Summary of Economic Growth (Weil, 2013) - written and donated to WorldSupporter in 2014
Measurement of economic development: GDP versus PPP
The indicator commonly used to examine the degree of development of a country’s economy is the Gross Domestic Product (GDP). It measures the market value of all services or final goods produced in a country during a year. It can be calculated as either the total income earned in a country or the value of the output produced in a country.
Economic measurement with the GDP (output or national income) also includes potential problems. For instance, GDP also includes foreign investment and does then not represent wealth in that Country, but the foreign investment value. In addition, many aspects of economic wealth cannot be measured by GDP.
The source of a high total GDP value could be extensive population density, because more people are available as labour force. Therefore, when comparing countries with different population sizes it is advisable to compare the GDP per capita (GDP earned per capita). Despite these potential problems, GDP remains a rough estimate for comparing different living standards.
A further potential problem when comparing GDP values of different countries, is the influence of exchange rates, which are only determined by international traded goods. Therefore, converting different incomes in one exchange rate can create a wrong picture of the true purchasing value of a currency.
Therefore, the Purchasing Power Parity (PPP) provides a measurement of national income based on the relative purchasing power of a currency, measured by the price of a standardized basket, which contains a set of traded and non-traded goods and services. The PPP corrects the GDP per capita measures.
Measurement: growth rates of national income
A country’s growth rate of income can be used as a measurement of the speed of development/growth. The growth rate is important because a country that grows fast will move to a higher level of income in the future.
When working with income growth rates, two concepts of graph scales need to be considered:
The ratio scale (also called logarithmic scale) is mainly used for plotting variables like growth rates which grow over time. Spaces on the vertical axis correspond to proportionality differences in the variable.
The common linear scale uses equal spaces on the vertical axis, corresponding to equal differences in the variable.
The main difference between those concepts is visible when plotting a constant growing rate over time. The linear scale curve is exponential and the ratio scale curve is straight. (See p.31)
The rule of 72 can be used for dealing with growth rates. It is a formula for estimating the amount of time it takes for something to double given its growth rate. See attachment A.1 for the formula.
Income growth rates vary among countries and also vary during recent decades. The difference between increased output due to business cycles or due to economic growth is mainly time related. Growth is characterized as a long-run trend, whereas business cycles can be defined as short term fluctuations, like recessions, i.e. deviations from the long run trend.
The total income inequality in the world is the result of two inequalities:
The difference in income between countries (Between country equality)
Inequality of per capita income within a single country (Within country inequality).
The findings from inequality measurement:
Total inequality highly increased during the period 1820-1950, slowed down 1950-1992 and declined after 1980.
Today 60% of world total inequality is a result of between country inequality.
In 1820 87% of world inequality caused by within country inequality.
Growth during different periods:
Growth Before 1820
Only few data is available for the period before 1820. Still, a significantly low GDP per capita growth rate is characteristic for an economy, which was driven by strong fluctuations due to the dependency on harvest conditions or armed conflicts. However, the income difference gap between countries is still very small. The world political order is dominated by the rapidly progressing Western Europe expansion.
Growth Since 1820
Worldwide income growth accelerates, with highly increasing average GDP growth per capita, but also the gap between country equality increases. Compare: In 1820 the ratio of comparing wealth between rich and poor countries was 3:1 (3 times as rich), in 1998 the ratio increased to 19:1.
Growth during the last 35 years
During the last 35 years some countries have experienced high growth rates while others dealt with negative growth rates. The chart on page 35 gives an overview of the growth rates from country-groups in the period between 1975 and 2009. So called “growth miracles” like China face an average annual growth rate of between7,5 % to 8 %. Whereas “growth disasters” like Liberia and Zimbabwe have to face a rate between -4.5 % and -3 %.
Some basic tools
In order to chase the key question of why some countries are rich and whereas others are poor, we will use the basic tools for economic analysis.
Goods and services are produced using two inputs, namely labor and capital.
Capital refers to physical stock like machines, vehicles and other pieces of equipment used during the process of production as well as financial capital, like securities. The more capital that a worker has to work with, the more output the worker produces.
Differences in income between countries can be explained by differences in the capital available per worker in each country. These differences in capital can be explained by differences in investment. Investment is the goods and services used for production rather than for consumption. The investment rate is therefore the fraction of income, which is further invested. A higher investment rate might explain more capital available per worker.
Although investment explains a part of differences in income, most is explained by differences in productivity.
Productivity is the effectiveness, with which output is produced from a certain amount of inputs. Productivity differences can be caused by a technology difference.
Technology is defined by the state of available knowledge about how to do (produce) things. Technological progress increases the produced amount of output with the same input (e.g. Productivity). The way in which available technology and inputs are actually used in production output is called efficiency. The formula which combines technology, efficiency and productivity can be found in attachment B.1.
Factors which influence economic growth immediately are referred to as proximate causes of economic growth. The opposite is called ultimate causes of economic growth, which has only an indirect influence)
The underlying factors of why a country is poor or rich are called the fundamentals. They include culture or geography aspects and economic policies.
The production function
The production function describes the method to generate output, by relating the amount of input factors used to produce the output. These input factors are referred to as factors of production. Input factors are either labour or capital.
According to the productivity function, income inequality in two countries can be due to:
Differences due to factor accumulation.
Differences due to productivity
Both differences in factor accumulation and productivity.
A question that often has been asked is what influence an increase in savings would have on economic growth. Well the answer is that an increase in savings would raise the growth rate of output in the years immediately after it took place, but eventually the growth rate would return to its original level. However the growth rate has not changed in the long run, the level of output would be higher than it would have been when savings had not been increased.
Analysis of Data
Economic theories are often stated in the form of economics models, which are simplified representations of reality that can be used to analyse how economics variables are determined and how a change in one variable will affect others.
In order to find empirical proof for different economic models regarding economic growth, we will have to consider statistical evidence and therefore incorporate the basic statistical terms;
A scatter plot is used to sketch the relationship between two variables, one on the x-axis and one on the y-axis. Each observation is represented by a single point.
Outliers: observations which show a clear deviation from the normal pattern.
Correlation describes the relationship between two variables as one is changing. Is one increasing as the other one also increases (calories consumption/day increases together with GDP increasing) we define that relationship as a strong positive correlation. The degree of correlation is measured with a correlation coefficient, which can take a value between -1 and 1. A value of “0” states that there is no relationship between two variables; e.g. the amount of girls born is not dependent on the amount of sunshine days. There are three possible explanations for the correlation:
X causes Y: variable X affects variable Y.
Y causes X: variable Y affects variable X.
There is no direct causal relationship between X and Y: But there is a third variable, Z, that causes both X and Y. This third variable Z is known as an omitted variable; the two factors do not influence themselves, but are both subject to a change in a third variable.
Reverse causation describes the phenomenon that not X influences Y, but Y effects X. For example, the correlation between cars owned per family and the income, could be interpreted that having more cars will lead to higher income. However, the opposite is true; the two variables have a reverse causation.
Cross-sectional-data: Observations of different units at a single point in time. A way to use these date is to examine how economic variables change over time for a certain period or decade.
The nature of capital
The term ‘capital’ refers to physical stock of production means like machines, buildings, also infrastructure, used together with labor to produce output. Therefore, the more capital per worker available, the more output can be produced, which points out a striking relationship between capital accumulation and GDP. Differences of capital availability account therefore also for the worldwide income gap between economies. The theory, which tries to examine that relationship, is called Capital-based theory.
Five main key characteristics of capital:
The creation/production of capital is defined as investment.
Nature of enhanced productivity: more capital available will increase the output that a worker can produce.
Rivalry of Capital since capital items can only be used by limited amount of people at the same time.
Return of Capital: Because of its productivity enhancing (Point 2) characteristics and Rivalry nature (Point 3) capital will create a return, which is often the incentive to carry out investments in capital.
Depreciation; Capital stock will decline in its value over time, either through physical depreciation, reduced demand or obsolescence.
Relationship between capital and productivity
As noted in Point 2 above, capital has the characteristics to increase productivity and therefore output. To assess the degree of that correlation, we will use the production function which relates inputs used and output produced. The two production factors utilized are Labour (L) and Capital (K).
The return of both inputs (Capital and Labour) together has constant returns to scale; if we multiply the quantities of each input by some factor, the quantity output will increase by that same factor, and where each individual separate factor has a diminishing marginal return.
The diminishing marginal product holds on the other hand that adding one more unit of e.g. labour and holding capital constant will increase the output produced less than the unit before (and so on) and less than the input “1”. That law is described by the Cobb-Douglas production function, see attachment C.1 for the formula.
Where A is a measurement for productivity, and ∝ takes values between 0 and 1, which describes the composition of how much capital is used in relation to labour (and vice versa). Therefore, a country with a higher productivity A will have a higher output for a fixed amount of Capital and Labour.
Another implication of the marginal (diminishing) product of labour/capital is that a firm will set the wages (for labour) and rental rate (occurring cost when renting a capital good) in the competitive market equal to its MPL (marginal product of labour) or MPK (marginal product of Capital).
The capital’s share of income is the fraction of national income, Y, that is paid out as rent on capital. See attachment C.2 for the formula of the capital’s share of income.
The Solow model
Robert Solow formulated the neoclassical economic growth model which incorporates Labour, Capital and technological change to explain differences in levels of income per capita and called this model the Solow model. The model focuses on the amount of physical capital that each worker has to work with.
The change in capital is determined by two factors:
Investment in capital, which increases capital stock, which we will call 'γ'
Depreciation of capital over time, which reduces the total value of capital which we name 'δ'.
Consequently, the change in capital (per worker in this case) can be written in a formula, see attachment C.3.
Hence, as investment is larger than depreciation, capital grows, is investment smaller than depreciation, the capital will shrink. The steady-state scenario of an economy occurs, when depreciation of capital available per worker is equal to the investment in capital stock per worker. Hence in the steady-state, the capital will not change over time. That is a stable equilibrium; as soon as investment is greater than depreciation, the capital will grow until it reaches the steady-state equilibrium. On the other hand, if depreciation is higher, capital stock will decrease and move back to the equilibrium. The shifting towards the equilibrium is called convergence towards the steady state.
A change in δ or γ, depreciation or investment, will shift either the depreciation, which is assumed to be a straight curve, or the investment with a diminishing growth curve and will thus move the steady state equilibrium.
If we plug the steady-state level of capital per worker into the production function we get an equation of the steady-state level of output per worker, see attachment C.4.
Solow compares the differences in the level of income per worker between two countries by comparing their steady-state levels of output, which is done by dividing one output level in the steady-state equilibrium by the other. Assuming the same level of productivity, the same depreciation rate but differences in the rate of investment, if that is given, we are able to calculate a numerical result, which represents the multiple level of income of country A compared to country B. Therefore, we can interpret the Solow model as a theory of income differences, because it allows us to compare different income level.
If two countries have the same rate of investment but different levels of income, the country with lower income will have higher growth.
If two countries have the same level of income but different rates of investment, then the country with a higher rate of investment will have higher growth.
A country that raises its level of investment will experience an increase in its rate of income growth.
Nevertheless, can we use it to explain growth differences between two economies? In the steady-state level theory, the possibility is not incorporated that countries grow over a long period, because with the steady-state theory each country is supposed to reach its stable steady state equilibrium. Hence, the theory can only be applied if we assume that the countries are located in a convergence towards the steady state.
Investment and Saving
The investment rate plays an important role in Solow’s theory of income differences, because it determines the growth of capital stock. Different rates of investment lead to different steady state levels.
In order to examine what determines the investment rate we will first focus on the saving rate; the rate to which people save. It is determined by the opportunity costs of saving. But the reason why savings rates differ cannot purely be explained by how much people can afford to save, e.g. live above the existence minimum. Factors which influence the saving rate and every economic model are either:
Endogenous variables: Determined within the model.
Exogenous variables: Are taken as given when we analyse a model, they are determined outside the mode.
To reduce the complexity of the theory, we assume that saving is endogenous, thus not determined by flows of investment among countries. Therefore, all capital which is saved has to be used for domestic investment, see attachment C.5.
If saving is dependent on income, we can corporate the assumption that an economy can have two saving rates; one for high income, one for low income. Thus, that economy is able to have multiple steady-states (in this case two). If a country is stuck at the lower saving rate, the economy is in danger to be trapped there, because at the low savings rate, the economy has a lower income, which in turn determines the lower savings rate. Thus, the initial level of income determines to which steady-state the economy will move.
The main link between the population size, the population growth and economic growth is that an increase in the population will increase the input factor labour but also the need for the supply of natural resources.
Population growth needs to be distanced from population size; a high growth rate is always dependent on the population base; if a small population size experiences an accelerated growth rate, the total population would be still small.
Furthermore the growth rate is negatively correlated to the GDP per capita. (See figure 4.1 on page 103)
Population and output over the long run
Population figures grew worldwide in a significantly slow pace before the growth rates took off around 1800, from 0,09 % (from 1st century 18th century) to 1,8 % (19th century). Therefore, the high population growth rate trend is a rather recent phenomenon.
Thomas Malthus (1766-1834) observed that, without resource or health (fertility) constraints population will grow unlimited. Therefore, growth is only constraint by limiting circumstances, like poverty and fertility. In the inversion of that argument, the Malthusian model states that population growth will eventually reduce income per capita because the population size has increased. Thus population growth will not improve the standard of living. People are not healthier, happier or richer; there are just more of them.
The graphical conversion of the model can be seen in figure 4.4 on page 109.
Part a) of the graphical model describes the influence of the population size on Income per capita. Since a high population size puts pressure on Income and resources, the relationship is negatively related; the higher the population size, the lower is the Income per capita. Thus, the curve is sloping downward.
Panel b) translates the income per capita from above into a growth rate. Please recall that populations grow fast in this mode, if they are not facing constraints regarding resources or fertility. Consequently, a high Income per Capita, due to small population size, is translated in a positive growth rate and vice versa. That relationship therefore is graphed as a upward sloping curve; the more income per capita available, the higher the growth rate.
This model will lead to a steady-state of population growth, i.e. “0” population growth through the following mechanism. Starting at a point with a low population size, as above described it leads to a high level of population growth. However, as soon as the population growth increases, the size of the population will increase. Therefore, we start again with a slightly larger population size, a slightly smaller income per capita, and thus a smaller but still positive growth rate.
That mechanism will repeat the effects until the growth rate has reached the value “0, then nothing will alter anymore; the population is at a steady-state. When starting at a high population size, the associated low growth rate will gradually reduce the population size until the growth rate is again equal to “0”.
The introduction of new resources will shift the curve relating population size and income per capita outwards, since the constraining resources are now less limited.
The only solution Malthus offers is that only reduced fertility (through “moral constraint”) will lead to a higher living standard. “Moral constraint” implies that the growth rate curve will shift downward and therefore connect the same level of income per capita with a lower growth rate.
The Malthusian model clearly does not apply to the world today. This can be seen from evidence from the living standards nowadays. The assumption that a high level per income will automatically lead to higher fertility does not hold. Developed countries with the highest level of income have also the lowest population growth rates.
Nevertheless, the Malthusian model recognizes the influence of constraining resources on the population, which still holds today (even though not in the historical scale).
Solow model and Population Growth
The capital-based theory of growth focuses on the role of capital, therefore we have to assess the influence of population growth on capital, rather than the population size in the Malthusian model.
As the population grows rapidly but the capital stock stays constant, the capital available per worker will decrease. That mechanism is called capital dilution. Please recall the Solow model that incorporates the growth rate of investment (γ) and depreciation (δ) to describe the change in capital per worker (output), see attachment D.1.
Capital dilution (i.e. less capital due to more workers with a fixed amount of capital available) works in the same way as capital depreciation. If investment does not simultaneously increase the change in capital will be lower than before and thus lead to a lower steady-state, and therefore to lower output. That mechanism might explain why countries with a high growth rate are worse off than countries with low population growth rate.
Therefore, the Solow model explains the low income level of fast growing populations, through the channel of Capital dilution.
Assume an exogenous rate of population growth n, which is equal to the growth rate of the labor force. The equation determining the change in capital is changed now, see attachment D.2.
See attachment D.3 for a figure that shows how raising the population growth rate from n1 to n2 affects the steady state level of capital per worker, k, and the steady state level of output per worker, y.
Factors of Population growth
The Malthusian model also explains how the size of population is determined. The model treats population as an endogenous variable, whereas the Solow model treats it as a exogenous variable.
The growth rate of any population is defined as the birth-rate–mortality rate. The share of fertility and mortality change as the country economically develops.
Demographic transition is a useful framework for organizing our thinking about population growth. At low stages of the countries development, fertility (with a very high rate) exceeds mortality (also with a relatively high rate).
As the country develops, mortality will decrease first, due to higher hygienic and medical improvements. Fertility will first stay constant and therefore will lead to a very high growth rate. With increased development, fertility will also fall and with completed developmental status, both fertility and mortality will be at lower rates.
Most developed countries completed the demographic transition stages, whereas the population in developed countries is still transforming.
As stated above, the growth rate is dependent on mortality and fertility, we will therefore analyse the transitions of both factors during the demographic transition.
Mortality transition and fertility transition: When the changes in the population growth result from interaction of changing patterns of death and birth.
A common measurement of mortality is the life expectancy at birth, the average number of years that a newborn baby is expected to live. In the period of the last 200 years, the life expectancy at birth increased rapidly, depressing the rate of mortality. The rate of mortality decreased more sharply in developing countries over the last few years, than it did at early stages of today developed countries.
As mentioned above, the underlying reasons for a decrease in the mortality rate are based on the improvements in the standard of living. That includes a better nutrition, advanced public health policies, like providing clean drinking water and better medical treatments. That also explains why Mortality transition was faster in developing countries; they experienced the advantage of profiting from the developed countries technologies to enhance the living standard all at once.
The Total Fertility Rate (TFR): The indicator measuring fertility, by stating the number of children a woman could give birth to when she lived through the potential child bearing years and experienced the current age-specific fertility rates at each age. As the Mortality rate, the Fertility rates also decreased significantly in the last 200 years.
The Total Fertility Rate lacks the possibility of an early death of the woman, since it gives the rate of children, a woman would give birth to if she lives through the childbearing years. Contrary, the Net Rate of Reproduction (NRR) gives the numbers of daughters each girl who has born can be expected to give birth to, including the possibility of death before childbearing years. Thus, the NRR combines fertility with mortality. A NRR of “1” implies that the population is growing with a 0 % rate, so the population is constant. Whereas a NRR of “2” means that the populations as a whole will double every generation.
Explaining fertility transaction
The transition of mortality is based on few obvious factors, whereas the reduction of fertility lacks obvious reasons. Explaining fertility is difficult. Over the years many cultures have tried to control family size to control fertility growth.
The idea that economic growth is the best way to reduce fertility was summarized at an United Nations(UN) conference in 1974. What was said there, is that the higher the developmental statues of an economy, the lower the fertility rate. There are four channels that discuss why development leads to lower fertility:
Effect of Mortality reduction
The decrease in mortality might actually be one cause of reduced fertility. This is because as the life expectancy of children increases, families might have fewer children because it is not necessary anymore to have more children to secure the survival of few.
Substitution and income effect
The more income per capita parents have, the higher are the opportunity costs of time for having children, e.g. the wages. When your wage is higher, children are relative more expensive. That phenomenon is called the substitution effect.
Another implication of a higher income is the risen living standard, which families want to keep when having children. Therefore the expenditures for children in high income families are higher than for low-income families. The high expenditures might hinder fertility. The latter effect is referred to as Income effect; when you are richer you can afford more of everything.
Resource flows between parents and children
In developing countries children tend to start working and therefore providing the family at earlier age than in developed countries. Therefore, the costs of child support are significantly larger in developed countries. In addition, in developing countries kids are supporting their parents as a kind of pension, which is not necessary in developed countries. However, do people base their decision of having children not solely on economic reasons, therefore resource flows cannot account for all of the fertility reduction.
Quality-Quantity trade-offs
Parents hope that the resources devoted to rearing and educating their children will have payoffs that improve the quality of the children. When parents are old it could be that they rely on the support of their children. When the children do not support their parents at old age, they may be happier by their children’s happiness. In this way investing in the live/quality of their child will provide them with benefits in the future.
Recall from Chapter 2, when we introduced the production function, which describes the produced output as a function of total productivity factors used.
Productivity is therefore the effectiveness with which the factors of production were converted into the final product/output.
Productivity in the production function
Since the production function describes the relationship of input factors and produced output, the function can be sketched in a graph, with the axis representing output (in this case per worker) and on the x-axis the factors (per worker). This graph allows us to assess 3 different reasons for output differences between two countries (let’s call them A and B).
The slope of the production function represents the efficiency (i.e. the productivity), because a higher slope, i.e. higher productivity will produce more output by the same input used.
There are three possible sources of differences in output per worker. (See figure 7.1 on page 201)
Country 1 and Country 2 are sharing the same production function (e.g. also same productivity). If Country 1 is more abundant in factors of production per worker it is therefore able to produce more output than Country 2. The higher factor level leads to a higher intersection on the productivity function and therefore also a higher output level. Therefore, the gap between the output levels between the two countries is caused by factor accumulation in country 1.
Both economies are facing different production functions, with different slopes (i.e. productivities) but the factors of production per worker are identical. Country 1 has a production function with a steeper slope than Country 2 and is therefore able to convert the same level of input factors into a higher output. According to the production equation (when holding the factors of production constant) the increase of output must be due to a higher productivity.
In the third scenario, both starting scenarios from scenario 1 and 2 are combined; Country 1 has a more productive production function (i.e. steeper slope) and a higher production factor accumulation. Therefore, also a combination of differences in production function and input factor availability can lead to a difference in output.
Thus, the possible sources of differences in output between countries can be based on different factor availability, different productivity (higher production function slope) or both combined.
Comparing the level of Productivity among countries
In order to compare quantitative output differences between countries, caused by productivity, we will use the Cobb-Douglas function, introduced in Chapter 3, see attachment E.1.
Please note that we inserted h as a measurement for the quantity of human capital. If we convert the Cobb-Douglas function in per worker terms, we divide it by “L” and therefore get a formula which you can find in attachment E.2.
To compare the level of output of countries we divide the formula of the first country by the other. That results in an equation that can be found in attachment E.3.
This shows that countries can differ in their levels of output because of differences in productivity, factor accumulation or both. The larger the ratio of output in two countries, the larger a productivity gap we would infer. The larger the gap in accumulation of factors, the smaller the productivity gap we would infer.
After rearranging that term we find an equation to compare the level of productivity. We cannot measure productivity directly but with a formula we can measure it indirectly. See attachment E.4 for the formula.
Development accounting: The technique for breaking down differences in income into the part that is accounted for by differences in productivity and the part accounted for by differences in factor accumulation.
Differences in the growth rate of productivity among countries
From the previous equations we can derive an equation for the growth rate of productivity, see attachment E.5. We can transform this formula into symbols, where the subscript g stands for the growth rate of that variable, see attachment E.6. Using the technique from this formula is called growth accounting.
Reconsider the Cobb-Douglas production function with Output as a function of Capital and Labour. As we found before, an economy might reach a steady-state, because capital has the nature of diminishing returns and labour is only limited available. Therefore the only factor which can lift an economy out of the steady-state is A, as long as it can grow. (With K and L at the limit, so they cannot increase further to increase output) Please recall that A is a measurement for productivity, thus technology.
Attributes of technology
Investment is needed in order to finance new technology (through the investment in R&D-Research and Development)
Technologies are non-tangible, unlike the other factors of production, labour and capital. Thus unlike L and K, technologies are non-rival. Non-rivalry implies that an unlimited amount of people can use that factor at the same time.
Because of its non-rivalry inventors might not be able to protect their technologies, with free transfer of ideas damaging the profitability of the technology for the inventor. Excludability is said to be low, which means that it is hard to protect own technology from free transfusion.
The largest fraction of R&D activity is done by the private sector, e.g. independent firms. The incentives for companies to invest in R&D are mainly profit considerations, in order to maximise profits. With new technologies a firm might be able to build up a comparative advantage or even create a monopoly. To evaluate the profitability of new technology the company takes the potential market size for the new technology, the degree of excludability (protection ability) and the upfront investment sum into account. A crucial threat of the majority of private investment into new technologies is that new technologies have to fulfil the criteria of profitability and not welfare enhancing for the whole society.
Joseph Schumpeter formulated with his theory of “creative destruction” a potential threat starting from new technologies. A new technology implemented by one firm can lead to destruction of old technologies used by its competitors. Take for example the implementation of telephones and their influence on the telegraph. Therefore new technology can lead to destruction of former knowledge.
A patent is a grant made by a government that confers on the creator of an invention the sole right to make, use and sell that invention for a set period of time, generally 20 years. To receive a patent, an inventor must produce something that is both novel(not something that was already known) an nonobvious. Generally an inventor must file for a patent separately in each country where they want to protect their invention.
Sometimes patents are not the best solution to protect innovations because patenting an invention requires a detailed public description. It is easy for competitors to come up with a product that is almost the same and bring it out directly when the patent has expired. They are also only useful if the legal sanctions against copying an invention can be enforced.
The impact of technology on growth
In the One-country world model
First we only consider one country for our analysis of R&D’s impact on growth. That excludes technology transfer between countries and implies that all technology used must have been created in that economy. Therefore, we will regard two models; first the influence on output per worker and after that the productivity growth change.
For the influence on the worker’s output we will regard the production function, but disregard physical and human capital and only take the labour into account. With γ representing the fraction of the labour force which is engaged in R&D the production function for the output per worker can be derived, see attachment F.1.
Therefore, the output per worker is higher, the smaller γ (the share of R&D workforce) is, (or the bigger A is). That finding seems a paradox, but becomes clear when considering that less people doing R&D means more workers producing more output (in the short run).
On the other hand, regarding the growth rate of technology, which is the change in A and thus ∆Y (see productivity function) is equal to another formula, see attachment E.2.
Whereas μ is the cost of creating new technologies and “ γ” still the fraction of workers engaged in R&D. Ậ is the productivity growth rate. Therefore with this model, increasing the number of “γ”, e.g. more R&D personnel will increase output.
The two ways of analysing the influence of R&D brought us to two different findings; are they not combinable? Yes, the first finding, that increasing the R&D labour force will decrease the output, because of less persons working today will decrease output today, holds only for the short run.
In the long run, that is what the second equation states; an increase in the R&D labour force will enhance output. Also the bigger the population (equal to L in the second equation) the larger the growth rate of technology.
Of course, this model is rather limited, because it does not consider cross-border technology acquaintance.
Two-country model
For the two-country approach we have to incorporate the possibility of technological transition from one country to the other. Consequently, we have to add
Imitation: coping an existing technology
Innovation: the new invention of technology.
The two countries are divided in a technological “leader”, which uses innovation for own technology. The second country is a technological “follower”, coping already invented technologies by using imitation. We assume that both countries account for the same population size, hence L1=L2=L, but according to the “leader-follower” system, the technological level (A) differs. Leader has a higher level of A and also higher costs of creating new innovations.
For the “leader”, that uses innovation, the formula for one country approach is applicable since the leader will not copy knowledge and is therefore reliant on own innovation for its economy. See attachment E.3 for the formula of the growth rate of technology for the leader.
The only difference recognisable is that country “leader” is facing the costs μi, the costs of inventing technologies from the scratch.
The “follow” country only applies the imitation approach, thus not creating own technology but coping the knowledge from the leader country. We assume that the bigger the technological gap between leader and follower, the lower is the cost of acquiring the new technology. If the difference is infinitely large, the cost of copying the technology falls to “0”. Therefore, the country “follower” has a similar equation for the growth rate of technology as country “leader”, see attachment E.4.
The only difference is that country “follower” is facing costs “μc”. See attachment E.5 for the formula of μc.
Thus, the two countries are facing different level of costs and are confronted with different levels of γ, i.e. the share of R&D labour force out of the total labour force, because the leading country needs to invent everything, for which it needs more R&D workforce.
Because both countries are interacting, due to technology transfer, we have to think about their relationship. In addition we assume that both countries have the same growth rate, i.e. γF = γL. This is because if not, for example as country “follower” would have a higher growth rate than country “leader”, it would become the new “leader”, which is impossible since they spend less on R&D (in form of R&D staff, recall that γ is smaller for “follower” than for “leader”).
If, on the other hand the original “leading” country would gain in the growth rate, the technological gap would widen and country “follower” could benefit more from the imitation. The bigger the gap the more benefit).
Consequently both countries are facing the same growth rate, when deviating from that equilibrium, both countries will always move back to the original equilibrium (as long as factors are held constant) because of the above described mechanism. The countries are in a steady-state.
Remember from the one country analysis that an increase in “γ”, i.e. share of R&D workforce increased the growth rate in the long-run. Contrary, if γF (i.e. R&D in “follower” country),increased only to a point at which it still holds: γL>γF, country “follower” will be able to increase the growth rate but end up at the same growth rate as before. (the “jump” in the curve can be seen on p. 227, 8.5 a) ). In the two-country model, an increase in γF therefore leas only to a temporary boost in the growth rate, unlike in the one-country model where it leads to a permanent increase. That is due to the steady state equilibrium.
The transfer of technologies
The transfusion of knowledge from developed (e.g. leading countries) to developing countries can be subject to some barriers. The barriers we will examine are the “appropriate/ adoption of technology” and the influence of tacit knowledge.
Appropriate/ adoption of technology includes the possibility that new technologies are not useful for the following country, since they cannot be adopted. Take for example, a technology influence which requires a high level of the input factors capital or labour, if they are not given, the technology cannot be incorporated. Furthermore new technologies might be lacking the capability of the new invention, e.g. importing a TV without having electricity. Because the poor country is lacking capital, it does not benefit as the rich country does.
The concept of tacit knowledge, which is knowledge learned over years of experience transferred from person to person that is not in written form, complicates the knowledge transfer. This is because it implies that in order to implement a new technology, background knowledge, which is not teachable, hence rather informal training (practical experience) is needed.
Embodied technological progress is a new technology which requires new equipment to be used with. Therefore, technological change is also dependent on the replacement of the surrounded equipment, which leads to infrequent replacements. Take for example the introduction of 3 D movie technology, which also required the theatres to implement new projectors. A typical disembodied technology is software, since it can be updated, without purchasing a new computer.
That can lead to the fact that firms replace the equipment seldom and replace the old capital goods with the newest technology. The replacement occurs in jumps and is therefore called leapfrogging.
New technologies, which are just developed and in production, are referred to as Cutting edge of technology. It has the nature of wearing off rapidly- former cutting-edge technologies like the telegraph and replace with new cutting-edge technology, e.g. the mobile phone.
Historical overview
Technological progress before the 18th century
From the A.D. 500 to 1500, income per capita in Europe did not grow at all. The population only grew at a rate of 0.1% during this period. The value of A rose with 1.39. In the period after this from 1500-1700, there was a fast increase of economic growth in Europe. Both income per capita and A rose. But still this these growth rates of productivity were extremely slow compared to growth rates in the world today.
The industrial revolution
The Industrial Revolution is dated between 1760 and 1830 in Britain with major and rapid technological progress within a wide range of sectors, including agricultural, manufacturing (e.g. textiles), metallurgy (coal as source for fuel for steam power) and energy (e.g. steam engines). This revolution was the most significant turning point in the history of technological progress.
The rapid technological change spread to the rest of Europe and North America and lead to an accelerated increase of the average income of the broad population. Moreover, the structure of the economy changed; the share of the labour force employed in the agricultural sector decreased sharply and increased in the industrial and mining sector. That came along with a change in the living structure; for the first time, the major part of the population lived in cities. On the other hand, Britain faced a rather slow (compared to nowadays standard) GDP growth rate of only 0,5 % during the Industrial revolution and growth did not stop after 1830, the end of the British revolution. GDP growth rate was limited due to the fact that the industrial revolution was constraint to few industries.
Technological Progress after the industrial revolution
In the period after the Industrial Revolution, the US economy overtook Britain and became the new world leader in advanced technologies and in GDP per capita. Two trends are noticeable during that remarkable period; first the transformation of the daily life technologies reached new levels, the invention of the electronic light bulb, automobile, refrigerator, telephone, aviation travel or TV change the daily life substantially. It took several decades for the new technologies to spread over the world, a process that is known as diffusion. The second phenomenon is the productivity slowdown starting around 1972 in the developed world. After the long period of incomparable productivity growth it finally slowed down.
The technology Production function
Please recall the “normal” production function we dealt with in Chapter 2; a function which relates input factors used (capital, labour) with the resulting output. Instead of the output produced in an economy, the output of the technology production function is new technologies created and the inputs include labour and human capital (researchers) as well as capital (laboratories, computes). For this the equation in attachment G.1 is used.
The main concern is that the inputs in the productivity function have grown substantially (in the factors of Capital and Labour), whereas the growth rate of technology has not.
Fishing out effect. ”Fishing out” because researchers are having difficulties to fish a “big fish” out of a small pond, because all easy inventions (big fishes) have already been caught. That is due to the accumulativeness of knowledge; researchers do not only have a broader base of already-existing knowledge, but it also takes more effort for researchers to acquire all relevant prior knowledge, in addition to the difficulties of the fishing out effect, that all easy inventions are already made. The technology production function above does not take into consideration the past. But with the information, that “L” inputs rose over the last years significant and the information that Ậ stayed constant or even decreased, points at an additional factor influences the rate of technological growth (e.g. fishing out effect), which is not explicitly listed in the technology function.
Another aspect, which we have to assess with the production formula above, is the decreasing returns to scale in technology production. The formula implies that the production of technologies have a constant return to scale, i.e. if you double the amount of R&D workers, the technology produced should also double. That assumption however is not realistic; devoting more R&D effort might lead to parallel invention, that is two or more developer (teams) are working on the same task, but only the first one to finish will gain the patent. Therefore, more effort in R&D will not lead to a constant return, but rather a diminishing return to scale in technology production.
General purpose-technologies will have a massive, far-reaching impact on the local economy and will change it substantially, like the steam engine or electricity networks.
Moore’s law (after G. Moore, a founder of Intel Corporation) stated in 1965 that every 18 month the power of Intel processors will double which held to be true up to today. The importance of that law is that G. Moore succeeded to predict the technological pace of new technologies during a time at which computers did not seem to have such an impact.
Differential Technology Progress in different sectors
Technological progress pace might vary substantially across different sectors. The differences between rapid changing technology industries, like communication and slow changing sectors e.g. teachers is reflected in the relative price of goods. Goods that encounter a lot of productivity growth are relatively cheaper than slow growing technology goods. That relationship can also be seen when comparing goods versus services.
The production technologies for goods developed most rapidly in the economy, whereas the technology progress in service sector grew little over time. Therefore, according to the differential production ratio (i.e. price for goods / price of service), service is relatively more expansive. Unfortunately the trend of consumption also changed over time; The People’s consumption (in this case in the U.S) of services rose extremely in the 2nd half of the 20th century, which increases the total expenditure, since the services increased in price. That shift of expenditures, i.e. increase of service demand and relative increase in service price is called the cost disease, first discovered by the economist William Baumol.
The governmental intervention in the economy affects various resorts of economic growth we have already dealt with. It influences the quality and quantity of factor accumulation, both human and physical, either through education (human~), or investment in infrastructure (physical~), but also it yields an impact on the pace of technological change through its patent system. But the most important role of the government regarding the economy is the efficiency to build a profound framework consistent of taxation, administration of laws, regulation and other tools to build a stable basis of economic activities.
In order to analyse different economic policies two perceptions are important:
The normative approach: aimed at advising government on how it should act. It follows the prescriptive path, asking for the ideal behaviour, or what the government should do in order to promote economic growth.
The positive approach rather focuses on the reasoning of governmental acting, why do government react as they do? Attempts to describe rather than prescribe government actions.
Defining government’s proper role in the economy: the normative approach
The degree to which a government should intervene in market structures is heavily debated and the answers range from no interaction at all (laissez faire) to complete government control.
Some advocates of governmental interference state that it is necessary to interact as soon as the market cannot supply the features or efficient outcome which would be favourable for the society. Since the market fails to provide those outcomes, we are talking about market failure.
We will discuss four different forms of market failure; handling public goods, externalities, monopolies or coordination failures.
Public goods are failed to be supplied by the market because the profit margin is either too low or it is difficult to charge people for the usage. Examples for public goods include airports, infrastructure, education or even national defence.
A second reason for governments to interact because of market failure is the phenomenon of externalities. Externalities are incidental influences of an economic activity on people who are not involved in that activity. Take for example the externalities of education; that is the indirect influence of a person’s education on his direct environment.
Many economists assume that the benefit of one person’s education benefits the society even more than him, e.g. because he might persuade other people to follow an education or will just have a positive influence on his environment. Those externalities are not taking into account by the individual decision maker, e.g. the student who faces the decision whether to persuade more years of schooling or not.
Therefore the government needs to stimulate activities which will evoke positive externalities. Similarly, negative externalities are often a by-product of market operating firms, e.g. pollution of a plant, and need to be constraint by regulations from the government.
In addition, the existence of monopolies requires the interaction of governmental regulation in order to prevent the sole company of too much market power and inefficient high prices.
The fourth market failure reason to intervene is potential coordination failures, including the coordination of flows of in the coordination of business chains. If a firm does not want to invest in a certain business because it fears that there are no appropriate suppliers for it. Firms which want to supply think that there is no market. The government has to interact in that communication stagnancy.
Besides the reason of market failure to interact, the government has, depending on the political view, the role of redistribution of income.
The main argument of the advocates who argue for a limited or no intervention from the government is the possibility of government failure, i.e. that a government does not have the ability (e.g. quality of the officials) to interact in the market. If the government failure is greater than the market failure, caused e.g. by a monopolist, the overall damage will be larger than without the government interaction. That phenomenon is called equity-efficiency trade-off.
The implications of contra government invention are privatization; handing over former governmental activities to the private sector and deregulation; removing governmental supervision from private companies.
After World War II, Europe experienced an increasing government interaction in form of welfare states, including national health care, unemployment insurances or pensions. That trend reversed at the end of the 20th century, less government interaction more privatization and deregulation
How government affects growth
The impact of government invention can have varies roles, we will focus in particular on the three aspects: Rule of law, Taxation and efficiency, the practice of governmental planning.
Rule of law
One of the most important public goods that governments provide is the rule of law. By providing a legal, juridical framework for business interactions (e.g. contracts) the government creates a plan-able, stable certainty for economic activity. The result of an effective rule of law can be seen in a strong correlation between productivity and rule of law.
Taxation and efficiency
The prime influence of government on the economy is through taxes; the bigger the governmental expenditures the bigger the need for revenue (through mostly taxes). As the income of a country rises, the governmental spending rises more than proportionally, because a bigger and more developed economy requires more regulation. That increase of government expenditures as an economy develops is called Wagner’s law (formulated by Adolph Wagner 1883). That law implies that developing countries should have less government expenditures, but the opposite can be observed in many developing countries. Many have higher government spending than today-developed countries at that stage.
Consider a market situation with a downward sloping demand and an upward sloping supply curve. Under free market conditions, the quantity supplied (price paid) it at its market equilibrium. The market is working efficient. Imposing a tax on the good traded, will increase the amount paid by costumers and decrease the price received by the suppliers (See page 361). Therefore it will drive a wedge between the prices of demanders (pay) and suppliers (receive). That wedge represents the tax collected by the government per unit traded. The quantity traded (please note: less than with free market equilibrium) is called the tax base. After multiplying it with the tax collected per unit you get the total tax revenue.
The larger the tax collected per unit, the less the quantity is traded, and the bigger is the inefficiency on the market.
Governmental planning
For the reasons above a government might decide to intervene strongly in the economy and plan economic activities central. Even though economists with a free-market orientation stress the failure of central governmental planning, there are some successful examples, in which government intervention lead to high economic growth.
South Korea and Taiwan, for example succeeded with a mix of public enterprises and infant industry protection to reach a high level of growth and development. The reasons why government planning worked well are that the bureaucracy worked efficient and that public enterprises had to function after the profit seeking aspect and could be therefore easily transformed into private enterprises. But in most cases, the central planning policies did not succeed to encourage economic growth.
The strategies used to enforce governmental planning are: State enterprises, marketing boards, Trade restrictions.
State enterprises: Companies that are owned by the government are especially crucial in key sectors, like banking or raw material industries. Even though they are not privately owned they should fulfil the criteria of private owned companies, e.g. profit seeking.
Government-owned banks: In no industry has government control been viewed as being more important than in banking. Government-owned banks have in theory enormous leverage to overcome market failures. Control of banking also allows the government to accomplish social objectives such as distributing resources to unprivileged population groups or regions.
Marketing Boards: Those governmental owned boards have the function to buy farmers output and sell further on the international market. By centralizing the farmer’s crops, the government hopes to obtain a higher price on the world market, as if the farmers would gain if they sold it individually.
Trade restrictions: In order to protect the domestic industry, government might impose quotas (i.e. limited number of imports) or tariffs (i.e. taxes on imports) for foreign imports. Quotas or tariffs shall often help infant industries, e.g. new founded industries and protect them from international competition. But by imposing trade restrictions, the government might assist to build up an inefficient industry because pressure from competition is missing.
A country that is caught in a conflict trap may not differ in any fundamental way from a country that is peaceful and prosperous. Circumstances and luck may have been all that made the difference.
The positive approach: Why Governments react in an unfavourable way for the economy
Until now we considered the normative approach in order to describe what governments should do. But in some case the normative and positive, i.e. what they should do and what they actually do differ; in this section we will try to assess reasons for this gap.
Different intentions
The government might do things in order to enhance the national interest, which might not be favourable for the economy. Therefore, the government and the economy are not always aiming for the same goal. Other examples for that gap are minimum wages (beneficial for the national interest but not for the economy) or pollution reductions by companies.
Corruption, Kleptocracy and the economic effect
Corruption in governmental structures hinders efficient bureaucracy and therefore the efficient development of the economy. The form of corruption that occurs in very high levels of the state is called Kleptocracy (i.e. “rule by thieves”). The impact of corruption on the economy can be seen in two phenomena;
The first is that the efficiency of production is decreased due to the possibility that governmental contracts are not made with the most efficient firm, but with the firm which bids most or because of the simple reason that tax money is wasted.
The second, more subtle impact is that policy makers will decide over new regulations with the goal to maximise their corruption’s income, rather than effective market policies.
Self-preservation
Governments might not choose for the best policies as a tactic in order to keep in the position to wield power. For example, as a growth of the economy would only influence one part of the population, which does unfortunately not belong to the elective group of the ruling government, the government might not have interest to persuade economic growth then. A historic example of the latter is Russia, which feared in the early 19th century riots, as industrial workers would be concentrated in cities (not farmers on the countryside anymore) and industrialization would threaten the wealth of elites. Therefore Russia stayed backward in its economic development.
Developing countries and bad governance
It seems that there is a correlation between the level of development in the economy and the quality of governance. Often poor countries tend to have especially bad governments. But the question is, whether bad governments are the result of underdevelopment or the cause.
1st view: Bad governments result of underdevelopment
In favour for the phenomenon, that a bad government is not the cause of low national income, but the other way around, is the fact, that in the early developing history of today developed countries also had very corrupt and inefficient governments. A second underlying reason is that as soon as national income increases, the quality of government might increase, due to risen governmental wages paid to governmental staff (to cut off one of the main reasons of corruption).
2nd view: Bad government is the reason of underdevelopment
Regarding the influence a government can have (as discussed earlier) many economist believe that because of that influence, governments are the prime reason for the underdevelopment of the domestic economy.
The main proof for that theory is the experience with former colonies, because 22 of 30 most corrupt countries are former European colonies. The former European colonies mainly extracted profits to the “mother” countries, without building sustainable economic structures. After the period of colonialism ended, the structures of profit seeking and extracting were kept, and the foreign colonial power was replaced by local rulers or the native elite. And because this structures last until today, the economy is not able to develop but rather being exploited.
In addition, former colonialism influences the current development level, because foreign colonial rulers divided the land not under historical and natural aspects, but rather how it suited them best. Therefore they created “states” with different ethnical groups, which do not feel that they belong together. If you take a look at the map of Africa, you can observe unnatural straight borderlines. Those states carry a high risk of conflicts and are thus not favourable for economic growth.
On the contrary, there are former colonies which developed wealthy economies, like Australia, the USA or Canada, but the nature of those colonies was not purely extractional and the European settlers adopted European governmental systems.
In order to compare the developmental state of different countries we used GDP or the average income per capita until now. But those numbers do not provide information about the distribution of the income, which is crucial, since developing countries are often characterized by a large gap between incomes.
Income inequality: the facts
The measurement of the distribution of income can be approached on two ways:
Divide the total income into several equal sized intervals and then observe how many people are in each group
Divide the population in equal sized groups and then compare the average income of every group.
When sketching the income distribution, several statistical keywords are important;
the mean is the normal average of values
the median the exact middle of the observations, the number of the observation which has exactly the same amount of observations below and above.
Furthermore, income data is always skewed; not symmetric around the means but has a long tail to one side, to the right side, where high incomes are.
The Gini coefficient measures the degree of income inequality in a single number, which makes it easier comparable. The Gini coefficient can take values between 0 (no inequality) and 1 (perfect inequality). To calculate the coefficient we have to introduce the Lorenz Curve, which relates how much (starting with the lowest income households) low income households account for the percentage of total income. If you rank the income distribution from low to high, you basically ask, How much of the total income are provided by the lowest income households? In order to calculate that curve, that question will be repeated for all percentages.
Simon Kuznet observed in his hypothesis the development of income inequality during industrialisation and urbanisation. According to Kuznet inequality will first increase because urban inequality tends to be higher than rural inequality. At later stages of economic development, equality tends to adjust. Therefore, Kuznet’s curve is an inverted U-shaped curve when relating GDP per capita with the inequality. With the highest inequality found for medium GDP per capita, i.e. medium stage of industrialisation.
The factors causing inequality
The source of inequality within a country is based on differences among the population. The differences can relate to the field of human capital (education, health condition), the origin (rural or urban) or the ownership of physical capital, and of cause simple luck.
We will reduce the source of inequality to the simple difference in education, measurable in years of schooling (reduced to year 0-4). The return on the education years is an increased income with longer education compared to less years of schooling. Thus, the longer the education the higher the income will be.
Therefore we will use the distribution of how many people having how many years of education and the return to education, to calculate the Gini coefficient and compare that in two different countries. The model building will assist to determine the reasons for differences in income distributions and changes over time.
Model 1:
Country A and B have the same distribution of education (i.e. for both countries the same amount underwent 0, 1, 4 years of schooling) but they differ in the return on the education. Country A offers 10 % return whereas Country B only has 5 %. Because of the lower educational return in Country B, the income will not differ as much as in country A because of the cumulative nature of the educational returns (Gini coefficient of 0.068 for A and 0,035 for B.)
Model 2
Another source of a higher Gini coefficient is the educational distribution. In this second theoretical model, the countries do not differ in their return to education, but in the distribution of the how many people experienced different years of schooling. Country A has the normal distribution as in model 1, but Country B has a more narrow distribution this time; i.e. less students of the only 0 or 4 years of education and more students had undergone an education for the median amount of years. We come to the finding that, in this comparison, the Country B, has a smaller Gini coefficient.
That model is however constraint by its simplicity, but it demonstrates how a change in the population structure or the return to education influences the income distribution. This modelling proofs Kutznets theory; as a country develops, the return on education (capital) tend to increase, which will, as seen in model 1 increase the inequality. The higher returns will stimulate the population to take longer years of schooling, this (model 2) and the fact that the further the country develops the less will the return be, will decrease the inequality eventually.
The phenomenon of sharply rising inequality occurred in the most advanced economies after World War II. Possible underlying reasons for that paradox (because after Kuznet it should be very small) can be:
Technological Advances and return to labour: Due to new arising technological progress, the return to the educated labour increased again. This was due to higher productivity, because of the complementing technologies for jobs persuaded by educated persons. Therefore as soon as the technological innovation slows down, the inequality will decrease as well.
International Trade and increase of rate of return: When engaging in international trade, the good which one country is abundant in but the other not, will experience an increase in the rate of return to that good (e.g. labour), which will rise the inequality as well.
“Superstar” dynamic: A recent phenomenon, which holds that the top-educated people of an occupation earn significantly more than slightly less educated persons. Take for example Top managers or Top athletes, which earn enormous amount more than insignificant lower qualified managers/athletes. Superstar Payments tend to increase inequality because the return on very high qualification rose.
Those three examples are channels through which the income inequality can arise even in high developed countries.
How income inequality effects growth
Domestic income inequality is able to effect economic growth on four different levels:
Income inequality and Accumulation of Physical capital
Income inequality has a positive effect on economic growth through the instrument of physical capital, the savings rate. As the income increases, the savings rate will raise simultaneously, e.g. a person who earns more tends to save more.
Therefore, more people have a higher income, i.e. the higher the income gap; the more will be saved in total. We examined the effect of a risen savings rate before: the economy will be able to reach a higher steady-state and therefore have a higher level of output. For the savings rate it might not be favourable to redistribute income, because only if capital is accumulated it will have a high savings rate. Some income is distributed from the rich to the poor; the savings rate will suffer, because people with a lower income tend to save less.
Income inequality and the Accumulation of Human capital
Unlike the positive influence on Physical capita, income inequality tends to have a negative impact on Human capital. The contrast is due to the differences between Human and Physical capital; Human capital investment is limited, whereas investment in Physical capital is rather unlimited. That is because it is possible to own Physical capital, e.g. tools or factories, but it is not possible to transfer the ownership of Human capital, e.g. being the owner of the education of somebody else.
The inequality assumption can be expressed with the example of two persons and their investment options. Let’s consider the case that one is rich and the other poor and how their investment decisions differ. We assume that Human capital has diminishing marginal product; the more we invest the less we get as extra return, whereas the marginal product of physical capital stays constant, no matter how much a person already invested. That is because the personal investment in physical capital is diminutive compared to total investment the overall rate is also diminishing.
Taking the two persons again in consideration, we find that a person with less income will first invest in Human capital, whereas as income rises, the second person will tend to invest in human capital up to the intersection point and then in physical capital.
If now redistribution from the rich to poor person would take place, and we assume that the poorer person has not reached the intersection point yet, the poor person would invest the extra income in more Human capital. That leads to a reduced investment by the rich person in physical income, and the higher investment in human capital by the poor person with the higher return than the physical capital before will increase the total return (i.e. output). Therefore the more equal the income, the more beneficial for the Human capital.
The opposite effect of inequality (positive for Physical, negative for Human Capital) has a different implication for different economic situations. Consider the economic stage at the end of the 19th century. Since the driving force of the economic development was physical accumulation, e.g. technological change, a strong income inequality could have been beneficial for economic growth, because the inequality is positive for physical capital accumulation. On the other hand, growth in developing countries today is more Human Capital based therefore income inequality has a highly negative impact on economic growth.
Productivity and Income Redistributions (Taxation)
Income redistribution occurs when the government, for the reason of income inequality takes a share of the income of the high-income population and transfer it to people with low income. This redistribution has two effects on every person;
First the obvious fact, that the disposable income will either increase or decrease. The disposable income is the pre-tax income (purely what a worker earns before taxes are collected) minus the taxes paid and plus the transfer income received.
The second, more subtle effect is that because of the taxation, productivity will tend to decrease the more the tax rate increases which will lower the pre-tax income. Inequality and efficiency are conflictive implications; whereas inequality implies a higher taxation, efficiency calls for no taxation.
In order to find the desired tax rate, regarding the relationship between inequality and efficiency, we will build a model in which the government only redistributes income. First the government collects the same fraction of income from everybody. That means that people with a high income will pay more. The redistribution follows the principle of a lump-sum transfer; everybody receives the same amount from the taxes collected. (e.g. if the country has 4 inhabitants, which pay, according to their different income, 2 $, 8$ 10 $ and 12 $, everybody would receive a lump sum transfer of 8 $). In addition, the equality of income is easier reached with a high tax rate even though it will decrease the productivity.
The effect on workers:
Workers who have pre-tax income above the mean (in our example 8 $)
A worker, who’s pre-tax income is above the mean, will have to pay more (e.g. 10$) than he gets redistributed again from the government (8 $). Furthermore, the effect of reduced productivity due to the taxes will reduce his pre-tax income further. Hence, as soon as a worker earns more than the average he will be against redistribution.
Worker has a pre-tax income exactly the mean
The lump-sum fee the worker will get redistributed is exactly the same amount he had to pay as taxes (=8 $), therefore in that manner he does not mind the redistribution. But the underlying effect of the reduced efficiency due to tax imposition will decrease his pre-tax income and therefore people earning the mean lump sum fee will also be in favour of no taxation.
Pre-tax Income below the mean
Workers with a pre-tax income below the mean will be the sole beneficial from the redistribution, since they will receive more than they had to pay (take for example the inhabitant who paid 2 $ and received 8 $.) In addition, his pre-tax income will be reduced due to the decreased efficiency. The worker will prefer a higher tax rate the greater the gap is between his income and the mean income.
The analysis above showed that people earning more than the mean income will be against imposing a tax rate (or for a lower rate), whereas people which an income below will favour one (or higher rate). The tax rate is primary a political decision, because when giving everybody a vote the majority preferring another rate will alter the tax rate due to elections.
Therefore when lining up the income in ascending order, (i.e. the related desired tax rate in descending order, remember, the higher the income the less desired tax rate), the median income will set the tax rate. Then the same amount will have a higher pre-tax income, and desire a lower tax rate, and on the other hand, the same amount of voters has a lower income and therefore desires a higher tax rate. The median pre-tax income person is called the median voter. The median of the distribution will always be below the mean for income distribution, therefore, the median voter will vote for a positive tax rate.
If the income inequality increases, that is the distribution of income becomes more skewed, the median will move further away below the mean; and thus the tax rate favoured by the new median voter will be higher (because further below mean). Therefore, higher inequality leads to higher redistribution and to increased inefficiency.
Unequal distribution may provoke pressure for distribution, if nondemocratic systems fail to adjust the median vote rate. Rising pressure might be expressed through increased political instability, as different groups aim for power, or crime, which is also a form of redistribution from the rich to the poor.
Economic Mobility
Up to now, we only considered the distribution of income for inequality, but the ease of diffusion from one income class the another should also be examined.
Economic mobility refers to the ease of moving between the income distributions. Furthermore, intergenerational mobility measures the ease of enhancing the family status from one generation to the next. The correlation of the Childs education depending on the family’s education can be used as a measurement for intergenerational mobility.
A correlation coefficient of “1” points out a strong dependency on the parents’ educational level and hints at a low intergenerational mobility. Thus, the intergenerational mobility is easier if the coefficient approaches zero. Another way of measurement is a so called transition matrix. It is a table showing the probabilities that individuals will move from one income group to another.
Effects of mobility on economic growth
A high economic mobility implies that the economy is able to make full use of all talents available, regardless their born income class; and that will enhance economic growth
A high degree of mobility can reduces inequality, and therefore decrease the pressure on political systems
Determinants of mobility
Mobility is more likely with an efficient and broad available education system.
Efficient institutions and governments can enhance the effect of mobility and hinder the sole pressure of interest groups.
The development for mobility is often dependent on family forming nature; if marriage is limited to the same income and social class, which is referred to as assortative mating, mobility and mixture is hindered.
If racial of ethnic discrimination takes place, children from that minority might not be able to move with ease to other income classes.
Culture is a collective term to unite shared values, attributes or beliefs in a society, which makes it distinction-able from other societies.
The influence of culture on economic growth
Not only are appropriate measurements for culture hard to find, it is also difficult to estimate the exact impact on economic growth. Therefore, we will try to approach the cultural influence by taking a closer look at subtopics of culture:
Openness towards Innovations
The technological level and hence the economic growth are dependent on the willingness of a society to adapt and recognize the value of foreign ideas. The difference in that willingness also determines developing gaps, for example when comparing Japan and the Islamic world. Japan, which is one of the most economically successful nations, was willing to absorb new technologies developed in Europe or the USA. On the other hand, the Islamic world showed the tendency to refuse to incorporate foreign technologies, which hindered economic growth.
Hard Work
The attitude towards labour differs across cultures and might explain the economic development. Even though the literature failed to find empirical proof for the thesis we assume that the valuation of leisure over work (vice versa) influences economic growth. The root of European work ethnic is Protestant ethnic reformation, which stressed that “all men were created to busy themselves with labour”(J.Calvin).
Saving attitude
As we saw before the saving rate has a large influence on the economy. Assuming that the cultural attitude towards saving differs, might explain different saving rates and therefore also differences in economic performance
Trust
Even though institutions and government regulations secure many business transactions, some are purely built on trust for both parties to fulfil an agreement. The degree of trustworthiness attributed to the members of a society influence economic growth; there is a strong positive correlation between investment and the percentage of the society that claims that most people can be trusted.
Social Capital
Social capital determines the level of interaction among the members of society; therefore, social capital forms the basis for trust. The higher the social capital between persons, interaction/friendship, the higher the trust. Besides trust, there are other attributes of social capital, which enhance the economic performance, e.g. information transfuses easier through social networks, regarding jobs or aid.
In addition, the quality of governance is also determined by social capital; a society with high Social capital is likelier to vote actively because they care more about the community.
Social Capability
The quality of social and cultural attributes and behaviour in a society is referred to with Social Capability. High social capability attributes enable the country to take economic opportunities, including technology transfer, factor flows of trade. First mentioned by Moses Abramovitz, Social Capability includes the determinants, which influence economic growth:
A earth-centred view, which sees life as important motive, rather than the unimportance of life
The population’s experiences with large scale corporations
Future orientation: future planning based on pragmatic science rather than superstition beliefs.
The possibility for the population to engage in market mechanism, like trade or through specialisation.
After Abramovitz, an underdeveloped country with a high social capability is able to bridge the economic development gap faster, which is proofed by a high correlation between social capability and the level per income. Social capability is measured with the Adelman-Morris index. But as the governmental structure, different social attitudes are helpful at one economic development stage, and not in another, e.g. the attribute of workforce was, before the industrialisation, mainly focused on strength, which does not hold today anymore.
The Determinants of Culture
After we examined the effects of Culture on economic growth, we shall turn to the question of what determines Culture. The factors of Culture include religion or history to name a few, but we will only consider factors which are exposed to economic influence. That includes the Climate and Natural Resources, Cultural Homogeneity or Population density impact.
Climate and Natural Resources
The direct linkage between economic behaviour and climate and natural resources is the attribute of saving or forward (in the future) looking manner. If the climate allows only seasonal agricultural harvest, people are forced to plan in advance for hard periods, whereas people experiencing all year round agricultural production, do not have to learn to plan forward. The same reasoning holds for the use of Natural Resources, if countries are abundant in resources they may not invest in future technologies, but instead rely on the resources.
Cultural Homogeneity and Social Capital
The level of Cultural Homogeneity, i.e. the degree to which a society is solely consistent of only one culture influences economic growth through the channels of social capital, including that social networks might be stronger if people share one culture or the level of trust is higher between people of the same culture.
The index of ethnic fractionalization measures the degree of ethnical homogeneity by stating the possibility that two random people of one society meet and do not share the same cultural background. Thus, the index of ethnic fractionalization of “0” illustrates that the society only consist of one ethnic group, because the chance of meeting another ethnical person is equal to zero, whereas the index of “0,5” states that the society hosts two different equal large ethnical groups.
A highly ethnical fractionated society has a negative impact on economic growth, due to a negative correlation between income and the index of ethnic fractionalization. Underlying possible reasons are difficulties of governance or historical reasons, like colonization. Besides ethnical, also linguistic and religious fractionalization tend to have an influence on economic growth. Linguistic fractionalization has, like the ethnical a negative impact for the same reason, that social capital is easier with two people sharing one language.
Contrary, researchers found out that countries with a high religious fractionalization have higher income then with less religious groups. That is because a large amount of religions is a sign for high tolerance of the government and that political systems have a democratic scope, which includes the protection of minorities.
Social Capability and population density
Population density influences social capability through the channel of more institutions and a higher abundance of the factor labour. Areas with a high amount of inhabitants have a greater need for regulations. Like extensive governmental structures or institutions, which are helpful to take advantage of new economic possibilities and therefore enhance Social Capability. The same reasoning holds for labour abundance.
Thus, a strong correlation describes the relationship between income growth and the degree of population density. The density of population itself is subject to geographical circumstances, the quality of government, foreign trade (to import food) and the level of technology (to increase the output used for food).
Cultural Change
We already noted that there is a relationship between cultural attributes and economic performance. However, it is appropriate to believe that economic growth alters culture. Factors of economic growth, like foreign ideas, Urbanization or increase educational level have a large-scale impact on cultural values.
The government is able, through various channels to determine the facets of culture. Governmental interaction might have the primary aim to target especially cultural change, or cultural change might only be a by-product of certain policies. The reason for government interaction in culture can have a non-economic (like the creation of a national unity) or economic promoting nature (e.g. promoting growth through modernization).
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