and T is time in years.  
 
For the East Asian countries, mentioned above, this means that they need only 14 years to double income given a rate of 5%. A country with a lower rate of, let’s say, 1% will need 70 years to double.  
 
Reasons for the significant differences across regions such as: 
East Asia; growth through government intervention, equal income distribution…
Sub-Saharan Africa; low / no growth due to unstable government, high population growth rate and bad infrastructure…
Latin America; low / no growth due to debt crisis … will be broadly discussed later.
 
Now we have seen that countries are able to significantly differ from the average growth rate, it is interesting to see how the changes are for a low-income country to develop to a middle-income country or for a high-income country towards a middle-income country.  To analyze this, we can use a matrix invented by Quah. He divided the 102 countries, evaluated by Summers & Heston, into 5 categories. Respectively: ¼, ½, 1, 2 and ∞, which relate the country’s per capita income to the world’s per capita income. (So ¼ means that the per capita income of the country is 4 times less than the world’s per
capita income). The 5x5 matrix has the 5 categories on the rows as well as the columns. Each row
describes the percentage of the countries which were in the category indicated by the row, which moved to another (or the same) category after a given period. Quah uses the time period: 1962 – 1984.
 
 
 
The diagonal shows for 4 of the 5 categories (except 1/2) the highest number which means that a country will a higher chance of being in the same category than moving to another. This case is the strongest for the group of countries which have a per capita income of more than twice the world per capita income. Another conclusion is that countries in the middle category are far more mobile than in the lowest and highest category. This underlines the rule that poverty as well as wealth feeds itself. However, there are some arguments against this rule. For example, being a low-income country can be advantageous because there is a large supply of new and good technologies of the developed countries which can give an extreme input for the low-income country’s output. Therefore, conclusions might be ambiguous.  
 
Distribution
Some of the world’s largest cities in developing countries (Mexico city, Rio de Janeiro, Bombay, Manila) clearly show the huge gap between the rich and the poor within countries. Data of Deininger and Squire show the income shares of the poorest 40% and the richest 20% within countries. On average we see that the poorest 40% earns about 15% of total income and that the richest 20% earns about half the total income. Countries with a per capita income until 2500 dollars show a divergence of the shares
in income. Countries with a per capita income higher than 8000 dollars show a relative high convergence of the income shares of the poorest 40% and the richest 20%. Again, insights in income distribution are also discussed further in a later stage.  
 
Societal Consequences
We have seen that using GNP per capita to valuate the life of the inhabitants does not provide a good estimate. Especially in the middle-income countries, the distribution is quite unequal. Moreover, the income distribution does not tell much about the quality of life concerning health, education and human rights. Countries with quite similar GNP levels and distribution shares might considerably differ in aspects such as: Life expectancy, literacy, infant mortality and access to drinking water. Many of these
differences are determined by government policies. Even low-income countries might score far better than middle-income countries.  
 
To get a better picture about the status of a nation’s welfare the United Nations Development Programme (UNDP) publishes the Human development report. This report combines a number of aspects (as the ones mentioned earlier) into a single index number, the Human Development Index. There a three major groups: health, education and income. The first two groups consist of a small number of aspects.
Income is measured using PPP and considers diminishing marginal utility. The final index number has a value between 0 and 1, indicating the fraction of ultimate development. For industrial countries this HDI number is about 0,916 and for developing countries 0.570 (1.6 times less). The number varies more between the inhabitants of the latter countries than it varies within developing countries.  
Income and Human Development compared
It can offer quite some interesting results to compare the ranking lists of countries measured in per capita income or human development. Some high-income countries might perform considerable worse on human development than low-income countries. However, GDP seems to be a good overall estimate of development. How well GDP is an estimate for single aspects can be examined by use of a scatter diagram. That is a diagram with one independent and on dependent variable. In independent variable
might be GDP in this case (x-axis) and the independent variable can be life expectancy, infant mortality rate or adult literacy (y-axis). Each country’s number is placed within the diagram. If the diagram shows a clear upward sloping diagonal, there is a large positive correlation between the two variables. A negative correlation (mortality & GDP) shows a downward sloping diagonal. Since GDP seems to be a good indicator for most of the human development aspects, the theory of development economics must begin with study of per capita income. After this, the study of distribution might clear up some of the disruptions in the diagrams. However, there will always be disruptions which cannot be clearly explained. We will try to explain most of them by explaining the most important pressures.  
 
Country Characteristics
Demographically, low-income countries have high birth and death rates. As the country develops, the death rate decreases and after a certain time period the birth rate start to show the same downward move. The high population growth rate has an ambiguous effect: total income must grow faster than the population level in order to have a higher per capita income level. The increased supply of labor as an input facto might stimulate production. However, the relative supply of labour, capital and technology will determine if the increase in labour will outweigh the increased number of people to share income. Another implication of a high population growth rate is that the overall age is quite low. Because the majority of the population is young, aspects such as: child labour and low education will become more presently.
 
Production in low-income countries will depend more on agriculture (also self-consumption), than high-income countries. For low-, middle- and high income countries the percentages of agriculture in total output is respectively: 30%, 20% and 1-7%. Also the supply of labour for agriculture is enormous for low- and middle-income countries compared to high-income countries. Considering the productivity of agriculture, which is quite low compared to other industries, the resources available are clearly not used
in their optimal way. The low productivity as well as the influence of the media pushes the inhabitants from the rural to the urban regions. This migration, for a change of a better life, makes sure that the population growth rate in urban regions might be twice as high in the rural regions.  
 
The industry in which someone works can be divided into three sectors: primary (agriculture), secondary (industrial products) and tertiary (services). Since a high income level coincides with a large proportion of consumption in the services sector (travel, restaurants, banking), it is not a questionable result that in developed countries a large share of the population is working in the tertiary sector. This may increase up to a level of 70% of the total labour force. What actually is surprising is that even in developing countries this level may be around 60 or 70%. In contrast to the important role of agriculture, many people seek for fortune in the informal sector (on-street salesman, shoe-polishers etc.). Since they do not fit in the primary nor the secondary sector, there are counted as workers in the tertiary sector.  
 
The last characteristic is the involvement of international trade. The percentage of imports and exports of GNP versus the per capita income might differ from 10% (USA, Mexico and India), up to >100%  (Singapore and Hong Kong). Also the composition of the type of products may vary across countries. Where developing countries mostly export primary products, developed countries mostly export capital intensive products and consumer-durables. Moreover, the type of exportable products may also depend
on the theory of comparative advantage. This theory states that: the country will export the product in which it has an advantage compared to the other countries. This advantage may be achieved due to technology, cost advantages or input factor endowments. On the other hand, there are fewer differences regarding the amount and composition of the imports.  
 
The future of the exports and imports might largely depend on the type of products. Some economists argue that the future for primary products exporters might be negative. Other economists disagree on that (as usual), and state there will be a larger market for the kind of products, especially for countries with a comparative advantage in this sector. The future of a country’s exports and imports might be evaluated by looking at the terms of trade (measure of the ratio of the price of the exports to the
price of the imports). Is the change in the terms of trade positive, then will the prospects for the future be brighter than in the other case. 

Chapter B: Growth

In the last chapter we saw the importance of growth rates. However, the large differences between them and the implications and consequences they have, increase the need for sound empirical studies. The whole process of growth analysis actually focuses on possibilities about the future rather than exact outcomes. In order to get a picture of development economics and most important about growth, we cannot go without empirical evidence as well as a few distinct approaches. To serve as a basis for
further investigation we will address certain economic growth theories.  
 
Economic growth today
During the last decade, we faced a 2% growth rate as being normal. This is really a view from the modern economic growth. In earlier centuries the leading countries (The Netherlands: 1580-1820, United Kingdom: 1820-1890 and United States: 1890-1989) have shown annual growth of respectively: 0.2%, 1.2% and 2.2%. Two-centuries ago, a leading country would have been considered as stagnant given today’s norms of growth. Moreover, a 2% annual growth is now considered as normal, instead of good
and appreciated. This modern economic growth improves living standard so quickly that a person can easily face twice a doubling of the GDP level in his life.  
 
On average, developed countries showed a GDP in 1913 1.8 times higher than in 1870. In 1987 it was 6.7 times higher than 1870! Given the current transformation, the developing countries will show a similar growth. However, early statistics about GDP level of developing countries are mostly not available; we can say that after the WOII (when colonialism ended) these countries began to grow. Before that, they showed
stagnant and backward economies.  
 
In contrast with earlier periods, the developing countries have a more difficult task to accomplish. In order to close the gap, the developing countries do not only need to grow, they have to grow faster than the developed countries. For most of them, this will acquire growth rates as they have never seen before. However, no single country can be blamed for the differences among countries; every country can help to close the gap between them.  
 
Theories
We begin the analysis of growth theories by looking at the easiest form of the economy and its flows.
 
An economy produces a number of commodities. The production of these commodities distributes income. This income is again spent on the produced commodities. Simply put: the production of commodities generates income, which in turn is spend on those commodities. The commodities can be divided in two types of goods. First, there are the consumption goods bought by the households. Second, there are capital goods: goods which are used to produce other goods. These capital goods are bought by
firms. Given the theory that households’ income is all spend on consumer goods, where does it leave the market for capital goods? Each household has the choice between consumption and saving. For most households, the emphasis will be on consumption. Moreover, many households borrow money (mortgage etc.). On the whole, national saving exceeds national borrowing. This net saving acts as a supply of
money for firms. They can use this money to invest, i.e. buy capital goods.
 
The starting point of economic growth theory starts at the savings of the households, because without any savings there would be no resources for economic expansion by firms. The macro-economic balance, consumption is equal to production except for the savings (leakage) which equals to investments (injections), serves as the basic idea for all growth models.  
 
Growth is possible when investments exceed the amount needed for replacement by firms. This shows the importance of saving.  
 
Algebra:
A translation from the above into algebra enables us to add some additional features.
C = consumption, Y = total output, S = net saving (savings - borrowing).
The economy is closed and we add different time periods: t = 0,1,2,3…
 
Y(t) = C (t)  + S (t)    and: Y(t) = C (t)  + I (t)  so that: S (t) = I (t)
 
Regarding Investment we add the national Capital Stock = K, of which a fraction, δ, depreciates.
 
K (t + 1) = (1 - δ) K (t) + I (t)
 
The equation above shows the development of the Capital stock (decreased by depreciation and increased by the new supply of capital).  
 
Before we arrive at the first important model, the Harrod-Domar equation, we must add the saving rate, s, which is calculated by: S (t) / Y (t). Another aspect is the capital-output ratio, θ, which is calculated by K (t) / Y (t) and represents the amount of capital needed to produce 1 unit of output. Rearranging the previous equation we get:
 
Harrod-Domar equation:   s / θ = g + δ,  
where g represents the overall growth rate. This growth rate could now be analyzed easily. The growth rate will be higher if: the rate of savings (s) increases and when the capital-output ratio (θ) decreases. One additional step would be to find the equation for GNP per capita growth. We add: population (P) and population growth rate (n).  
 
Now: s / θ = (1 + g*) (1 + n) – (1 – δ).  
Where g* is GNP per capita growth. So this equation bundles the fundamental aspects of growth: ability to save / invest, ability to convert capital in output, rate of capital depreciation and the rate of population growth. A somewhat simpler version and approximation of the equation is: s / θ = g* + n + δ.
 
Harrod-Domar implications
One of the main aspects of the model is the capital-output ratio. In the equation this is represented by a single parameter. In fact, this is hardly possible to measure as all industries differ in the way they can change capital into output. Even within industries this changes, therefore, the ratio represents an average and can be used for the so- called ‘if-then’ statements.  
 
Moreover, all variables do not only explain growth, they are themselves also explained by growth. They are endogenous, so there are quite some different forces present in the model.
 
The rate of savings in developing countries is usually low, since the majority of the population earns just enough or perhaps not enough to pay for the necessities of life. Governmental policy will hardly affect the savings rate, as there is just no room for saving. Resources for investments must come from other sources, such as aid or external credit. Even in developed countries the saving rate may be considerably low, like in the United States. Leaving exceptions, we could state that middle-income countries have more funds available for savings / investments compared to low-income countries. Besides the clear absolute difference, middle-income countries can also relatively spend more on saving than low-income countries. However, it is not clear what the effect is on relative saving for high-income countries. The population from high-income countries does not feel the same urge to save for the countries sake, as
there is enough available. This makes extra consumption more attractive for this population; therefore it is not clear whether the spending to consumption ratio will be higher than in middle-income countries.  
 
The Harrod-Domar model does not make any distinction between income levels, despite that the growth rate might be influenced by the saving ratio and therefore the income level. Adding a relation between income per capita and growth rates makes this neutrality disappear.  
 
There is not only a strong link between income levels and the growth rate; there is also a relation between population growth rate and the development of a country. Developing countries show high birth rates as well as death rates. Actually the high death rate forces parents to have more children to reach the number of surviving offspring. When a developing country starts growing, the overall health care usually improves the surviving chances of children, thus lowers the death rate. On the other hand, birth rates seem to stay at the same level for a while. This has a significant impact on the population growth rate. In a graph with the growth rate vertically and the per capita income horizontally drawn, the growth rate per capita would represent a horizontal line in de Harrod-Domar model, however as we just discussed, it would inverse-u shaped. Initially an increase in per capita income would increase overall growth, than decrease overall growth (due to a lower death rate) and finally increase again when the birth rate declines. To sum up, the demographic transition will determine whether a country will grow per capita following an increase in growth rate.  
 
In the same way, a policy from the government which stimulates parents to have less children can also have a positive effect on the long run of per capita growth. A lesson from the discussion above is that variables in the growth model must be considered as endogenous instead of exogenous.   
 
Solow model
The model of Solow differs from the Harrod-Domar model in the role of diminishing returns of production factors. Both capital and labor are needed for production and a country’s endowment of both will determine which and how much products a country will produce. From the previous model we will keep the equations which state: Savings equal investment, capital accumulation and savings is a constant fraction of total income. We can obtain:
 
K (t + 1) = (1 - δ) K (t) + s Y (t)  and  (1 + n) k (t + 1) = (1 - δ) k (t) + s y (t).
 
The last equation explains the new per capita capital stock (depreciated per capita capital plus the current per capita savings), the right-hand side combines the capital stock with population growth. Next, we will introduce the production function with diminishing marginal returns. This means that additional labor or capital per capita will produce less output than the previous. Also, with a relative shortage of labor, the
capital-output ratio will fall. The model of Solow suggests that there exists a steady state of the per capita capital stock.  
 
Whether a country faces an initial high or low endowment of capital, and therefore a low or high capital-output ratio, a certain steady state will be reached. A high endowment means that the rate of expansion of aggregate capital is low, so population growth will exceed the growth of per capita capital. The steady state of per capita capital stock will be lower than the initial level. Conversely, a low endowment can make a more rapid expansion which exceeds population growth. The steady state level will now be above the initial level. This means that the long-run capital-labor ratio must be constant. In the Solow model there is for this reason no long-run growth per capita. Per capita growth will be in line with population growth. The major difference between the model of Solow and the one of Harrod-Domar is the diminishing returns. Consequently, the Solow model has a steady state and the Harrod-Domar can grow unlimited. It is not clear which one of the models in more realistic.  
 
Variables in the Solow model are the rate of savings, rate of depreciation and the growth rate of population. Together they determine the steady state and per capita income in the long-run. The steady state level, K*, has a per capita output level of Y*. The next equation will describe the steady state level:
 
K* / Y* = s / (n + δ).
The equation must be in balance, an increase in the rate of savings will have to be offset by a higher capital-output ratio. The steady state level of K* will be higher, which increases long-run level of per capita capital.   
 
Note that population growth has a double effect: higher population growth lowers the level of per capita income in the steady state, on the other hand needs total income to grow faster because in the long run steady state the economic growth has to equal population growth. This double effect is derived from the fact that labor is both an input factor in the model as well as the consumer of final goods. We can differentiate between the level effects and the growth effects. Where the level effect determines the
height of the starting point, the growth effect determines the rate at which the variable moves along.  
 
On the contrary, the saving rate has only a level effect on the steady state per capita income level. An increase in savings increases output on the short term and, therefore, a higher long run income level. The income growth has not changed actually; growth will stay in line with population growth.  
 
Technology
In the previous part we ignored the influence of technical progress. Actually, we assumed diminishing marginal returns which declines the growth rate of output and capital. However, if technological progress and knowledge gaining outweighs the diminishing returns, it is possible to have sustained capital growth.  
 
The technical progress contributes to efficiency or the productivity of labor. This can be due to education, technical know-how and other advances. To translate this to the model we can start with the equation of capital accumulation (which stays the same), and move to the efficiency units of the population.  
 
L (t) = E (t) P (t),
 
where L is the amount of efficiency labor units, E the productivity and P the working population. Both the efficiency and the population grow overtime. Again, we divide by the population to get the per capita variables. By dividing by the effective population we will get the per efficiency unit of labor variables: k^ and y^.
 
(1 + n) ( 1 + π) k^ (t + 1) = (1 – δ) k^ (t) + sy^ (t)
 
Where π is the growth rate of productivity, k^ and y^ the capital and output per efficiency unit of labor. K^ may rise or fall overtime. If k^ is rising, the growth of physical capital is larger than the population growth and the technical progress combined. On a moment in time, output per efficiency unit will grow less as diminishing returns come in. K^ will decline after that point. It does not matter in which position a country begins, it will always move to its steady state point of capital per efficiency unit of labor, again.   
Convergence
The prediction of the Solow model is that countries will converge. After the introduction of technical progress we can use the Solow model and the Harrod-Domar model to evaluate how realistic it is to expect convergence.
 
Unconditional convergence
The first form of convergence is the one of unconditional convergence. It assumes that there is no reason for countries to have different rates of saving, technical progress and population growth and capital depreciation. As we saw earlier, the starting point of a country does not matter for the steady state. Therefore, every country will end up at the same k^* level. This outcome might sound a little odd, but the assumption of the same exogenous parameters would suggest the same long run levels. However, we are not sure whether the similarity of parameters actually holds in reality. Let us start searching for empirical evidence for the hypothesis of convergence.  
 
When searching for data, we face the same difficulties as mentioned earlier. The necessary data is only available for the most recent decades for many countries. There are two solutions: look at a small collection of countries with a lot historical data or look at a large collection of countries over a smaller time horizon.  We will evaluate both.
 
Small collection
We can use Baumol’s research for testing the hypothesis. He examined the per capita income growth rates and levels of 16 countries from 1870 until 1979. His data can be plotted in a graph with on the vertical axis the log of per capita income growth from 1870 – 1979 and on the horizontal axis the log per capita income in 1870. The graph shows a clear downward sloping line of data. However, there is a pitfall when using the countries in this case. They are all rich countries now, but were they rich in 1870? If some of them were middle- or low-income countries why not add other countries which still have a middle or low income level? This would sketch a different, and less sound, picture about convergence. This selection bias, selecting only the countries which performed well, is using wisdom after the event.  
De Long improved the research by adding another 7 countries which had the same potential of convergence, but did not succeed that well. Inserting the new data in the graph shows a different picture. There is no reason to believe in convergence anymore. De Long also mentioned that in the 1870 data there is enough reason to assume there are large measurement errors.  
 
Large collection
An alternative approach is to use a large set of countries. Unfortunately, we can only look at the last few decades due to unavailable data. An advantage is that with a high number of countries, statistical errors are smoothed out. As mentioned earlier, this kind of research shows us that there seems to be no process of convergence in the last few decades. Despite poor countries increased their absolute income GNP; they have not gained relative to the rich countries.  
 
Parente and Prescott analyzed 102 countries’ GDP level relative to that of the US. If unconditional convergence would exist we would expect that the standard deviation would drop overtime. However, the research pointed out that it actually increased 18 per cent.  
 
Conditional convergence
For the last part of this chapter we move to conditional convergence. A somewhat weaker position which states that countries can differ in their variables (such as savings rate, population growth etc.) and move to a steady state point. This point does not have to be the same for all countries, indeed it will differ across countries since we now allow the variables to differ.  
 
We keep the assumption that knowledge can flow freely. Since we know from the Solow model that growth rates are only determined by the technical process, we will have to assume that growth rates per capita will converge. Starting point can differ due to differing variables, but the paths should be the same. To test this, and convergence, we will have to reexamine the data about steady states, growth rates and starting points.  
 
Data
Our aim is to find the relation between per capita income and the various parameters.  We will use earlier equations to start with:
 
K^* /  Y^*    ≈     s / (n + π + δ)
 
In order to evaluate output and capital better, we introduce a production function: the Cobb-Douglas production function.
 
Y = K^a L^1-a ,   a is a parameter between 0 and 1.
 
Rearranging and dividing by L we obtain a per effective labor function. Inserting this into the function above, we obtain:
 
Y^* ≈ (s / (n + π + δ)) ^a/(1-a)
 
If we express the equation above in logarithmic style and rewrite in per capita form, we can introduce a time horizon for the technical process. Finally, we obtain:
 
LN y (t) ≈ A +     a / (1 - a) LN s    –    a / (1 - a) LN (n + π + δ),    
 
where the first term A is the collection of terms:  LN E (0) + t LN (1 + π). Despite most variables are unknown, we will make estimations and predictions.  We have the following predictions: savings has a positive level affect on per capita income and population growth a negative one. Also, the approximate magnitude of the variables is 0.5.  
 
Mankiw, Romer and Weil used the equations above and analyzed this topic. They assumed π and δ to be around 5% per year. Estimations for s and y made them able to conclude several things.  

• More than 50% of worldwide GDP variation can be attributed to the variables s and n.  
• Coefficients s and n are approximately 1.42 and -1.97 respectively. Both have a significant effect. The first one has a positive effect and the second a negative one.

Conclusions
Savings and population growth have the predicted impact. However, their estimation are higher than predicted by the theory. Once we do not assume that all variables are equal between countries we see that the Solow model makes more sense. If it is true that all future growth rates will depend on the technical progress, what will that mean for the flow of technical knowledge across countries? We now have a somewhat better picture about the fundamentals of growth theories. Next chapter we will discuss some
new theories which concentrate on different aspects.

Chapter C  New theories

In the previous chapter we saw that we still face some difficulties concerning growth models. We saw implications for the Harrod-Domar and the Solow model. Moreover, assumptions about technology, capital and output may result in a model which has no real touch anymore with reality. Besides assuming some differences in variables we actually should try to explain them. This chapter we will look at some more models which built upon the two models we already discussed. Again, we should not expect them to answer all our questions and predict all variables precisely. What we can learn is how some fundamental models are used to built upon for further research. The new models will focus more on human capital than the previous.

Human Capital
New studies concentrated on the role of the population. In traditional models they are just seen as a production factor: labor. However, especially rich countries are able to invest resources to educate more skilled-labor. These skilled-laborers can deal with more sophisticated machines, invent or create new ideas or processes. Rich countries are relatively far more endowed with skilled-labor than poor countries. We must somehow adopt this aspect in a new model. It is possible to use the Solow model and change one important aspect. Households can either spend or save their money, these savings can be in physical capital. We now add the savings for education. A household is now able to invest time and money in their member’s education. We start with an equation for physical and human capital:
 
Y = K^a H^{1 – a}
 
We assume no depreciation, a constant population level and the three parameters are per capita measures. Further, a part of Y is saved for the accumulation of physical capital (s) and a part is saved for human capital (q). We can see how both types of capital grow overtime:
 
K (t + 1) – k (t)                                          h (t + 1) – h (t)
———————   = s r ^{1 – a}     and           ——————— = q r^{– a}
      k (t)                                                              h (t)
 
where r is the ratio of long run human to physical capital. Simplifying both equations into a ratio:
 
R = q / s. Ratio r can be used to calculate the long-run growth rate, since all variables should grow at the same rate. The long-run growth rate of all variables can be explained using:
 
Long-run growth rate = S^aq^{1 – a}
 
From the last equation we can draw some implications and conclusions:

• Countries with similar saving and technology parameters will grow at the same rate. They do not have to converge, due to different initial starting points. Note also that even though physical capital depreciates, the combination of both physical and human capital can show constant returns to scale. Both rates of savings have a level as well as a growth effect and these kind of theories are called endogenous growth theories 
• In the model we have two factors: physical and human capital. We can assume they face a constant return to scale due to the growth effects. If we would add a third: unskilled labor, we would not be able to assume constant returns (because we add an exogenous variable) but we would face diminishing returns to scale. 
• We can predict that the coefficient of population growth exceeds the coefficient of physical savings. The explanation for this is that an increase in population growth will lower per capita levels and therefore lower both types of savings. On the contrary, an increase in physical savings will not have an effect on current  human capital.
• The endowment of unskilled labour, physical and human capital are very important for a country’s future. Especially the relative endowments (factor ratios) have a converging or diverging effect on income per capita among countries. Convergence will happen if the poor countries are able to condition human capital and grow faster than the rich ones. Divergence will happen if rich countries are able to control the level of per capita income. This way, countries with more human capital will grow faster.  Since rich countries are usually the ones with more human capital both effects will smooth each other out.

Human capital measurement
We saw from earlier research (Summers-Heston) that there is little evidence for unconditional convergence. Can we improve this if we do regression analysis for human capital data? Let us regress the average growth in per capita real GDP (1965-1985) against the baseline per capita GDP 1960 and school enrolment (estimate for human capital level). School enrolment consists of primary and secondary enrolment data, and both have a positive and significant. Conditioning for human capital, the coefficient on per capita GDP is negative and significant. These outcomes are in line with earlier implications and conclusions.  
 
Different growth rates can be explained by this. For example, the rapid growth of Japan and South-Korea with low levels of physical capital and high levels of human capital. Also, the slower growth of the sub-Saharan countries with relative low school enrolments versus higher levels of GDP per capita.  
 
Technology
After out in-dept analysis of human capital we will now focus more on technology or the technical process and its consequences for output ratio. The endogenous models we described (Harrod-Domar and the human capital theories) state that all input factor together imply constant returns to scale, which enables endogenous growth.  
 
Where technology improvements in the history were results from individual inventors, nowadays many large firms invest heavily in research and development. There are two advantages of technical innovation: the direct advantages (cost savings, revenues from new products etc.) and the spill-over effects, where the global society (competitors, other industries and consumers) gains from the findings from R&D. It is obvious that the first is an incentive for innovation, where the second can have a negative effect on
the level of innovation. A third effect can be that the spill-over effects encourage new innovation (to keep a favourable position).  
 
Model
We will start with some basics to build a model for this concept. An economy has a fixed amount of human capital which can be used to produce final goods or invest in knowledge. This investment can be seen as an attempt to invent more productive machines or machines of a wider variety. We have to make a distinction between the quantity and quality of the machines. The quantity refers to the amount of capital, where the quality refers to the state of knowledge. This is translated into to following
production function.
 
Y (t) = E (t)^γ K (t) ^a [u H] ^{1 – a}
 
Where E (t) represents the amount of technical know-how, K (t) the capital stock and u the fraction of human capital used to produce goods.  
 
The growth rate of knowledge can be showed as: a (1 - u) H. Capital grows still at: s Y (t).
The current representation of innovation in this model, offers a trade-off for firms: produce today or invest in tomorrow. This trade-off is denoted by the parameter u. There are many influences on this parameter: direct advantages, spill-over effects, government intervention and the type of market (perfect competitive or monopolistic).  
 
Externalities
A different view regarding technology innovation concentrates on externalities. The concept is best described when an investment of an individual has effects for others. There can be positive externalities, when others enjoy from the investment, and negative externalities, when others suffer from the investment. With this in mind, it can be that an individual actually looses from its investment (for example when he/she is not able to recover the initial cost with revenues), but that the society will gain from the investment due to spill-over effects and positive externalities. Let us put this in a model
with a few firms within an economy.
 
Y (t) = E (t) K (t) ^a P (t) ^{1 – a}
 
Where P is labor employed and E the measure of overall productivity. The productivity measure is stated as the total positive externalities of all capital accumulation by all firms. Investing in innovation now is no individual concept anymore, but expressed as the gain for total society.  
 
E (t) = a K* (t) ^β
 
where K*is the average capital stock. Substituting this into the previous equation result in:
 
Y (t) = a K* (t) ^β  K (t) ^a  P (t) ^{1 – a}
 
In a case where all investments are determined by only one person, the investment decision would result in the most preferable amount for the society. If these investments are made by all individual owners there would be underinvestment, since they would not appreciate the positive externalities towards the others. That is the difference between social marginal benefits and private marginal benefits. The second
conclusion that can be drawn from the equation is that all the individual constant returns to scale from the firms can lead to increasing returns to scale for the society.  
 
A slightly different view regarding externalities (whether they are positive or negative) is the one about complementarities. This theory suggests that firms influence each other in their investment decision. If a few firms invest heavily they will encourage others to enjoy from the higher profits in the future (higher average investment level), in the same way could under investing lead to lower investments by others. This could mean that two identical economies can have different growth rates only because the
investments prospects of firms differ.  
 
Total factor productivity
We have discussed several aspects of technical progress so far. We now introduce a précis measure of this technical progress: the total factor productivity. We begin with a simple production function with variables: Y, K, P and E for output, capital, labor and knowledge measures. The variables Y, K and P can be measured, for E it is more difficult. We will estimate E with some simple algebra. We first assume no technical progress, so that every increase in output is contributed by increased amount of either capital or labor (given a fixed marginal product of capital and labor). We denote these marginal products of inputs and translate them into their income shares, σk and σp, for capital and labor. If we compare the increase in income and the increase in capital and labor input, we would expect them to be equal if there is not technical progress. If they are not equal we can conclude there must have been some technical progress. We refer to this amount as total factor productivity (TFP). The whole equation is stated
below:
∆ Y (t)                 ∆ K (t)                   ∆ P (t)
——— = σk (t) ———— +  σp (t) ———— + TFP (t)
  Y (t)                     K (t)                     P (t)
 
Since all variables can be measured except for TFP, the residual of the equation can be attributed to technical progress. This model is only concerned with changes, not with absolute levels of the economy. When trying to find data for the variables above, one should carefully select the right numbers. Especially, numbers for the labor force and the growth of capital stock may be quite complex. This model only holds when the production function exhibits constant returns to scale and the factors are paid their marginal product level.  
 
Empirical study: the Asian miracle
Eight countries showed a massive increase in their growth rates over the period 1965-1990. We will look at their sources of growth. The factors which increased very rapidly were: capital (both physical and human) and the technical progress. The rate of savings was low initially, but it increased rapidly also. Human capital levels were quite high compared to per capita income levels. Another important aspects is that these countries had very open economies and policies aimed at openness.  
 
Analysis of the World bank showed that about two-third of the growth can be attributed to the accumulation of capital and labor with, as most important factor, the status of primary education. The remaining part (one-third) can be attributed to technical progress or TFP growth.
 
Young also studied the reasons behind the tremendous growth. He searched for the right data to use to equation above and found that TFP growth did not have such a large part of total growth. Improvement of the labor force and capital stock were far more important. Differences between the World bank and Young’s findings can be attributed to different numbers used for population / labor force growth and differences in how they treated physical versus human capital accumulation.  

Chapter D: History and expectations

Up until now, we discussed the concept of growth in relation with convergence. There is no evidence for unconditional convergence, and conditional convergence is also a difficult matter as it requires quite some variables to be equal between countries. What if saving rates and others are not determined globally, but are determined (at least partly) by the history of a nation? In this chapter we will look into the concept of differences between countries’ variables at an historical point of view. Is there an urge
to converge since we are all human beings or will cultural differences allow countries to be different from each other? We will concentrate on both history and expectations and try to explain some complex issues.
 
We already introduced the concepts of externalities and complementarities in the previous part. We will continue with that topic (especially complementarities), since it plays an important role within cultural differences. Within a country one type of product or process can be such a success that it captures the majority of the market or becomes a habit (for example the qwerty-keyboard). This can take for many years causing large differences among countries.
 
Linkages
Due to complementarities, players can face more than just one equilibrium. It will take quite some coordination to end up in the best one. We saw this in the example about investment decisions among different firms earlier. Since coordination can be quite difficult in most cases (many players, large regions, no information), individual expectations about the actions of others are very important. All players together are called a network which is connected by linkages. There are two kinds of linkages:
forward, when a firm affects the supply of another and backward, when a firm affects the demand of another.  
 
The concept of linkages can be important for the chance of success of policies. Since a push / increase in one firm will stimulate others, it is important to have a clear picture of the situation in hand. Stimulation of a depressed economy (big push) must be done by investing the right amount of money in the right places among different industries. However, to give a depressed economy a real boost, it will require an enormous investment.  A good example of such was the Marshall plan, for survival of the post-war
Europe. The allocation of the investments is of course a difficult story.
 
Contrary to the big push approach, Hirschman’s idea was to stimulate the economy based on the linkages. Instead of a balanced growth, he chose for an unbalanced growth by only investing in key sectors of the economy. By consequence, other sector will be pushed forward. There are several mechanisms to search for the key sectors of an economy.
 
The first is to analyze the number of linkages and the configuration of the economy’s industries. Besides the number of linkages it is important to measure the strength of the linkages. The strength is partly determined by whether it is a forward or backward linkage. A forward one reduces the price of one of the inputs and a backward one increases the price of the output and therefore higher production which probably is a better stimulation for the economy.  Another difference is the role of information: lower price can send out the wrong message and a higher output or price often shows a healthy / profitable situation. Moreover, the government should not only concentrate on profitable sectors, unprofitable sectors (like highway construction or other infrastructure) can be very crucial for development.  
 
Expectations
Now we know that a country’s history plays a large role for the situation the country is in, and we know that players must change their expectations to improve their current situation, we must investigate how these expectations can be changed. We know from some different areas that expectations can be changed quite suddenly (fashion etc.) and move from a bad equilibrium to a good one.   
 
An example which shows the importance of expectations and coordination failure is the one where an industry will need special skilled labor to improve the sector as a whole, but since there is not yet any education for that type, current labor demand from that industry is low. Since the demand is low, governmental or private institutions do not see the urge to build these education facilities or students may not see the opportunity to take similar available studies.  
 
Model
Cases with two options (special study vs. others or qwerty vs. innovative keyboards) can be showed graphically in a model where both options are displayed in the number of users and rate of return. In many cases the old and traditional (history) option has more users and due to the upward sloping return curve, users of that option face a higher return. Once they move to the other option there are less users and therefore a lower return. However, when expectations change and all users know that when they
move all to the other option they would all enjoy the higher return, because this option has a upward sloping return curve with an initial higher starting point.  

 
Due to the upward sloping return curves, there are only two real outcomes: all users choose option one or they all choose option two. Expectations will determine which one will happen. However, a critical component in the model is time. Option changes and price / return changes take time. Since the current return is often higher than the return of the new (but better) option, users wait for others to move first and move themselves later on.  
 
Increasing returns
The concept of increasing returns can be the reason that poor countries/ economies cannot move themselves out of a low-level trap. Profits increase when more products return are sold, or costs per product decrease when more products are sold. However, when the market is small or the initial prices are too high to reach a large market it is not possible to gain from increasing returns.  
 
An example will show that this concept is similar to model above. A poor country has a small market for automobiles. That domestic market is currently occupied by foreign manufacturers. Despite that, there is room for a domestic manufacturer who will make cars specially designed for domestic conditions (for example bad roads). Due to mass production the prices of the foreign cars are lower than the initial prices of the domestic cars. Only when there are enough users that will buy a domestic car, the prices will be
lower (partly because lower input factor prices). Again, the time problem arises: users do not want to be the first and do not switch all together at the same time. However, this problem also exists in rich countries. Only we have sound financial markets, where producers can get a loan if conditions are satisfactory. In many poor countries, the capital market is insufficient. To sum up, there are three problems which arise: switching delays, increasing returns and insufficient capital markets.  
 
Intermediates
Another disadvantage for poor countries is the relation between intermediates and final goods. When a country has a low and depressed economy, the demand for final goods is low. Therefore, there is less demand for intermediate products and innovation of new intermediate products in discouraged. Intermediate goods, which make production quicker, cheaper or easier, will than be changed back to labor, which again raises the price of final goods and evolves in lower productivity. This vicious circle is reversed for well-performing countries: increased demand for final product encourages new and
more intermediates, which increases productivity and reduces costs and results in higher demand for final products.
 
Market characteristics
Another way to look at externalities is as consequences of imperfect markets. One’s decisions which effect another (positive or negative) can be measured in terms of money, time or other variables. If there would be a market for these consequences, some difficulties could be solved in a perfect competitive market. As we can all imagine, some externalities cannot be transformed to a ‘good’ in a competitive market (they are non tradable or demand impossible communication and interaction).
 
Norms and values
We have already made clear that differences among countries can be caused by differences in history and culture. So far, we have not yet discussed the influence of norms and values on a countries situation. Are women supposed to work? Is it acceptable to lend money? These are questions that deal with issues which can be quite important for a nation’s well-being. However, the way a country deals with these
issues depends on culture and there does not exist a single good answer to these issues.  
 
On the contrary, there are some issues which do have a straightforward answer. That answers may not always be around in poor countries. These issues are issues regarding child-labor, -education, –mortality etc. It is not necessary to say that changing these problems requires a lot of effort (time, money and people).
A somewhat more complex issue regarding norms and values is the one concerning house-farmers. House-farmers are families who grow rice at their own property. That is their way of making money and to survive. However, substituting some land for other purposes and increasing joint production may bring many benefits (increased productivity, more income, wealth). This process may be contradicting to any cultural norms and values, and is therefore discouraged. Change in norms and values usually takes a lot of time and requires some people who start changing, despite all negative reactions.  
 
Status-quo
The final aspect we will discuss regarding a country’s history is its effect on policies at stake. There are always some people against and some people for a policy. This is mainly based on the result of the policy: will people gain or lose from it? The concept of Public finance concentrates on determining what the welfare effect will be. If there will be a net gain, the policy must be performed, if there is a net loss the policy will not be performed. When there is a net gain, some of the gain (preferable in terms of money)
can be used to compensate the losers.  
 
There are a few difficulties in dealing this way with policies and other important decisions. Not everything can be measured or valued. Especially sadness, diseases or death are hard to measure. It is also possible that people will show costs or benefits which are not credible or exaggerate them. A second problem might be that it is still unclear or complex to figure out who will be the losers and who will be the gainers. A third problem might be that even if it is possible to point out the losers and gainers it is
not doable to arrange the compensation for the losers. And finally, a problem or maybe unfair aspect, is that parties may have different bargaining power or lobby power. This way a small group of influential people may arrange policies which are quite negative for the majority of the poor population.  

Chapter E: Economical disparity

So far we have discussed levels of income between entire countries and world’s distribution. This chapter we will focus on the distribution of income within a country. An equal distribution is desirable (at least for most people) and an unequal distribution often requires governmental policies to smoothen differences in the income levels. From a moral view we would suggest that there is no valid reason for people to earn different incomes and enjoy different wealth levels. However, as we all face in the real
world, wealth prospects are partly determined at the day we are born. The situation of the parents plays an important role in an individual’s future. We can analyze inequality at two different levels: the intrinsic and the functional level. The intrinsic level is concerned with morality and welfare, the functional level is concerned with the economical consequences of inequality and its influence on aggregate income growth.
 
Inequality is the fundamental disparity between individual’s decision to make certain material choices, while others cannot make those same choices. These disparities can come from personal differences as well as other fields, such as politics. Inequality within a country can be quite interesting because it shows why there are still large differences among people in similar situations (country-wise).  
 
Inequality can be viewed at in three different ways: the flow of current income, the distribution of wealth and the flow of income during a whole life-time. These ways differ in their time-span: short-term and long-term. The current income flow may not last forever and therefore inequalities may not be too harmful. Because of that, the mobility of flows is important. This mobility can, for example, refer to whether or not jobs (and their corresponding income-levels) are sticky or fluid. Furthermore, it is necessary to make a distinction how income is earned. There are several factors of production where individuals can benefit from: labor, capital, land etc. The functional distribution tells us something about the flows (wages, rent or profit) from the production factors. The personal distribution tells us something about what a household’s income consists of.  
 
This division between how factors are paid and how they are owned is necessary for a good view of inequality and can also give us insight in economical growth. This chapter we will also analyze some different ways of income distribution, and we will try to rank them accordingly.  
 
Measurement
It is quite clear of what is equally shared and what is unequally shared. Between two persons 50:50 is fair and anything other is less equal. Once we start talking about a whole society it is very important to measure the flows properly in order to permit any useful conclusions. The number of criteria has an enormous effect on the usefulness of the research but also on the effort which has to be made.  
 
We will start with a little algebra in order to rank different distribution in the end. Our society has N individuals, with index I for each generic individual, I = 1, 2, N. The income distribution is described by how much each individual earns (y1, y2, ..., yN). The anonymity principle states that it does not matter who earns a specific income, we just focus on how equal the distribution is. The population principle states that it does not matter how large a population is. Any distributions are proportional, so the same
distribution between two different sized countries is as equal or unequal as the other.  
 
Both principles make it really easier to compare distributions. Any data from a useful sample can be identified and put into income classes (from 100-200 euro) due to the anonymity principle. Due to the population principle we can afterwards define the numbers of individuals in percentages, so that real numbers do not matter anymore. This way we can better compare different distributions.  
 
We will introduce one more principle: the real income principle. Absolute income levels do not tell us everything about how equal it is divided. That depends on the other income levels. Therefore, we might as well express them relatively.  
 
Now we are able to show a country’s income distribution expressed in shares. Horizontally the share of total income and vertically the share of the population. We can now see which shares are earned by the poorest and the richest within a country.  
 
The Dalton principle is a fundamental criterion to compare and rank distribution. It states that a transfer of income from the ‘not richer’ to the ‘not poorer’ is called a regressive transfer. A sequence of regressive transfers always makes the distribution more unequal. Before we start we have to introduce an index which states how unequal income is divided. The index has to from of: I = I (y1. y2, …, yN). The index
needs to be the same for two populations which are of different size but of the same distribution.
 
Graphically, we can show the results in a Lorenz-curve. This shows the cumulative shares of populations and income. From this curve we can see that the poorest 20% earns 12% of total income and the poorest 90% earn 80% of total income. Another line which is drawn shows the equal distribution and therefore has a slope of 45 degrees. Each point at the Lorenz curve shows how much an individual earns of the total income by looking at the slope of the line at that point. Since we use a marginal contribution (starting with the poorest) this slope can never fall. The further away the Lorenz curve is from the diagonal the more unequal incomes are distributed. The Lorenz criterion states that if every point of the Lorenz curve is to the right of another Lorenz curve the former is more unequal than the latter. The Lorenz curve is consistent with the four other criteria that we already discussed.  
 
It is also possible for two Lorenz curve to intersect. This gives a more complex situation since we cannot easily state which is more equal. Moreover, to move from one to the other there cannot only be regressive transfers. Progressive transfers are income flows from the richest to the poorest and are necessary to move from the first distribution towards to other.  
 
There are actually two problems with Lorenz-curves: researchers are more interested in a single index number of inequality than a complete graphical description (less quantifiable) and when Lorenz curves cross they are difficult to rank their inequality. Therefore there are a few other algebraic measures:
 
Average income (total income by total population) is denoted by ц and the equation is:
  ц  = 1 / N ∑ Nj Yj,
 
there are M distinct incomes, in each income class j. The number of people earning that income is denoted by Nj. The summation symbol denotes the sum over the income classes 1 through M.  
 
Another measure is the range. Which is the difference between the richest and the poorest individual divided by the average income.  
 
R = 1 / ц  (Ym – Y1)
 
Kuznets introduced some ratios as measures which can be drawn from the Lorenz curve. He divides the incomes of the poorest x% by the richest y%, where x and y stand for 10, 20 and 40.  
 
A somewhat complex but useful measure is the mean absolute deviation. It takes the differences between all incomes and the mean, adds these differences and divides that by total income:
 
M = 1 / цN   ∑ Nj │Yj - ц│
 
However, this measure has an important drawback. The Dalton principle does not hold: a regressive transfer from a richer person to a poorer person (who are both equally far from the average income) does not result in a more equal estimation.  
 
Another, and familiar, estimation is the deviation from average income. It squares the differences with average income and therefore is more sensitive towards large deviations. The coefficient of variation is measured as follows:
 
C = 1 / ц  √ [ ∑ Nj / N (Yj - ц)²]
 
Finally we present the Gini coefficient. It takes the differences from all pairs instead of only with the average income level. After that it is divided by the population squared and average income.  
 
G = 1 / (2 N² ц) ∑ j ∑ k Nj Nk │Yj - Yk│
 
As you can see there is a double summation sign, which means that first all K’s are summed holding J constant. After that, we sum over all J’s holding K constant. All principles hold for the Gini coefficient and it is Lorenz consistent. It appears that the Gini coefficient is exactly the ratio of the area between the Lorenz curve and the 45 degrees line and the area below the 45 degrees line.  
 
To sum up, from the five measures we discussed, the first two can be handy when there is lack of sufficient data. The third is not in line with the Dalton principle and should not be used. The last two are good estimates and are in line with all out principles.  
 
The problem of crossing Lorenz curves is still present. In many cases the coefficient of variation and the Gini coefficient show different results when we calculate the indices of crossing Lorenz curves. In these cases we should just pay attention to the overall picture or Lorenz curve and draw our own interpretation.

Chapter F  Consequences of disparity

This chapter, we will focus on the consequences of inequality. It is not hard to imagine that inequality in developing countries has far more dramatic consequences than inequality in developed countries. Developing countries face poverty, undernourished, low saving rates, lack of financial resources etc. The linkage between inequality and the growth rate is the division of endowments. Current endowments build up stock for the future (savings > capital, education > human capital). The current division of endowments is ofcourse reflected in whether a country is equally or unequally divided.  
 
We will analyze the history, especially what the influence of the history is on the future’s endowments. We will also discuss what the usefulness of the history is. If free and competitive markets make sure inequality disappear and all countries will converge, the history plays an insignificant role.  
 
Income and Growth
Kuznets was the first who linked inequality to other economical concepts. He used his ratios (last chapter) to get an idea of the level of inequality. He mostly used the ratio of the richest 20% to the poorest 60%, which results in approximately >1.6 for developing and <1.6 for developed countries. Further research of Kuznets resulted in another finding: initially a small group benefits from certain process, which increases inequality. Later on, the benefits from these processes are more widely shared and inequality decreases again. This is called the inverted-U hypothesis (due to the shape of the graph: per capita income vs. inequality).
 
A nice example of such is called the tunnel effect described by Hirschman and Rothschild. It states that if people in a developing country are in a relative stagnant position, they will be enthusiastic to see any development around them, even if only others benefit. Their future will be brighter since they also expect to benefit in the long run. However, if the people around an individual keep on enjoying increased wealth
and the individual is still in his stagnant position, he will start getting angry and upset. Now his future does not look brighter anymore. This process abandons the process of ‘grow first, distribute later’. If societies are more homogenous in their endowments, such as developing countries, people will not appreciate their neighbours to benefit too much, contrarily to heterogeneous societies where people will be more indifferent to each others wealth increase.
 
It is quite hard to check whether the inverted-U hypothesis holds in the real world. Developing countries lack in good data about the past (centuries ago). Therefore we will try to check the hypothesis according another process. We will compare developing countries is different stages of inequality and growth (cross-section).  
 
Paukert was one of the first who did this kind of study. He evaluated more than 50 developing countries and ranked them according their per capita income (1965). After that, he found their poorest 40% and richest 20% income shares and plotted them in a graph. The income share of the poorest 40% decreases first if we move from the poorest countries to the somewhat richer developing countries. If we move to the ‘least poor’ countries this share increases again. The shares of the richest 20% show the opposite: they increase when we move from the poorest to the middle and decrease when we mover to the richer developing countries. This supports the inverted-U hypothesis.  
 
Another cross-section research was performed by Ahluwalia. He ran the regression equation:
 
Si = A + by + cy² + D + error,
 
Where Si is the income share per quintile (20%), y is the logarithm of per capita GNP, D is a dummy variable (1 for a socialist country, 0 for others) and A, b and c are parameters. It is an exponential equation to allow different signs of inequality change. We know that for the lowest quintile inequality is U-shaped. Therefore, b should be negative and c should be positive. However, for the highest quintile they should show opposite signs. The regression shows that for all quintiles except the highest, b is
negative and c positive. For the highest quintile, b is positive and c is negative. This is in line with the expectations. However, as with many explanatory models, we have to be careful in addressing the right conclusions to it. There is quite some variation in the results and per capita income may not explain all of inequality.
 
Another implication of cross-section analysis is that we have to assume countries are similar in many aspects. Obviously, this is not the case in the real world. On the other hand, we already mentioned the problem with addressing single countries over a large time-span. Lack of ‘old’ data prevents researchers to adopt this kind of analysis. There is a middle approach: countries are different, but there is still a connection between them. In this model, the parameters A, b and c can vary for all countries. It is possible that curves show the same movement only differ at their levels. An example of this is called the Latin-effect: Latin American countries are the middle-income developing countries, where some Asian countries are the richer developing countries and finally the African countries the poorer developing countries. All countries have high inequality levels. The inverted-U hypothesis might be just true due to structural and geographical characteristics.
 
We can control this concept to regress every country with a bundle of observations. There are some countries which show a direct U-shaped curve and some which show an inverted U-shaped curve. Moreover, outcomes seem to be really sensitive to the use of outliers, 80% of the countries show no significant relation between inequality and income levels.  
 
There are three ways that per capita can rise and they differ in the way they influence inequality. The first one is overall growth, where the whole economy grows gradually and accumulates wealth. The second one is where one or a few industries face rapid growth and individuals working in those sectors will benefit. This creates more inequality. The third one compensates the second one, and it happens when the people who benefited earlier start consuming from their benefits, so that others will benefit in turn. In the real world these three ways are a continuous process. There are a few implications we can draw from the above:  If growth first increases inequality (benefiting upcoming industries) and later on compensates for it, we should see that developed countries where upcoming industries are already implemented face a lower inequality compared to developing countries which are in the middle of the upcoming industries process.  
 
Technical progress benefits certain industries. In developed countries, technologies are implemented in all kinds of sectors, which gives decreases inequality. In developing countries however, only a few sectors are submitted to technical progress which increases inequality. Moreover, technologies tend to move work from labour to capital; especially low-skilled laborers suffer. Obviously, this harms developing countries more than developed ones.
 
Savings and growth
As we have seen before, saving rates plays a significant role in long-run per capita
income. The relation between inequality and saving rates is not very straightforward.
Some economics state that the rich in an unequal developing country are the only ones
who can save money, boost the economy and later on everyone will benefit from that.
Economics use this as a reason for a liberal government which does not redistribute
income, since it eventually will be redistributed. However, others state that
redistribution of income will enable much more people to save, boost the economy and
benefit later on. What the exact difference is between both scenarios will depend on
the saving behavior of people, which we will discuss below.
We introduce the concept of marginal saving rates to find out how people change their
saving behavior at different levels of income. Let us assume two countries, each with
two people. In the first country both earn 50.000 euro and in the second country one
earns 20.000 and the other 80.000 euro. Marginal saving rates will determine in which
country more will be saved and more money is available for investment. If the marginal
saving rate is increasing, which means that with a higher income an individual will
relatively save more, it means that their will be more saved when an euro is transferred
from a poor to a rich individual. In the second country (20.000 vs. 80.000) will be saved
more. With decreasing marginal saving rates the opposite is true. 
Before we start to look at actual data of saving and income levels we have to take
several aspects into account: a developing country’s poor population will need a
majority of his income for first needs (such as food, clothing and shelter). This
decreases the ability to save, even if they would be willing to save. On the complete
other side, the very rich people might not need to save anymore beyond a certain
threshold. Every additional euro is largely spent on luxury goods. People from the low
to the middle income levels might save a relatively high share of income, for their
children’s education and future. From our assumptions we can draw a graph with our
expectations of the relation between income level and savings:

Redistributive policies can have a positive or negative effect on the saving rate and
therefore also on the growth rate and the long-term per capita income level. The story
becomes quite sad once we start focusing on the really poor countries. The majority
lives under the minimal income level, so it would be very important to redistribute the
income from the rich to the poor. However, this has a dramatic impact on the country’s
growth rate. Since the population has now just enough for each individual to spend,
nothing is saved and the economy will stagnate and leave the country worse off. 
Redistribution is middle-income countries can have a very good effect on growth rates,
since income from the wealthy is given to the less wealthy who save relatively more. A
second aspect can be added to the phenomenon of saving. There appears to be an
urge to save fed by aspirations set by the rich people. Middle-income households will
try to reach this life-style and save a lot. Again, low-income households do not have the
possibility to save, since they have to spend a lot or all of their income on current
consumption. 
Politics
As we saw large inequality has negative effects on growth and, of course, a negative
effect on a nation’s welfare. For these two reasons, governments may choose to set
policies to redistribute income or sources of income from the rich to the poor. They can
do this, for example by confiscating land from large landlords and supply small farmers
with a little land, or tax income from large landlords and redistribute that to the small
farmers. For setting these policies, governments must obtain the right data in order to
make the right decision and must also keep the election in mind.  
Confiscating or taxing the existing wealth base can be quite hard since there is not
enough information about ownership or wealthy people found ways to escape from it.
As an alternative, many governments tax the flow of income from endowments. Such a
‘tax on the margin’ had only a negative impact on the level of investment. Both an
income and a lump-sum tax have negative effect on consumption, only an income tax
has an additional negative price effect on the rate of saving. 
Demand composition
As income increases the consumption pattern changes, where food has played a large
part at low levels of income its share decreases as income increases. Furthermore, the
demand composition increases demand for certain goods, therefore that industry will
increase and people from that industry will benefit. A higher demand for luxury goods
(which are mostly capital-intensive) will increase returns on the production factor
capital, which is held mostly by the richer people. This circle shows that inequality
causes more inequality. If the luxury good appears to be labor-intensive the opposite is
true. Therefore it is important to analyze who consumes what. 
Markets
Both capital and goods markets are well-functioning mechanism, which are always
taken for granted. It is well-functioning because we have certain rules and punishment
if somebody does not do what he is obliged to do. The problem with the capital market,
especially the borrowing opportunities is that people need to be reliable and trustworthy
for the amount the borrow plus interest. For low-income households it is quite hard to
get a loan, to start a business, invest in a business or educate your children. Banks
offer loans in exchange for collateral which makes sure the loan is repaid. However,
small businesses have only a small amount of available collateral, which may result in
that no banks are willing to lend the money.  
Occupation
We assume a country in which an individual can choose between three occupations:
subsistence worker, industrial worker or entrepreneur. The first two work for a fixed
wage (w) and the entrepreneur will earn profits. The business of the entrepreneur will
hire M laborers at wage w to produce output Q. Profit is equal to Q – wM. If the
business is financed with a loan, the entrepreneur will have to pay interest as well: (1 +
r) I. Profit becomes: Q – wM – (1 + r) I. To measure the costs of default we assume
collateral is W and in the next period it is equal to (1 + r) W. The cost of default is F and
a fraction of the profits. Putting all this information in an equation will get:
W ≥ I – (F + λ (q - mw)) / (1 + r),
Where λ is the fraction of lost profits. For entrepreneurs with wealth lower than the
equation states, is it impossible to receive a loan from the bank. 
We can look how the occupation is divided among the population, at high wages rates,
for example, the portion of people who can get a loan will drop. On the other hand, the
wage rate is ofcourse the main incentive for people for choosing to work or not (supply
of labor). We can graph the labor market with a curve for the demand for labor and one
for the supply of labor. The wage rate will determine the number of entrepreneurs and
the number of people working in which occupation. Moreover, the distribution of wealth
determines who is able to become an entrepreneur and receive a higher return. 
Since people are able to save, they could be able to acquire wealth overtime. However,
also the start-up costs increase overtime because land, plants and human capital will
become more expensive. 
We have seen that low-income households do not have the possibilities to fully exploit
their capabilities, due to the financial restraints. Investment in education seems to be a
good way the ‘become’ human capital instead of a laborer. The trade-off here is that investment in education cannot be used as collateral to start a business later on.
Failure in the capital market causes failures in the labor market and education. 

Chapter G: Poverty and its characteristics

Inequality of income distribution and even the inequality of the income distribution
within nations result in some shocking poverty aspects. Undernutrition, ill health,
illiteracy and no education, hopes or future belong to a world some centuries ago.
Nowadays, poverty and its characteristics do not belong anymore in a world which has
the potential to let poverty disappear. In this chapter we will discuss multiple aspects of
poverty: its concept, its characteristics and its functional impact. 
People living in poverty are said to be living under the poverty line. This is a specific
level of income or access to goods. It can be estimated based on the minimal amount
of food, clothes and shelter or as a percentage of the mean income. Income is used as
the capacity to consume, to leave out differences among people’s preferences and
habits. On the other hand, notions of basic needs may vary per country. Besides the
absolute needs (nutrition, clothes and shelter) there are some needs more relative to
the specific society; these are the needs which make a person able to function in
society. 
It is important to make a distinction between temporary and chronic poverty because
both need different policies. Especially in developing countries, there are many people
under or around the poverty line with an unstable income level. In most cases their
income depends on the weather for their agriculture. 
Another aspect which deserves some more attention is the allocation of income within
a household. Also, the number of children and elderly is important since they consume
less than their adult equivalent. Moreover, larger households are able to spread fixed
costs over more members. 
Model and estimates
Now we discussed some qualifications and distinctions, we can build a model for the
poverty line. Again, y is income where i and j stand for individuals. The poverty line is
denoted by p and the mean income with m. We will start with two easy estimates of
poverty: head-count (HC) and head-count ratio (HCR). Head count is just the measure
of the absolute number of individuals living below the poverty line (Yi < p). The head-
count ratio is the number of people living below the poverty line relative to total
population (HCR = HC / n). The problem of these measures is that they are insensitive:
they do not make any distinction between different levels of poverty. 
We are confronted with another problem when authorities want to lower poverty
measures and redistribute some money. When authorities are focused on the head-
count measure and want to lower that amount, they would be more eager to distribute
money to the individuals just below the poverty line. They are the easiest (and
cheapest) individuals who lower the head count. Clearly, they are the individuals, below
the poverty line, who need the money the least. This process especially confronts
policymakers around elections and policymakers under watch by developed countries
(in trade for aid).
Another estimate is the poverty gap ratio (PGR) and is defined as the ratio of the
average of income needed to get all poor people to the poverty line, divided by the
mean income. This estimate does not really measure poverty itself, but the resources
needed to eradicate it.
              Σ _{Yi (p - Yi)
PGR = ————————
                      Nm
Best is to use both the head-count and poverty gap ratio in order to get a good view of
a nation’s poverty level and to be able to find the right policies. 
Empirical observations
We start with some numbers from the World Development Report (World Bank) and
use two different levels of poverty lines: 370 dollar/year and 275 dollar/year per person.
At 370 dollar (at 1985 PPP prices) we measure over one billion people below this line!
Between 1985 and 1990 this number has been quite constant. In all developing
countries the poverty rate was around 30%. If we would use the measure of 275 dollar,
there would still be 600 million people living in poverty. One implication of universal
measures is that they overestimate the “real poverty” in some countries and
underestimate in others.
Demography
There is a tendency with poor families to have many children. One report states that
roughly 30% of all households count 6 or more than 6 members. Of these, more than
half lives under the poverty line. The more children a poor family has, the harder it is to
feed them well and educate them. Therefore, family size may both be an effect of
poverty as well as a cause. 
On the other hand, it is difficult to state that there is a clear correlation between family
size and poverty for two reasons. The first is that larger families have more children
and that children often consume less than adults. This way it is hard to tell what
happens to per capita expenditures. The second reason is that larger families enjoy
economies of scale. One final remark regarding the composition of households is that a
report on Brazil showed that there are twice as many female-headed households
among the poor as among the non-poor.
Rural and urban
Poverty is higher in rural areas than in urban areas, even if we take differences in the
cost of living into account. Poverty is highly correlated with the lack of ownership of
productive assets. Moreover, there is a high correlation between poverty and small-
scale agriculture, especially in Africa. In the rural areas the poor are often the landless
or near-landless, in urban areas the poor often work in the informal sector. Most of the
work in this sector is self-employment such as vendors, traders, beggars or garbage
shifters. These ‘jobs’ are not subsequent to a minimal wage and therefore very
insecure. Moreover, it is almost impossible to stop working for a while in order to
acquire other / more skills. 
Nutrition
It is not necessary to say that there is a close connection between poverty and
undernourishment. Consequences of undernourishment or poor-quality of food are
quite severe: stunting, muscle wastage, less protection against diseases and the
inability to do productive work. In countries where the poverty line is calculated using
the prices of sufficient daily nutrition, it is straightforward that poverty and
undernourishment figures are alike. Despite the connection it is not clear whether an
increase in income ill coincide with an increase in nutrition. This is partly the case
because nutrition has both a functional role (better health, resistance and the ability to
work and earn money) and a more social and personal role. Each individual has his/her
own preferences regarding nutrition and nutrition can express status or wealth. This
way an increase in income may not increase nutrition. The combination of income and
calories tend to hold better. Another conclusion is that poorer families respond more to
food price changes. 
Functional impact
Since it is hard to say anything about happiness in relation to poverty, we skip the
discussion around this. We move along with discussing the more functional impact of
poverty: the causes as well as its consequences. We can divide the effects in a few
markets where they come together: Credit & insurance, nutrition and labour markets
and households.
Credit
It is almost impossible for the poor to obtain loans or get a credit in order to invest in a
productive activity. This happens due to a number of reasons. Firstly, poor people are
unable to come up with decent collateral for the loan. Collateral is necessary for the
entity which lends out money in case the project appears to be unsuccessful or to
secure against default. In developing countries there sometimes are informal markets
to obtain a credit where a person can use his labour as collateral. However, this occurs
only rarely. Secondly, it is for a lender quite risky to lend out money to a poor person
since at the time the loan needs to be repaid, the benefits of default start to increase.
For this reason it is more likely that a rich person will repay a loan than a poor person
(the rich person faces diminishing marginal utility of money). We already saw, in
previous chapter, that the entry deterrence of poor people to the credit market has a
negative impact on national income. It leaves opportunities for good investments
unused. 
Insurance
As we all know, people insure themselves against unfavourable things that might
happen. We can hedge against risks which we are not willing to bare, using insurance.
In order to be insured we have to pay a sum of money per period of time to the
insurance company, and in case your house burns down, the company will pay the
amount for which the house is insured for. In order to insure something it must be
verifiable, so that the company can calculate / estimate the payment. A second feature
of insurance is moral hazard. Moral hazard means that in case a person is insured,
he/she might not act as responsible anymore since all risks are bared by the insurance
company. Perfect insurance is therefore almost never the case. Insurance companies
add certain restrictions and implications to decrease the risk of moral hazard. 
The problem for insurance in developing countries is that there is lack of information
which makes certain things not verifiable. Therefore, the formal insurance market does
not fit well. The informal insurance market is more attractive for the level of the village
community, where they can self-insure as a group. Moreover, the risk of moral hazard
is less for poor people than for rich people, since the opportunity costs for the poor are
lower.
Nutrition
We already discussed some aspects of undernourishment and especially its
consequences. Now we will show the relation between undernourishment and the
ability to do productive work. For a good picture of the undernourishment we can think
of our body to consist of four components: Energy input, resting metabolism, energy
required for work and storage and borrowing. Energy input explains the periodic
consumption of food which will be transformed into energy. Resting metabolism
explains the amount of energy needed for the body to operate. It has to spend energy
for the body requirements such as: body temperature and heart action. 
Energy required for work states the amount of energy needed to work a day. Several
reports are written on this topic and they come up with an average number of kcal to
perform work. This amount may be higher for poor people in developing countries since
most of the jobs require harder work than in developed countries. Storage and
borrowing explains the balance between the first component and the second + third.
Short-run imbalances can be cushioned; long-run imbalances will cause people to gain
weight or breakdown of the body. 
We now face another poverty trap: low incomes create low nutrition and low nutrition is
capable of creating low incomes. 
Households
We now move to the ability to work productively within households. With a fixed income
and the work capacity curve in mind we know that: unequal consumption allocations
create greater household work capacity than equal allocations for levels of income
under a certain threshold. Above this threshold it is the other way around. However,
where theory might seem reasonable, in practise there would never be a starvation of a
family member to maximise household capacity. 
On the other hand, unequal nutrition distribution appears to be present in many
households. Reports show that women generally receive lower nutrition in all age
groups. Whether this refers to medical aspects or gender biases, it is interesting to see
how nutrition is allocated within households. 
Another aspect is education. What determines who will be send to school and who is
not? Reports state that in low-income countries, illiteracy is twice as high with women
than with men. Overall, poverty seems to reinforce some gender discrimination and
unequal treatment.}

Chapter H: Population

World population has never been as high as today. The number of years it took to
increase with a billion took respectively 123, 33, 14, 13 and 11 years. This shows
exponential growth. In this chapter we will analyze how economic development
influenced population growth, and in turn, how population growth affects economic
development. A hard issue regarding welfare is whether a large population is preferred
over a smaller population which can enjoy more luxury goods. We will discuss this
issue mainly based on per capita welfare. We can state that a enormous population
cannot be good since more people use the available resources, on the other hand we
can say that we need a minimal amount of people to come up with new inventions and
innovation. 
We will look at the growth numbers in developing countries and try to find its
consequences. We will also look at the numbers of the successful new developed
countries focus on demographic transition. Furthermore, we will take the discussion to
the micro level and analyze a household’s decision on how many children to raise. 
Birth and death rates
First, we have to understand some basic aspects of population growth: birth and
death rates. These rates are normally expressed in a number of newborn babies or deaths
per 1000 members each year. The population growth rate is the birth rate minus the death
rate. We have several groups with countries analyzed on their rates: Group 1 with the poorest
countries have both very high birth and death rates. Group 2 with poor countries have
already much lower death rates but still high birth rates. Group 3 and 4 with countries such as India, Bangladesh and China have done much effort to lower birth rates and also show relative low death rates. Group 5 with the Latin American countries show low death rates but are still unsuccessful in lowering their high birth rates. Finally, group 6, with countries in Southeast Asia has both low birth and death rates. The overall pattern we see is, that when per capita income increases the death rate decreases, after a period of time the birth rate also decreases. 

Looking primarily at population growth, rates can make sure you miss important
information. Two countries with the same population growth rate but with different birth
and death rates are probably very different in their demographic situation. The country
with higher birth and death rates typically has a younger population than the other. 
Age distribution
Later on we will see that the age distribution of a country has specific effects on the
development. Therefore it is important that we look at some information about age
distributions in developing countries. It might not surprise you that the average age in
developing countries is very low. This is mainly due to high birth and death rates.
Another key rate is the total fertility rate, which shows how many children a woman on
average is expected to receive. In developing countries this can be as high as 7 or 8 or
even higher! On the contrary, in developed countries this is 2 or even lower. 
On the other hand, a young population in a developing country usually shows lower
death rates because less young people die. This may seem strange: a country with
higher age-specific death rates in all age groups can have an overall lower death rate
due to its younger population. So, high population growth can lead to a younger
population and in turn to higher birth rates and lower death rates. For this reason, many
developing countries are inert. 
Demographic transition
High population growth rates are only something of the recent world. If we would
regress the 6 billion people today at a rate of 2% per year we would end up with 10
people a thousand years ago. The population did not increase (that much) until we
found ways to increase the output of mother earth. Especially in the 14th-16th
century very high death rates still smoothened out the higher birth rates. From the year 1700
better sanitation and higher agricultural productivity birth rates increased and death
rates decreased. 
Below you can see the geographical distribution of the world’s population:

This table offers some interesting information: between 1650 and 1933, Africa faced a
declining share mainly due to large emigration, while North America faced a rising
share due to immigration. Europe will have to face emigration as well, but, over this
period, saw its share rise. Now look at the last column and see the major differences:
the steadily growing regions of Europe and North America suddenly face a large
decline in world’s share of population. The developing regions: Latin America, Africa
and Asia face growing shares (respectively 2.3, 5.8 and 6%). Our conclusion might be
that we should not be frightened by the world’s population growth but more by the
relative growth of specific areas. We see that less than 20% of the population lives in
the developed region and already 80% lives in developing countries!
Birth rates
We already saw that the main reason for the high population growth rate is that the
high birth rates hold firm while the high death rates decline. We will now discuss some
of the reasons why birth rates remain high in a population at household level. We will
look at the developing countries as macro-inertia: the young population makes sure
that many children enter the reproductive age within some years. Besides that, there
also is micro-inertia: societal norms and socioeconomic factors which make sure
households choose to keep birth rates high. 
The decision on how many children a couple might want also depends on their belief
that some babies / children might die and that children must take care of them in
replacement of the missing social security system. Besides the consumption-good
aspect (enjoyment), children are an investment-good for many parents in developing
countries. Reason for this is that many markets are missing: social security fund,
employer-subsidized retirement plan, medical care and life security. Moreover,
households need all their income for current consumption and are not able to save for
themselves when they are old. When we take a practical look at the use of children, as
income-earning possibilities, it is not strange that birth rates are so high.
Moreover, some developing countries face a child morality rate of 15% and not every
child may be an adequate income earner. This also contributes to the number of
children a household might want. Another issue is that, whether it is justified or not, a
couple might prefer a son over a daughter, hoping for a better job and higher income. 
Strategies
Two different strategies are in place for couples to determine how many children they
prefer. The first strategy is called ‘hoarding’ and refers to the problem that parents do
not know in advance how successful and supportive their children will be. They have to
be stockpiled in advance, before the parents know which of them will provide the
required support. A different strategy is that of targeting. This way, children can be
attained sequentially and the survival and prospects of the first child decide whether
there should be a second. This strategy results in lower birth rates. The majority of the
parents in developing countries uses the first strategy and it might be very hard to
persuade them to use the second one. 
So far, we discussed the role of children as ‘investments’, on the other hand there are
costs concerned with raising them. There are direct costs: money spent on food,
clothes etc. and there are indirect or opportunity costs. For example, the time a parent
needs to be at home with the children instead of earning money elsewhere. In
developing countries where the opportunity costs are low (for example, low wages)
birth rates tend to be high. Also high unemployment lowers the opportunity costs and
increases birth rates. 
Benefits and costs of children can be put together and translated into utility as we are
used to do with microeconomic issues. Important is to make a good division between
the right benefits and costs. Children can than be put on an axis against other goods.
The budget line and utility curve will show the right effect. Some influences, for
example increased minimal wage, has both an income effect (more income to spend
on children) which increases the demand for it, as well as a substitution effect
(opportunity costs has gone up) which decreases the demand for children. 
Differences theory and real-world
We know that high birth rates are not optimal for the development of poor countries.
How is it than possible that there is such a large gap between what parents decide and
what would be the optimal way? There are three reasons for this: information &
uncertainty, externalities and social norms. 
The first concentrates on the fact that not all information is translated to all parents
about, for example, decreasing death rates. It also includes that parents do not know
what the life expectancy of their children is before they are born. Furthermore, there
are several externalities at stake which have an increasing effect on birth rates. Some
of these are free public education or transportation or subsidised housing or medical
care. They raise social cost and lower private costs, so that children become ‘less
expensive’ for their parents. The last reason, social norms, concentrates on
conformism. Conformism holds the social relationships and norms together. As we
know, norms can sometimes change but only a little bit overtime, thus it might take
quite a long time before large families is not the norm anymore. Religions are often
also important regarding this issue. Authorities might want to change the norms more
rapidly, with programs as birth control or family-planning. 
Population growth and economic development
As stated in the beginning of this chapter, has economic development its effect on
population growth, which we discussed above. Now, we will look at it the other way
around. What is the effect of population growth on economic development?
More people require more resources, on the other hand are more people available to
offset this. The target is to outweigh the increase in consumption with an increase in
production. According to Malthus, the direct effect of population growth per capita
income is negative. He states that economic development causes people to marry
earlier and also start younger with having more children. Recent experience on the
other hand, tells a different story: Economic development makes people more aware of
the costs of having children and when these costs rise, a downward pressure will be
put on the demand for children. Still it is difficult to say anything about the impact of
economic development on the birth rates. Various issues are at stake and the majority
of the parents do not make the decision to have children based on economic factors.
Therefore, it is better to treat population growth as being exogenous. 
Negative effects
Try to remember the Harrod-Domar model introduced earlier. Population growth has an
ambiguously negative effect on the rate of growth. However, an important assumption
was that the capital-output ratio is fixed. Since we can make a strong point that this
does not hold in the real-world, we move to the Solow model (also introduced earlier).
Now, with a production function, the steady-state rate of growth is independent of the
rate of savings and the rate of population growth. There is actually another effect: an
increased rate of population growth does change the level of the steady-state, not its
rate of growth. 
Another negative effect of population growth is that it lowers the rate of savings, since
children save less than adults. This causes a reduction in growth rates. Another
problem is that population growth will cause more inequality among the poor. 
Moreover, population growth has its negative effect on the environment and the
depletion of natural resources. 
Positive effects
One of the positive effects of population growth is the larger labour force. The Solow
model balances this out with the increased consumption. Besides that, more people
may have positive effect on technical progress: it makes new inventions more
interesting since there are more people in the market and there is a larger pool of
potential inventors. Just as before, when the population grew, it became important to
be more productive in agriculture. This necessity was the main driving force to
innovate. 
An important remark is that a larger market for producers is only interesting if these
extra people have an income to spend. A larger population also means a more diverse
population. This has a positive effect on innovations of different kinds. A larger market
and a larger pool of inventors are the demand/side and the supply/side effects on
technical progress.

Chapter I: Geography

Up until now we described economic growth, poverty and population growth in general,
however, these issues can be quite different within a specific country. That is why we
will analyze the uneven growth within a country, which can be uneven among different
groups in the society or among different regions: rural and urban regions. We already
saw that the majority often lives in rural areas where agriculture is the most dominant
source of income. As economic development proceeds, individuals start moving to the
urban areas. It is than necessary that farmers are able to produce more than just for
them; they have to be able to supply the entire country with food, so that there is supply
of labour available for the industrial sector. 
Urban / nonagricultural sectors
In urban and semi-urban areas, economic activity concentrates around the industrial
sector. This sector can be divided into two different sectors: the formal and informal
sector. Features of the formal sector are things such as a labour union for the workers,
collective bargaining, health and safety regulations, minimum wage, pension schemes,
taxes paid by the firm and subsidized facilities for the firm (electricity and
infrastructure). Setting up a firm in the formal sector can be quite difficult, time-
consuming and costly; on the other hand can the firm be insured against bankruptcy or
issue shares and pay out dividends. The second sector is the informal sector. Within
this sector, the owner of a firm can escape from some of the regulations and have to
give up some privileges for that. Activity in this sector is not necessarily illegal; it is a
vague part of the economy. Examples are: shoe-polishers, (professional) beggars and
owners of small selling stalls. You can imagine that this sector can be quite large. One
of the reasons is that set-up costs are quite low and if necessary it is possible to switch
profession. 
Rural / agricultural sectors
The large sector of agriculture would fit best with the informal sector described above.
Authorities are almost unable to tax farmers, on the other hand it is also very hard to
secure them against bad weather and secure a minimum wage. Not all agricultural
activity fits the informal sector; there are also large farming enterprises with hired
labourers. In both ways, farmers bare an incredible risk that bad weather will destroy
their harvest. One year they may earn an above-average income, but the next few
years may offer close-to-zero incomes. In developing countries, where agriculture plays
a major role, a year with bad weather can have a devastating effect on national
income, balance of payments and poverty figures. 
A good development is that authorities are becoming more active in supporting rural
areas; examples are offered credit and better infrastructure. Another development is
that more and more farmers start working together to provide better facilities and
technologies. They invest in irrigation, fertilizers, man power and technology and new
shared material. This reduces their risk, enables them to be more productive and it
lowers the costs.
Interaction
The most important interaction between the urban and rural regions is that in order to
develop the country needs to start up or improve the industrial sector. This sector has
to be provided with labour and those workers have to be supplied with food. Both have
to come from the agricultural sector. In time, the industrial sector can provide the
agricultural sector with durables such as tractors and pumps. Moreover, the industrial
sector is often involved with the foreign exchange of goods and knowledge; knowledge
of agriculture from other countries can be surpassed to their own agricultural sector. 
Lewis is one of the economists who wrote about the preferred economic activity within
a developing country. His model is based on duality: traditional and modern sectors.
Traditional and modern are the descriptions of both the agricultural and industrial
activity, the use of old and new technologies and the use of old and new ways of
organization. These descriptions can be a bit vague and misleading: the agricultural
sector can be very modern in its use of machines and way of operating, whereas small
firms in urban areas can be very traditional.
Surplus labour
According to Lewis, the agricultural sector has the role of labour-supply towards the
industrial sector. However, this is not an instantaneous action. The supply of labour can
only be slowly soaked up, since the development of the industrial sector is slowed
down by the lack of enough capital. The available capital and the capital accumulation
will determine the rate of growth of the industrial sector. The major difference with the
Harrod-Domar model is that Lewis assumes that labour supply is infinite; a downward
sloping production function in the agricultural sector enables labour the move without
too much problems towards the industrial sector. This diminishing marginal return from
labour appears also in many cases within the informal sector. Since supply is larger
than demand, there is easy access to additional labour. 
A few asymmetries cause the disruption between the close-to-zero marginal returns on
labour and the fact that labour is hired. One of these asymmetries is the existence of
traditional and modern sectors, another is the difference between the two sectors on
how many labour to use. Industrial firms generally hire employees up until the point
where marginal revenue equal marginal returns. Family-firms in the agricultural sector
usually overestimate the preferred number of employees and income is shared by all.
Lewis is not alone in his view: economists in Eastern Europe and the Soviet-Union
found the same existence of ‘surplus labour’. The use of this surplus labour in the
industrial sector can be of great importance for the economic development for a
country. 
Contrarily, there are some economists who doubt the existence of surplus labour. In
their opinion it is hard to believe that the marginal return of labour in the agricultural
sector is close to zero, and, if that would be the case why would these labourers move
to other sector where their marginal return and wage will be higher. According to Lewis,
there are some explanations for this.
Disguised unemployment: In the family-firm in rural areas income is shared by all
employees, which let them earn an average income instead of their marginal value.
This average income is higher in many cases. 
Labour versus labourers: Since it is of major importance that the agricultural sector
keeps producing enough to support the industrial sector, it can be thought that taking
away labour from this sector is not a wise idea. At this point it is useful to make a
distinction between labour and labourers. It can be possible to take away labourers and
keep the same level of output / labour. The idea is that the remaining labourers adjust
their input in order to keep the same level of output. Together with improving
technology, it is still possible to increase agricultural output. 
Another result from the movement of labour is that, eventually, wages will rise in the
agricultural sector. The originally unequal terms of trade start moving towards to
agricultural sector. There is a first turning point in the level of wages, and can be
thought of as the commercialization of agriculture. The migration form the rural area
towards the urban area, coincides with the capital accumulation of the industrial sector. 
Policy implications
Once labour starts to move from the agricultural sector towards the industrial sector,
the average income (shared-income) in the agricultural sector will immediately
increase. However, this implies a downward pressure on the migration towards the
urban area and industrial sector. To reduce this, authorities may choose to tax part of
the income earned in the agricultural sector. This way, there is still a stimulation for
labourers to migrate and wages in the industrial sector are not driven up. However, as
stated earlier it can be quite hard for the authorities to persuade farmers to pay taxes.
Moreover, politicians need the vote of the farmers. A third problem is that farmers may
have the idea that all long-term profits will be taxed away, which will lead to
underinvestment and to less productive technologies. 
Another possibility would be to subsidize farmers and motivate them to increase output.
To protect the industrial workers against higher food prices, authorities will have to
supply the food at a lower price on the market. 
Authorities have another alternative: they can systematically let their exchange rate be
overvalued. This way exports prices are kept low, this stimulates farmers to bring their
food to the domestic market instead of exporting it. 
Migration
In the beginning of this chapter we discussed the economic approach to migration;
however, the movement of people is not based entirely on economic issues. There
might be over- or undermigration, therefore it is important to find the right policies to
arrive at the preferred situation. The model we are going to use is the Harris-Todaro
model; it assumes that wages are higher in the formal industrial sector, which is the
reason why there is unemployment in this region. All legal requirements and secondary
benefits as well as the need for good quality labour cause these wages to exceed the
minimum or average wage. Higher wages also induce a threat for the employees that
they can be fired if they do not work well enough. The wage differences are the main
driving force for migration. Individuals choose to give up their secure agricultural job
and hope to be able to find as job in the urban region. 
According some basic economic fundamentals we would assume that wages would
equalize, since workers move to the higher wage-jobs as long as they can earn more.
This excess of supply lowers the higher wage and shifts the lower wage. However, an
implication in our model is that the urban wage is not fully flexible due to the reasons
mentioned above. Therefore, the market clearing process can be fully performed. 
The wage differences and the rush towards the urban region also explains the
existence of the large informal market. Since supply of labour is some much higher
than the demand for it, people need to try to earn money in a different way. To sum up,
from all the people who leave the rural area with hope to earn more, only a small
portion will find the preferred job in the formal urban sector. From the people who are
not able to get a job like this, a portion will start working in the informal urban sector.
This leaves a group of people who can not or do not want to work in this sector. They
will be unemployed or have to move back to the rural area for a job in agriculture. With
this having in mind, one can add probabilities to the different outcomes. Once the
expected income is equal to the income earned in agriculture, people would be
indifferent towards migration. 
Government
Governments have an opposing view towards the informal sector; this sector causes
pollution, crime, congestion and has a bad influence on the image of the city (which is
bad for tourism). This informal sector is the consequence of the high wages in the
formal urban sector. There are a few policies a government may introduce to put a
downward pressure on the informal sector. 
It may seem straightforward, but one policy may aim at increasing the employment in
the formal sector. The informal sector will shrink, relative to the total urban sector. On
the other hand, it can stimulate the migration towards the urban area and let the
informal sector increase again. A policy aiming at reducing the informal sector may as
well turn out to be increasing this sector. This paradox applies to more governmental
activities. For example, improving infrastructure in order to solve part of the congestion
will motivate more people to migrate towards the urban area, which will cause a larger
informal sector and, as a consequence, more congestion. The same is true for
improving facilities (health care, police department) and improving the environment in
the urban areas. 
Eliminating the informal sector should actually not even be the most important target of
the government, for a developing country it is more important to have an efficient
allocation of resources in order to let the country develop. One way to do this is to
strive for wage based on their marginal return. Since this is quite hard to analyze and
because lowering the informal sector may have the same results, we will continue with
policies aiming at reduction or removal of the informal sector.
One way to do this is to restrict migration. This policy will get rid of the informal sector;
however, it is probably not an efficient allocation of resources, since there are too few
workers available in the urban area. Another possibility is to subsidize employers per
employee. This lowers the real cost of employees. With a subsidy large enough to let
employees demand such an amount for labour that their wage will equal the increased
wage for agricultural work. Now, there is no reason anymore for migration. However,
this is also not an efficient allocation, since there are too many workers in the urban
area now.
There is another possibility which is more successful in achieving its targets: that is
both subsidizing the wages in the agricultural and formal industrial sector. Due to the
higher wage, there is more supply of labour in both sectors. People move from the
informal sector towards both other sectors. With the right level of subsidies, the
government can reach full employment in both sectors, with no informal sector
anymore. Moreover, the government does not need to introduce a policy with migration
restrictions. Whether these specific levels can be found by the government is, of
course, not very realistic. It is more important to understand what the effect is of this
policy and that they can strive towards an ideal world. 
Risk aversion
As we stated before, migration towards the urban area is quite risky, because there are
so many migrants, supply of labour exceeds demand which forces many people to
work in the informal sector or even be unemployed. A person can estimate its expected
income, add probabilities to different income levels and make a decision based on
those. Whether or not the person is prepared to take some risks will determine if he or
she should decide to move. People can be risk-averse, risk-neutral and risk-loving. 
Besides the risk, there are some other aspects which we did not mention yet, which
play an important role for the decision whether or not to migrate. A few of these are the
availability of information from the other sectors, to ability to migrate and social and
family norms.

Chapter J Land and agriculture (1)

In the previous chapter we described the interaction between rural and urban regions.
This chapter we will focus on the rural region and especially on agriculture. Features
such as: institutions, markets and the lives of the individuals living in this region will be
discussed. One of the major aspects is that the market for agricultural products is an
imperfect one. This implies that there are some difficulties in analyzing them: lack of
information, incentives and market limits. Due to this, informal institutions come into
play. Problems such as: unequal income distribution and inefficient allocations. We will
consider some examples.
Information
The first example shows the problem when there is no possibility to observe. A landlord
may have a group of employees working on the land. Ideally, all obligations and rights
would be settles in a contract. However, in some cases the landlord lives somewhere
else (urban region), how should the landlord check whether his employees work the
right amount of hours and behave properly? One way would be to check the output
produced by the employees. This solution does not serve very well: there are different
variables which can destroy the crops. Moreover, when there are more employees it is
hard to tell who does his or her best and who does not.
Another example: an institution serves to give out loans to poor farmers, in order to
invest in their land or machines. How should the institution judge whether the farmer is
good for the money? As discussed previously, it is hard for a poor farmer to deliver
collateral. Also an interest-rate premium may discourage the very poor, exactly the
people the institution wants to help. A recent solution is to give a bundled credit to a
group of farmers which live closely together. Once one of them defaults, all loans will
be cut off.
Incentives
Let us look back at the first example; a landlord might want to improve efficiency and
productivity. One way to do this is to introduce an income based on the employee’s
activities. Unless this might be a good idea, the same problem arises: how should the
landlord check how each employee performs? It seems unfair to judge the
performances which can be influenced by other variables than just the work of the
employee.
Another problem: in today’s world employer-employee contracts are not binding. An
employee has the right to quit; this leaves the employer with the problem whether he
should invest in the employee. 
Land
There are two different ways of how a rural and agricultural area can be designed. One
way, is that all land is divided under the people who live in that area. Each family takes
care of its own land. Many African countries faced this way of endowment distribution,
late examples are South Korea and Taiwan. Another way would be that there are only
a few landlords with a lot of land and they hire the people to work on their land and
compensate them with an income or with products from the land. Of course, in real life
it is a mix of both. What the most preferred way would be (besides the ethical issue)
depends on whether there are constant or increasing marginal return to scale.
The problem with analyzing the society, the division of production factors and the
income distribution is quite hard due to the market implications and asymmetries
mentioned earlier. Other production factors are animal power and credit & capital. 

Chapter K: Land and Agriculture (2)

This chapter concentrates on the market for land. Land is a very important source of
production in developing countries. First of all, bad access to land production can drive
many labourers to cities. Second, there is the question of the productivity of the market
for land. 
Ownership and tenancy
Gini coëfficients of land are far higher than gini’s of income in developing countries.
Inequality of land is higher in Latin America than in Asia. An explanation is a higher
population density in Asia. When you talk about ownership- in Asia the land owner
cultivates land, where in America hired labour cultivates the land. In Africa usually
groups of persons own and cultivate land. 
There are various forms of tenancy arrangement:
Latin America: largely fixed rent variety. The tenant pays the owner always a fixed rent.
So, the landlord is relieved of the risk of bad sales.
Asia: sharecropping. The owner pays the tenant a fixed percentage of the total sales,
which varies from 10% (Costa Rica) to 90% (Bangladesh). Here, owner and tenant
bear the risk of a bad crop together.
Land rental contracts
Contractual forms
Fixed rent contract: fixed sum of money or crop per year from tenant to owner.
Sharecropping: fixed percentage of sales to the tenant. Tenant may be responsible for
inputs as well. 
R = aY + F
Where R is total rent and Y is agricultural output. ‘a’ is the share of the land lord/owner.
In a fixed rent contract: ‘a=0’ and ‘F>0’. In a sharecropping contract: ‘a>0’ and ‘F=0’.
The share of the tenant is ‘1-a’. Third, if ‘a=0’ and ‘F<0’ this can be interpreted as a
pure wage contract, where w = -F. Then you must talk about a labourer and not about
a tenant. 
A old argument in economics is that fixed rent contracts are better than sharecropping.
Sharecropping had ‘marshallian inefficiency’, based on the ‘appropriate provision of
incentives’. Because the tenant doesn’t bear all the risk involved in sharecropping, he
has an incentive to undersupply his effect, if he is not monitored and controlled by the
landlord. 
But you can than ask: why not give the tenant 110% or 120% of extra output? 
See the graphs for an illustration:
The production function Y has diminishing marginal returns to labour. The cost of
labour supply can be inputs or forgone leisure time. L* is the optimum when the labour
is the owner and earns everything he produces. In graph 2 the fixed rent agreement is
shown. The optimum is the same as with the labourer owning the land. Graph 3 shows
that sharecropping has a lower optimum labour supply (L# < L*). Hence the economic
surplus (difference between costs and production) is lower, and sharecropping is
inefficient. It is not in the interest of the tenant to maximize economic surplus (welfare). 
In graph 4 you can see that increasing the share of the tenant to over 100%, increases
supply (L# > L*), but the economic surplus is not maximized. (Tip: draw the graphs
yourself.) So distortion in land contracts happens with (i) sharecropping (undersupply)
or (ii) a landowner that tries to maximize output Y (oversupply, see graph 4).

Risk
The question interesting now is? Even if it is inefficient why is sharecropping still so
persistent in the world? What are the pro’s of sharecropping? A possible answer is risk.
Off course fixed rent contracts are riskier, as can be seen in graph 2 and 3: the slope of
the production function is more steep in figure 2. If the tenants can compare the risky
outcome with a safe amount of money, and (!) they are risk averse, the optimal contract
may yield lower labour supply. If a person is risk averse 50% probability on 1000 dollar
yields lower utility than 100% probability on 500 dollar. 
Suppose an expected return to the landlord is in the case of sharecropping:
psG + (1-p)sB -> s = R/(pG + (1-p)B)
where G (good output), B (bad output), R (sure payment to the landlord in case of fixed
rent contract), p (probability of good output), s (the share of the landlord in
sharecropping).
E(sharecropping) = p(1-s)G + (1-p)(1-s)B
E(fixed rent) = p(G – R) + (1-p)(B – R)
With ‘s = R/(pG + (1-p)B)’ these expectations are the same. So due to the monetary
values the tenant is indifferent to the contracts. (Tip: calculate!)
But now compare the variability of the returns. The good returns are higher in case of
fixed rent contract (G-R > (1-s)G). The bad returns are lower in case of fixed rent
contracts (B – R > (1-s)B). (Tip: calculate.)
This means that a risk-averse tenant will prefer the sharecropping contract (a risk
neutral tenant will be indifferent). 
Other contracts
So if fixed rent and sharecropping both have negative points, why not engage in a
wage contract? 
1)  The landlord and the tenant may be risk averse. 
2)  The incentive problem is high for the tenant in the wage contract. With a fixed
wage, the tenant has less incentives. (Principal-agent model)
When there are only wage contracts and fixed rent contracts, the landlord can diversify
between high risk and low risk contracts. There are some criticisms:
1)  Fixed wage contracts have incentive problem, so it is not clear whether this
dominates sharecropping.
2)  Mixing contracts is difficult.
3)  The wage rate itself may be uncertain.
Other considerations
Double-incentive problem: when the share of the tenant is 100% the landlord has no
incentives to monitor the leased land. But if the share is lower, the tenant has less
incentives to supply welfare maximizing labour (L*).
Cost sharing of inputs: when output and costs are shared, there is undersupply of
labour, so this is inefficient. (Tip: draw a graph.)
Limited liability and sharecropping: what if the tenant is not able to pay a fixed rent?
he doesn’t have to pay back, he may take more risk (if B < 0, he cannot pay anything,
the E(fixed rent) is higher, calculate!). Off course, the richer the tenant, the less risk he
will take.
Screening: if there is a difference between high ability tenants and low ability tenants,
the landlord may offer different contracts to optimise on the ability-return ratio’s. A high
ability tenant will prefer a fixed rent contract. A low ability tenant will prefer a
sharecropping contract. But (i) abilities do not stay forever, (ii) maybe rents will be
raised if a high ability person reveals himself, (iii) if there is competition for tenants, the
role of screening disappears. 
Land ownership
Property rights were always difficult to enforce in developing countries. Furthermore
land is relative to labour scarce, so land inequality increased. This leads to four
questions:
1.  is inequality compatible with efficient production?
2.  Can efficiency losses be repaired by land rental markets?
3.  Would land sales from rich to poor redress the balance?
4.  What is the role of land reform?
Are large firms more productive than small firms? 
Productivity can be viewed as total factor productivity (TFP). But inputs are not the
same, and family labour is difficult to value. Productivity can also be viewed as ‘market
efficiency, this is when marginal product equals marginal costs. Furthermore output per
acre is higher on small plots than on large plots.  Technology can also play a role.
Small plots can employ capital-intensive methods. This is draft animals and machinery.
So there may be economies of scale in production.
Imperfect insurance markets and small-farm productivity: monitoring labour at
small farms is easier. When tenants are risk-neutral or have perfect access to the
insurance market, tenants have incentives to supply optimal labour L*. 

Imperfect labour markets and small-farm productivity: with unemployment (i.e.
higher wages) the opportunity cost for family labour is lower than for the employer
(wages are simply lowers to suns than unknowns). Without unemployment opportunity
cost is equal. (The cost of supply of family labour is less steep (see graph 1), this
means a higher labour supply.) It is not sure that family labour will be inefficient.
Small landowners can pool land to gain from economies of scale, but this may lead to
free-rider problems.
Empirical evidence
Productivity on owned land is 50% higher than on sharecropped land. Small firms (in
Brazil) are five times more productive than large firms. But in high-risk environments
these advantages are smaller. Access to insurance and credit can deal with these
uncertainties. 
Land sales
If small firms are more efficient, in an efficient land markets sales from large to small
firms must occur. This doesn’t happen. The contrary happens. Land also has the ability
to serve as collateral. If this value is higher than expected (extra) income streams from
small farms, this can be an argument. Otherwise not.
Land reform
Another option is land reform. This is hard to establish, because farms may have
political power. This will keep the status quo. Land reform can also have disruptive
effects (see Zimbabwe).

Chapter L: Credit

Limits to credit and insurance
Credit markets may not function smoothly, because (i) there may be involuntary default
and (ii) voluntary or strategic default. Involuntary default may happen when there is
weak enforcement, and the borrower invests the loan in a risky project. In case of
international debt, as in the national case of developing countries, this weak
enforcement can be shown. 
Sources of demand for credit
1.  demand for fixed capital: production building, machinery
2.  demand for working capital: production activity
3.  demand for consumer credit
Working capital is needed at the beginning of the crop cycle. Consumer credit is
needed to smooth consumption over time.
Rural credit markets
Who provides rural credit?

• institutional lenders: these institutions (banks, governments, credit bureaus). The main problem is that these lenders don’t know the characteristics and activities of their clientele. Because banks bear the downside risk (they incur a loss when a creditor defaults, due to limited liability), and creditors bear the upside risk (they gain when the project has a better result). This means, that the
• creditor has an incentive to take excessive risks. Collateral could help this problem. But the problem is that rural creditors usually don’t have collateral, so banks discriminate against poor borrowers. The only valuable thing poor borrowers have is labour, and banks don’t take labour as collateral.
• Informal lenders: a large landowner, an employer of rural labour. They can reach out to poor borrowers. The rest of the chapter will be about this form. The share of this form is declining, but still present in many developing countries (>50%).

Characteristics of rural credit markets:
informational constraints: lack of information regarding the use of the loan. Lack of
information about the repayment decision. All features of credit markets can be
understood as results of these information problems.
Segmentation: many credit relationships are personalized.
Interlinkage: many moneylenders are landlords or shopkeepers. The loans are usually
made to tenants, creditors or labourers.
Interest rate variation: because of segmentation interest rate varies over regions and
moneylenders. Furthermore they are usually very high, up to 7% a month. Due to
segmentation and informational problems, arbitrage can not happen here, and price
differences are high.
Rationing: upper limits on how much a creditor receives from a lender. So some
Exclusivity: lenders insists borrowers to deal with him exclusively. 
Theories of informal credit markets
Two questions arise (i) does segmentation lead to monopoly, and (ii) is monopoly an
explanation of high interest rates.
Lender’s risk arises due to (i) involuntary and (ii) voluntary default. Zero profits for the
lender implies:
.p(1+i)L – (1+r)L = 0 -> i = (1+r)/p - 1
Where, p (probability of default), i (interest rate in competitive equilibrium in informal
sector), L (amount of the loan) and r (opportunity cost of funds for the lender, say the
formal interest rate). If p is 0,5, i would be 1 + 2r! So, it is essential for low interest rates
and a functioning market that p is as high as possible. 
Furthermore it is important to note that L may vary with p. Larger loans may have a
lower probability of repayment. So, loans are only made for working capital and
consumption purposes.
Default and credit rationing
Borrowers may not be permitted to lend more ‘at the going interest rate’, this is credit
rationing. The probability of default leads to this credit rationing. 
Say f(L) is the production function, where L is the loan. L(1+i) is the repayment, where i
is the interest rate. And f(L) – L(1+i) is the profit of the borrower, iL is the profit of the
lender. See, that when i decreases, the demanded loan increases and, the profits for
the borrowers increases.

The borrowers have always access to an alternative profit A, so the lender cannot
increase i, such that f(L) – L(1 + i) < A. So i* equals f(L) – L(1 + i) = A.
Now, introduce the possibility of strategic default. Let N be the amount of periods of
decisions. The participation constraint for the borrower is:
.f(L) – L(1+i) ≥ A
The constraint for no default is:
N[F(L) – L(1 + i)] ≥ f(L) + (N – 1)A
Here the profits from period N, exceed the profits of default in period N-1. This will give
the borrower the incentive to repay. This no default constraint results in (calculate):
.f(L) – N/(N-1) * L(1+ i) ≥ A
And see, that ‘N/(N-1) * (1+ i)L > (1 + i)L’, the slope of the no default constraint is
strictly higher, so the loan is strictly lower (tip: draw a graph!). This is called credit
rationing: a lower loan will give the borrower the incentive to repay.
Interlinked transactions
Landlords are often the principal source of credit for their tenants, using labour or even
their rights to tenancy as some form of collateral. In an environment where there is
weak enforcement, uncertainty is high, and information is badly available this is a
convenient way transacting, while there is no economic synergy between the two
activities. Pure moneylenders are rare in developing countries. 
Why is interlinkage an observed mode in developing countries?
1.  Hidden interest: in some countries (mostly islamic), charging interest is
forbidden or shunned. 
2.  Interlinkages and information: a farmer may ask from the tenant to repay in the
form of output. In this sense, the tenant can operate under the normal routine,
and may pay of with output in the case of default. In this sense the loan will not
be a by-product.
3.  Interlinkages and enforcement: interlinkage can prevent strategic default. For
example in the case of credit rationing. Second, the lender may better observe
when the labourer is not having an appropriate level of effort. Furthermore,
when deviations from the contract cannot be performed on both fronts (labour
contract and loan contract), this form has an very good enforcement.
Microfinance
Microfinance grows around the world, in amount and in attention. A group take’s a loan,
and when one member default, no group member is allowed to borrow again. So
monitoring is decentralized from the lender to the group. This creates a form of self-
selection of groups, so that only good (low default) will apply for loans. Some specific
implications:
1.  Positive assortative matching: good credit risks will come together, and bad risk
will be driven out of the market. Nobody wants to collude with bad risks (except
for bad risks themselves.)
2.  Peer monitoring: every group member monitors it’s colleagues. So excessive
risk-taking is minimized. 
3.  Potential drawbacks: when one group member defaults, other group members
will default also. With peer monitoring group members may choose very safe
outcomes, which are not socially optimal. So an overconservative choice. And
finally group-based schemes lack flexibility, the worse-performing member
slows down the whole group.
Still microfinance drives on subsidies. Also, there are fixed costs per borrower, and
small loans, may have higher fixed costs than higher loans. It is difficult to show where
the loans performed also better. Also, the very poor, will not have access to this system
at all.