Samenvatting verplichte stof

Deze samenvatting is gebaseerd op het studiejaar 2013-2014.

A. Macroeconomics in general

The most important concept macro economists use are:

1. Aggregate output (GDP)

2. Unemployment

3. Inflation

These three concepts are all connected with each other.

1. Aggregate output

• Market value of all the final goods and services in the economy

• The sum of all the added value in the economy

• Sum of incomes in the economy

Two types of GDP:

Real GDP

--> Measured in constant prices. Goods x constant price. Adjusted for inflation (Yt)

Nominal GDP

--> Measured in current prices. Goods x current prices (€Yt)

GDP growth rate: (Yt - Yt-1) / Yt-1

GDP increases (positive growth rate) is called an expansion

GDP decreases (negative growth rate) is called a recession

2. Unemployment

Unemployment: All the people who are jobless but are looking for one. Is the unemployment a good indicator? Well, it is hard to say whether a person is looking for a job or not. There are persons who are looking for a job, for example students who like to work after graduating but are not legally registered as jobless. There are also people who are registered as unemployed but gave up looking for a job, these people are called discouraged workers.

Unemployment (U) + Employment (N) = labour force

Unemployment rate (u) : U/L

The unemployment rate tells you a lot about the economy. For example how rich an economy is or how easy it is to lose a job and finding a new one.

3. Inflation

Inflation: Rise in the price level

Deflation: Decrease of the price level

Calculating the inflation:

1. GDP deflator

In real GDP you're calculating with constant prices and with nominal GDP you calculate with 'real' prices. So to calculate the fluctuation in price you use the following equation:

Pt is called the GDP deflator. Pt is an index number. In the 'begin year' nominal GDP was equal to real GDP because the prices of this year where the constant prices. In the begin year Pt is 1.

2. Consumer price index

The consumers want to know how much they can consume. Another way to calculate what the fluctuation in price is, is to look at the average price of consumption.

Why is inflation important for an economy?

--> You want have the same level of purchasing power so when the prices increase, you want you're wage to rise the same amount

--> If you know what the inflation will be, you can choose whether you'll invest now or wait till a moment that prices are lower.

In macroeconomics you’re speaking of three different time frames:

Short run (few years). In the short run markets are not fully able to adjust. Changes in output are often the result of movements in demand.

Medium run (a decade). Changes in output are often the result of changes in factors such as capital stock, the level of technology and the size of labour force.

Long run (>few decades). Changes in output are the result of changes in factors as education systems, saving rate and education system.

Macro economists use a lot of models.

Models are defined as tools to simplify the complex reality. Models are always true, but they don't give an explanation.

Within models their exist two types of numbers.

1. Endogenous. A endogenous number is something you have to calculate yourself. Y is for example endogenous, it's not constant and you have to calculate it.

2. Exogenous. A exogenous number is a given number and you have to take it for granted. For example G, the governmental expenses are often given and constant.

B.The goods market

Goods market (simple) model:

-Production = Demand (Z=Y)

-closed economy

Consumption (C)

C are all the goods and services that consumers buy. Disposable income (Y-T) is the amount of money that is left after consumers paid taxes and received transfers --> C: (Y-T) + Co

Behavior equation, how much does a consumer like to consume and how much does he wants to save? -->C: Co + C1(Y-T)

Investment (I)

Purchase of capital goods. Their exist two different types of investments, one by households (residential investments) who buy houses or apartments and one by firms (non-residential) buying things for their firm. I is in this simple model an exogenous, constant number. --> I: Io

Government (G)

The sum of government spending on goods and services. T= taxes, this is what the government 'earns'. T+G = fiscal policy. In words, T&G are the instruments of the government, with T&G they have an influence in the economy. T&G are also exogenous. --> G: Go

International Trade (NZ)

Export - Import

In a closed economy, like this one, NZ equals zero.

Demand for goods --> Z

Z: C + I + G

Z: Co + C1(Y-T) + Io + Go : Y (equilibrium condition)

When you want to calculate with this equation, for example to calculate the change in Y you could simplify the equation:

Now, you can easily see what kind of effect a the change in, for example G will have on Y.

Delta Y: Delta G x 1/(1-C1).

1/(1-C1) is called the multiplier. Because C1

Savings: Supply capital

Borrows: Demand capital

Total saving (S) = Private savings + Public savings (government)

Y-C-T= All the money consumers save

T-G= All the money a government save

(Y-C-T) + (T-G) : Stotal

Since Y: C+I+G, it is logic to say that Y-C-G : I. When you subtract taxes from both side you get:

Y -T -C -G : I -T

Y - T -C : I + G -T Since Y-T-C : private saving and G-T: Public saving you can say that:

(Y -T -C) - (G - T) : I

So S: I in the equilibrium. This is called the IS relation.

C. The financial market / money market

Money --> payment for transactions

Functions money:

1. Unit of account (provides the terms in which prices are quoted)

2. Money is a medium of exchange

3. Money is a store of value

There are two types of money. You can hold money in currency and hold money in deposit accounts. When do you invest the money in bonds and when will you keep it in your wallet? This depends on two things:

1. The opportunity cost of holding money (in other words, what will you miss by not invest in bonds, because when you hold money, you won't receive interest (i))

2. Number of transactions you make (When you make a lot of transactions, you must be sure that you have enough money on hand, otherwise you'll have to sell bonds to often)

If you have a money market account you indirectly invest in bonds. The money market funds hold all the money of many people and invest it in bonds to make profit.

The demand for money (money that people want to hold in their pockets) is described in the following equation:

Md=€YL(i)

In words: When you multiply the nominal income with the interest rate you will find the money that people want to hold. This is a negative relationship because when the interest rate goes up, more people will invest in bonds and the demand for money will decrease. In the other direction: when the interest rate goes down, more people choose to not invest in bonds and the money demand will increase.

The graph of the demand function is has a downwards slope, when the interest is decreasing, more people want to hold their money. Note that: When €Y changes, there will be a shift of the curve. When €Y rises, the curve will shift to the right. (decrease of Y means a automatically rise of money) You will see a shift from 1 to 2. The interest rate stays the same. When Interest is changing, there will be a shift along the curve, from point 1 to point 3. This is caused by the increasing demand for money.

The money supplied is all the money that the central bank supplies. The central bank does not make the money in a machine every day and just make more money when the economy needs it. The way they supply money is buy selling and buying government bonds. The money supply rises when the central bank buys government bonds. They buy the bonds with money, so they offer money to the government. When the central bank sells the bonds the money supply decreases. This actions from the central bank are called open market operations. The money supply function is given by the equation:

Ms=M

Also in the financial market there exists an equilibrium --> Ms=Md --> M=€YL(i)

This equilibrium relation is called the LM relation

Fiscal policy in financial market is called monetary policy : The central bank is able to change the interest rate by changing the supply money. The central bank can so control the interest rate, but there is one problem. The interest rate can't be lower than zero. The central bank could decrease the interest rate by supplying more money (buy bonds) but when the interest rate is equal to zero, supplying more money is of no need. This problem is called the liquidity trap.

There also exists financial intermediaries. Financial intermediaries are funds that on one side receive funds from people and firms and on the other side make loans to other people and firms. A bank is an example of a financial intermediaries.

The money they get from people and firms are called deposit accounts and are their liabilities. The bank keeps some money they receive as a reserve. When a bank keeps all their money received as a reserve it is called full reserve banking. It is called fractional reserve banking when a bank keeps a fraction of the deposits as a reserve. The reserve ratio (θ) tells you which percentage the bank keeps as a reserve from the total deposits accounts. The reserve are held in cash and in deposits accounts from the central bank. The rest is invested in bonds or to make loans. The assets of a bank is the sum of the reserve, the loans and the bonds.

The total sum of demand of money is the demand for currency by people plus the demand for reserves by banks.

Demand for money:

Dd= θ(1-c)Md (Demand for deposits accounts by CB) + cMd (Demand for currency by people) Note: c is the share of money held as a currency

cMd + θ(1-c)Md = Md (c+ θ(1-c)) = (c+ θ (1-c)) €YL(i)

From the equation above you can see that the money multiplier is equal to 1: (c+ θ (1-c))

D. The IS-LM relation

Goods market meets the financial market (IS-LM model)

Goods market:

In part B we saw that investment was a exogenous number, it was a given, constant number. In reality, investments depends on two things:

1. Level of sales

How more a firm sells, how more a firm needs to invest I: I(Y)

(positive relation)

2. The interest rate

How higher the interest rate, how riskier it is to borrow money for new investment. I: I(i) (negative relation)

I = I(Y,i)

Y= Co + C1(Y-T) + I(Y,i) + Go

Because the goods market depends now also on i, we can draw the following figure:

When I increases --> I increases --> Y increases

This curve is called the IS curve. This curve is a line of all the equilibriums in the goods market.

The IS curve will shift when there is a change in the exogenous factors, G and T.

From IS 1 to IS 2: G increases or T decreases

From IS 1 to IS 3: G decreases or T increases

Financial market:

In the financial market we saw that the demand for money already depends on i.

To compare the IS curve with the financial market we have to write M= €YL(i) as M=YL(i) because the IS curve is related to the real income (Y) and not the nominal income (€Y)

To write the equation w.r.t the nominal income the equation looks like this:

M/P = YL(i) (Note: (€Y/P) = Y )

This is equation is called the LM-relation. Now we can draw this relation in the same graph as the IS curve:

When Y increases, the demand for money increases but money supply will stay the same. Because of this, i has to go up to let the Md and Ms intersect, so i will increase when Y increases.

This curve is called the LM curve and is a line of all the equilibriums in the financial market.

The curve will shift when there is a change in the money supply or a change in price level:

When money supply increases there will be a shift from LM 1 to LM 3.

When money supply decreases there will be a shift from LM 1 to LM 2.

We have seen that the IS and the LM curve fit in the same graph. When you draw these curves in the same graph they will intersect. Where these lines intersect there is an equilibrium.

Effects of fiscal policy in IS-LM equilibrium

1. Fiscal contraction (consolidation) T ↑ or G ↓.

T increases/G decreases --> C (Y-T↑) + I + G↓ --> Y↓ --> C↓ --> Y↓ --> etc.

The IS curve shifts to the left and a new equilibrium is founded. (see page 91 figure c)

2. Fiscal expansion T↓ or G↑

T↓/G↑ --> C(Y-T↓) + I + G↑ --> Y↑ --> C↑ --> Y↑ --> etc.

The IS curve shifts to the right and a new equilibrium is founded

Effects of monetary policy in the IS-LM equilibrium

1. Monetary contraction (tightening)

Money supply decreases

The LM curve shifts to the left and a new equilibrium is founded

2. Monetary expansion

Money supply increases

The LM curve shifts to the right and a new equilibrium is founded (see page 92 figure 5.9)

Policy mix: combination of fiscal and monetary policy

Why do you use a policy mix?

• When you want to increase / decrease I but Y has to stay constant

• When you want to reduce budget deficit but Y has to stay constant

Etc.

Example :

1.LM and IS intersect in ●.

2.The government increases their taxes (T)

3.This leads to a shift of the IS curve to the left

4.A new equilibrium is founded in ●●

5.Y is not allowed to decrease, so LM has to shift to the right by increasing money supply

6.A new equilibrium is founded ●●● with a lower level off interest and the same level of output, Y.

NB: The liquidity trap does still exist! Shifting the LM curve is of no use when i equals zero.

Till so far, we have only seen graphs to illustrate what will happen to the equilibriums. We can also use the equations for IS and LM to calculate the changes in i and Y.

Y= (Co + C1(Y-T)) + ( I +d1Y - d2i) + G

Y(1-C1-d1)= Co+I+G-C1T –d2i

Let’s call Co+I+G+C1T A

--> Y= (1/1-C1-d1)A – (d2/1-C1-d1)i

In the first part of these equation changes will exogenous changes, they don’t depend on Y or i. In the second part of these equation changes will be endogenous, because they depend on i.

Exogenous changes (shift of the curve) = (1/ 1-C1-1)x Delta A (see page 97 figure 5.12)

Endogenous changes (shift along the curve) = - (d2/1-C1-d1)x Delta i (see page 98 figure 5.13)

E. Openness in the economy

Openness in the goods market:

Consumers get the choice: will they buy domestic or foreign products? Important in this decision is the exchange rate. How expensive / cheap are foreign product expressed in your own currency? There are to different methods to look at this exchange rate:

1. When you use the nominal exchange rate you look at the price of domestic goods relative to foreign goods. The rate in which one countries currency trades to another counties currency

2. You can also use the real exchange rate. Then you use the rate at which one countries goods are trade for foreign goods. This is descripted in the following equation: έ= EP/P*. You divide the prices of your own goods by the prices of the foreign goods

Increase in exchange rate: Appreciation

Decrease in exchange rate: Depreciation

In an open economy NX is not equal to zero.

NX= Export(X) –Import (IM)

NX= X- (IM: έ)

Note: Because the imports are given in foreign goods, you must divide it by the exchange rate

NX depends on Y, Y* and on έ.

Y: When Y increases, imports will increase (negative relation with NX)

Y*: When the aggregate output of a foreign country increases, they will import more and your export will increase (positive relation with NX)

έ: When the exchange rate increases, import will increase because foreign product will be cheaper in proportion to the domestic prices. The export will decrease because your price are now more expensive for foreign countries.

The IS curve will remain downwards sloping. The only change in the IS curve caused by adding import and export is that the slope will be different. When Y will increase, some of the output will leak to imports. Because of this the slope of the IS curve is flatter.

Openness in financial markets:

Investors get also a choice. Will they buy domestic or foreign bonds? Important in this decision are two things:

1. Differences in interest rate. In which countries is the interest rate the highest?

2. Differences in exchange rate between these countries. A higher level of interest does not explicitly mean a higher income on bonds. You have to keep in mind that you have to ‘translate’ the income you got from holding foreign bonds in your own currency. Sometimes this means that a higher level of i in foreign countries does not refer to a higher income from your foreign bonds. There is an equation that describes this problem

(1+it) = (1=i*t)(Et:Eet+1) --> This is called the interest parity condition

This condition is not always true, there are a lot of risks and transactions costs when you invest in foreign bonds. So also if it is more attractive to invest in foreign bonds according to the interest parity condition, a lot of investors will stick to domestic bonds.

The LM curve will stay exactly the same, because money supply is exogenous

The interest parity condition implies that exchange rate and interest depends on each other. E= (1+i)(1+i*)Ee

This means when the ‘new’ IS and LM curve intersect there is an equilibrium founded which gives use a number for I, we can see which number belongs to the exchange rate. The slope of the interest parity condition is upwards sloping. From the equation above we can see that i and E have a positive relation. (see page 131 figure 6.11)

From this picture you can see that fiscal or monetary policy can change the exchange rate. This is easily explained in words, when for example, the government increase their spending G↑ and the IS curve shifts to the right, interest will increases. When interest increases, your domestic bonds are more attractive to foreign investors. This will lead to an appreciation of the currency.

F. Labour market

Determination of wages

1.Unemployment

Whole population: The whole population exist of al the people in the working age and the population out of working age (65). The working population consists of the labour force and the people out of the labour force. The labour force consists of the sum of employment and unemployment

--> Some economists say that the unemployment rate is no good indication of the employment/unemployment ratio, because of the discouraged workers. These people are unemployed but are not actively looking for a job, but when they find one they will take it. In this case, the economists say, it’s better to look at the non-employment rate: employed population in working age/ unemployed population in working age.

2. Wages

How are wages determined?

• Collective bargaining

Firms and unions negotiation

There are common forces at work in all countries, although they differ from country to country. Two facts prove the fact that there exists collective bargaining.

1. Wages exceed the reservation wage (wage that makes people indifferent between working or being unemployed)

Why do firms pay more than the reservation wage? Because of the efficiency wage theories. Firms believe that an employer works more productively, more efficient and the turnover rate would be lower (less workers will quit their job)

But how much the wage exceeds the reservation wage depends on two things:

-->Nature of the job

High-tech firms pay higher wages than firms where workers’ activities are more a routine.

-->Labour market conditions

Low unemployment --> high turnover (easy to find a new job)

To prevent a high turnover wages will be higher

2. Wages depends on labour market conditions

Level of bargaining power depends on:

• Costs of replacing worker (nature of the job)

• How hard is it to find a new job

How high the unemployment is, is a very important factor for the level of bargaining power.

When the unemployment is high --> Easy to find new employers for the firm + hard to find a new job for the employers --> less bargaining power.

When the unemployment is low --> Hard to find new employers for the firm + easy to find a new job for the employers --> more bargaining power.

Wages

Wages equation:

W= PeF(u,z)

Pe= expected price level

u= Unemployment rate

z= All other variables

1.Pe

Nominal wages = real wages x price

W = real wages x P

Your nominal wages tells you how much money you’ll get. In fact, this is not the most important thing to know. Firms and employers are more interested in how much they can buy with their wage. This is the reason that you look at real wage instead of nominal wage.

What happens when P changes?

P↑ --> You can buy less with the same nominal income --> real wage decreases --> Employers want a higher nominal income

They want the real wages to stay constant.

The expected price level is used because, to determine the nominal wages for the next few years. (These wages are always determined for a few years in the future) they look at the price fluctuation they expect in the following years. This is a positive relation, how higher they expect P to be, how higher they’ll set W.

2.u

When the unemployment rate is low --> easy to find new job (as we have seen before) --> higher bargaining power --> higher wages.

The relation between unemployment and wages is as you can see, negative.

All other variables

Of course the unemployment rate and the expected price level are not the only factors that determine the wage. These are some examples of other factors:

-Unemployment insurance

When there is some insurance to workers who loose their job it’s less stressful to become workless. As a cause of the insurance, the turnover rate will be higher which leads to higher wages. (Positive effect)

-Employment protection

When there’s a high State protection for workers, it becomes more expensive to fire workers. Because of the higher bargaining power, wages will be higher. (Positive effect)

-Minimum wage

By setting a minimum wage, wages can’t be too low.

Prices

How high/low the firm the price will set depends on the costs of production.

The production function:

Total output=Labour productivity x workers

Y=A x N

Labour productivity is for now a constant number, when we say A=1, the equation looks like this:

Y= 1x N

Y=N

When production increases with 1, the cost will increase with 1x the cost of employment, which is wages. 1x W= W

So the marginal costs is W

The equation of the price looks like this:

P= (1+μ) W

μ = mark-up

In a perfectly competitive market the mark-up is equal to zero because MC=MP. (W=P) When there is less competition, the mark-up is > 0.

The product market regulation determines how competitive a product is. When there are for example a lot of trade barriers there is less competition.

So μ= f(PMR)

PMR = product market regulation

This is a positive relation: When PMR is high --> Low competition --> higher mark-up.

To determine the unemployment we have to plot the wage setting relation and the price setting relation in the same graph.

As we noted before, the wage-setting relation:

W = PF(u,z)

But since we are more interested in the real wage than in nominal wage we rewrite the equation like this:

W/P =F(u,z) --> Negative relation, so downwards sloping line

The price-setting relation:

P=(1+μ)W

To plot the price-setting relation in the same graph as the wage setting relation we have to adjust this equation.

W/P = 1/ (1+μ)

--> μ is exogenous in this graph so a constant number. This causes that the price-setting relation is a vertical line.

When the W/P determined by price-setting and the W/P determined by wage-setting equal you’ll find the natural rate of unemployment.

Shifting of the Wage-setting (WS):

Employment protection increases --> z increases --> W/P increases for same u --> W/P shifts to the right --> natural rate of unemployment goes up

(for graphical explanation see page 153, figure 7.13)

Shifting of the Price-setting (PS):

When pmr decreases --> more competition --> Mark-up goes up --> W/P decreases --> PS shifts down --> Natural rate of unemployment becomes higher.

Unemployment rate: Unemployment / Labour force= U/L=(L-N)/L=1- (N/L)

So u= 1- (N/L)

To rewrite this formula in terms of employment you get N/L= 1-u --> N= L(1-u)

So from this equation you can calculate the natural level of employment (N) from the natural level of unemployment (u)

From the natural level of employment we can derive the equation for the natural level of output since we know that Y=N.

So u= 1- (Y/L)

And F(1-(Y/L),z) = 1/ (1+μ)

Now, we have derived the output, Y in the medium run through presuming that the unemployment rate is equal to the natural rate of unemployment and that Pe=P

G. Aggregate Supply and demand

Equilibriums in the AD-AS

Short run:

Pe is given.

In the short run it’s possible that in the equilibrium of AD-AS let’s say point B, P is not equal to Pe and so Y is not equal to Yn, because Pe is given. (See page 167 fig. 8.5)

Medium run:

In the medium run the output wants to be equal to the natural level of output. This is explained by the following example.

In a certain economy, Y>Yn.

As you can see in for example in figure 8.6 on page 168:

When Y exceeds Yn, P>Pe. Since wage-setters base their wage upon the expected price, they’ll see that they set the wages too low. As a cause of this, wage-setters expect the next period P to be higher. (Pe’>Pe)

In the equation of P, you can see that when Pe goes up, P will go up.

--> P= (1+ μ)PeF(1-(Y/L),z)

--> AS curve shifts upwards

This will happen as long as Y doesn’t equal Yn, because when Y is bigger than Yn, P is higher than Pe and the previous steps will repeat. (See figure 8.6 on page 168)

So the big difference between the short run and the medium run is that eventually, in the medium run, Y=Yn and in the short run Y doesn’t have to equal Yn.

Dynamic effects in the AD-AS model

1.Monetary expansion (AD)

M increases --> AD: Y= Y((M/P),G,T) increases.

Short run:

AD shifts to the right (up)

Y’ becomes bigger than Yn

P becomes bigger than Pe

Medium run

AD shifts to the right

But because in the medium run Y has to equal Yn, AS has to shift up (to the left) (For graphical explaination see page 170 figure 8.7)

2. Decrease budget deficit (AD)

G decreases --> AD: Y= Y((M/P),G,T) decreases

Short run:

AD shifts to the left (down)

Y’ becomes smaller than Yn

P’ becomes lower than Pe

Medium run:

When the AD shifts to the left, AS has to shift right because Y has to equal Yn (See figure 8.9 page 172)

What happens in the meanwhile with our old friend the IS-LM curve in the medium run?

Point 1:

M increases --> LM shifts right --> Because AD shifts right P increases --> M/P decreases --> LM shifts a little bit back --> Because AS shifts to the left, P increases more --> LM shift to his old place. (See figure 8.8b page 171)

This effect is called the neutrality of money

Point 2:

G decreases --> IS shifts to the right --> Because AD shifts to the left, P decreases --> M/P increases --> LM shifts to the right --> Because AS will respond and shift to the left P decreases further --> LM decreases --> Output is back at Yn

(See figure 8.11b page 174)

What happens in the meanwhile with the investments?

Medium run:

Because Y=Yn

IS: Y= C(Yn-T) + G + I(Yni)

Yn-T is unchanged and G decreases. i deceases so I increases.

Short run:

Y decreases so I decrease.

3. Price of oil (AS)

When the price of oil goes up, the cost of production will go up. This will cause a increase in P since P is determined by the costs of production. When P increases --> W/P decreases

W/P =1/(1+μ)

So when the left side of the equation decreases, the right side has to decrease too. Because the mark-up is the only variable, the mark-up has to increase to let this right side decrease too. When 1/ (1+ μ) decreases, the PS curve will shift down. The equilibrium of WS and PS is now at a higher level of u.

When u increases, N decreases. Since Y=N Y will shift down (AS will shift left) Yn>Y’

Because AS had shifted, there’s a new point where Yn=Y and Pe=P. And remember, in the Medium run, the AS will shift until Yn=Y again.

H. Growth in the economy

We care about growth because we care about the standard of living. The standard of living is an important indicator.

How can we measure the size of the standard of living per country?

Just translating one’s currency in the currency of the other country via exchange rates is not the best thing to do because:

1.Exchange rate fluctuates a lot

2.The price of living varies a lot from country to country

The solution is to use the Purchasing Parity Power (PPP). Here you use the real GDP, so you look at how much somebody can buy, instead of how much money someone has. Some remarks pop-up:

1.We are more interested in how much we can consume rather than how much the output (GDP) would be. But since consumption and output move in the same direction this problem is not disturbing.

2.Productivity is more important than the total output. When you calculate output per worker you get a clearer and more precise view of an economy. (Soon we will adjust this remark and start calculating with the output per worker)

3.We probably care about the standard of living because we care about happiness. But is there a relation between happiness and standard of living? Research proved that there is a positive relation between this factors bút until a certain level.

Since 1950 there are two main conclusions with regarding to growth:

1.Increase in output per person

2.The difference between output per worker between countries decreased.

Long ago there wasn’t any growth in the economy. This was caused by the Malthusian trap. Any rise of the productivity would lead to an increase in the population that leads to a decrease in the productivity per person.

Aggregate production function: Y = F(K,N)

Two sorts of input determine production. The first one is K, capital. This is the sum of all the machines, plants and office buildings. The second one is N, labour. The amount of people that is working.

The state of technology determines how much input leads to how much output.

Returns to scale:

What happens with output if you double the input?

-->Constant return to scale

(2K,2L) --> 2Y

Output will double

--> Decreasing return to scale

<

p>(2K,2L) --> <2Y

Output will be less than double

--> Increasing returns to scale

(2K,2L) --> >2Y

Output will be more than double

When one input stays the same but the other one, let’s say labour increases you’ll get a decreasing return to labour. To explain this you can look at an example. When the amount of secretaries grows but the amount of computer stays the same, the growth of output will finally be smaller than the increase of labour (secretaries). This is also vice versa with increasing capital but the same amount of labour. This is called the decreasing returns to production factors.

Output per worker: Y/N

Y/N= F(K/N, N/N) = F(K/N,1)

K/N is capital per worker, we will use this a lot in the next parts.

The relation between output per worker (Y/N) and capital per worker (K/N) is positive. But because of decrease returns to capital, the growth of Y/N, when K/N increases will become smaller and smaller.

Now we can say that the growth of production is coming from two things:

1.Capital accumulation (K/N increases)

2.Technological progress.

I. Capital and output

Capital and output affect each other in different ways.

1.The amount of capital affect the amount of output directly

2.The amount of output determines the amount of capital indirectly

You can see that the amount of capital affects output directly in the function of output per worker Y/N= f(K/N)

--> To make it more simple we say that f(K/N) = F((K/N),1)

When K changes, Y will automatically change. This is a positive relation, when K increases, Output will increase.

We make two assumptions:

-Employment (N) is a constant (exogenous) number. As a result of this, the labour force and unemployment are also constant because. L=N+U

-To focus on the role of capital we assume that there’s no technological progress

How does output indirectly affect capital?

--> Output affect investment/savings

In a closed economy we saw that I=S. When we assume that private savings is a percentage of income we get the equation: S=sY

Since I=S I=sY --> Positive relation, higher output implies higher investment and so higher savings.

--> Investment affects capital accumulation

How much does capital increase/decrease per year?

Let’s say that every year, capital depreciates with the amount delta (in my summary delta is a replacement for the lowercase Greek letter delta.)

Sow every year, the capital decreases with delta. The capital increases with the amount of investment made in that year. The equation look like this:

Kt+1= (1-delta)Kt + It

But because economist want to calculate in capital per worker we divide both sides by N.

Kt+1/N=((1-delta)( Kt/N)) +( It/N)

Actually, we are most interested in how much the change in capital (Kt+1 – Kt) is.

We can rewrite the equation so that we can see how much this change is.

(Kt+1)/N – ((Kt/N) = (s(.Yt/N)) –(delta.(Kt/N)

Now we know how that the change in capital in one year is equal to the right side of the equation above. In words: The change in capital is equal to the saving/investment per working minus the depreciation.

Since Y/N= f(K/N), we will write this equation as:

(Kt+1)/N – ((Kt/N) = (sf(Kt/N)) –(delta.(Kt/N)

When depreciation exceeds investment per worker there is a negative growth in capital. When investment exceeds depreciation per worker there’s a positive growth in capital.

To understand the dynamics of capital per worker w.r.t. output per worker we will plot a graph. I’ll take the example on page 250, figure 12.2. As you can see there are 3 lines plotted. The first one is output per worker (f(Kt.N)). This line grows, but the growth becomes smaller when capital per worker increases, this is caused by the decreasing returns to capital. Then the second line, investment per worker (sf(Kt/N)), this line is just the same as output per worker but then times the saving rate. Because the saving rate can’t be bigger than one, this line lies below the first line. The third and last line is the depreciation per worker (delta.(Kt/N)), since this the depreciation is constant per year, this is a straight line.

How do you come to a steady state?

A steady state is a state where there is no growth in capital per worker. In other words, the saving/investments per worker equal the depreciation per worker. In the long run, an economy will reach this point. Let me explain why with an example.

Assume that in a country the investment per worker exceeds the depreciation per worker. This will cause an increase in capital per worker, which will lead to an increase in output per worker. When the output per worker increases, the point on the line of output per worker shifts to the right. When investment still exceeds depreciation and capital, so output per worker increases, the point on this line will shift further to the right, until the moment that investment equals output. At this point you’re in the steady state.

How does the saving rate influence the growth in output?

Well, as we have seen, in the long run, the economy will be in the steady state where the growth rate is zero. This implies that the saving rate wouldn’t have any effect on the growth.

But, when a country has a higher savings rate, the second line will shift as s changes. The depreciation per worker and the investment/savings per worker will thus be equal at another amount of capital per worker. There will be for some time an increase in growth until they reached this level.

Do we really appreciate a higher savings rate? Since we really care about how much we can consume instead of how much we produce or save, the consumption per worker is also interesting. When the savings rate changes, there will happen two things:

Short/Medium run: Because the output is the sum of consumption and saving (and taxes) an increase in the savings will lead to a decrease in consumption.

Long run: In the long run a higher savings rate will mean a higher amount of capital per worker in steady state. When output per worker will increase, consumption will also increase.

So what savings rate is the best so that consumption is the highest? This is called the golden-rule of capital. In figure 12.7 (page 255) you can see that the best saving rate is between 0 and 1. (Which is rather obvious)

You can rewrite the production function in various ways. We have seen it before as Y=K, N. But mister Cobb-Douglas liked it more in this way: Y=√K, √N. We will just adapt this. When you divide both sides by N, as usual the equation looks like this:

Y/N=√(K/N).

So now we replace f(Kt/N) by the square root of K/N.

(Kt+1)/N – ((Kt/N) = (s(√ (Kt/N))) –(delta.(Kt/N)

With this numbers we can calculate what kind of impact a change in the savings rate has on the output per worker in steady state. You have to take 3 steps.

1.Take the square of both sides

2.Divide both sides by K/N

3.Rewrite the equation like K*/N=… (See page 258)

4.Calculate also Y*/N, which is the square root of K*/N

Now you can see what happen to K*/N when s changes. When you calculated this numbers, we can calculate the consumption per worker which is equal to output pw- depreciation pw.

C/N=Y/N – K/N

When you fill in the numbers you calculated for Y/N and K/N you’ll get: (s(1-s))/delta

There is another type of capital we have not introduced yet. This type of capital is called human capital. Economists take this kind of capital also in account because highly skilled workers are much more likely to be more productive.

J. Technological progress

First, we assumed that the production function could only be affected by capital (K) and labour (N). The production function looked like this: Y=F(K,N)

But as you read before, technological progress could lead to an increase in the production. So we will add technological progress to our production function. We name it A (productivity), because you could see the state of technology as how much can be produced by the given amount of labour and capital.

Our new Y will look like this:

Y=F(K,AN)

We multiply A by N so that it’s easy to calculate the relation between K,A and N. When you multiply N by A, you are not longer speaking of labour. Because you multiply the labour by the productivity you are speaking of effective labour.

All our equation will change a bit. Instead of dividing Y and K by N, you’ll now divide it by AN. We will not longer speak of output per worker or capital per worker, but we we’ll speak of output per effective worker and capital by effective worker.

There will also be a change in the steady state. As you remember, in steady state, capital per effective worker is constant. This implies that Investment per effective worker and depreciation per effective worker need to be equal. How high does the amount of investment/savings need to be to equal the change in capital? First we assumed that the change in capital was just the depreciation times the amount of capital. But the amount of labour (N) and technology (A) are also likely to change of time.

Capital per effective worker= Kt/AtNt

When the population increases:Nt increases, Nt x At increases so the level of capital per effective worker decreases.

When technology increases:At increases, At x Nt increases so the level of capital per effective worker decreases.

The change in A per worker is called Ga, and the growth rate of N is called Gn.

So put it in other words: in steady state, the growth rate is equal to the Gn+Ga. This is a balanced growth.

The change in capital per worker is not only the depreciation times the capital per worker, but now also the growth rates of N and A times capital per worker. So, saving per effective worker needs to be equal to the change in capital per effective worker:

Sf(K/ AN) = (delta + Ga + Gn) x (K/AN)

How does the saving rate affect the growth in steady state? Because the growth rate is equal to Ga+Gn, there’s a constant growth and the saving rate is not able to affect this growth. But as we have seen in the previous part, the equilibrium of change in capital (deltaxGaxGn) and the investments is at a higher level of output per effective worker, there’ll be for some time a bigger growth until it reached again the slope of Ga+Gn. Figure 13.4 on page 275 explains this

We talk all the time about technological progress, but what is this and how could there be a progress in it? The most technological progress in modern economies would be the result of the research and development (R&D) activities. The amount of R&D depends on the appropriability of research, how much do firms really benefit from their results of R&D. The appropriability of research depends also on different factors:

Nature of the research product.

Legal protection. When there won’t exist any patents, firms won’t be eager to discover new things. The will just wait till some other firm discovered it, see if it works on the market and copy it.