Macroeconomics Exercise 2 · Besien. C 0 = 400 tSEK per year: t = 25 percent. t = 50 percent: MPC = 0,8. T = 625 tSEK per year: T = 1250 tSEK per year. I = 100 tSEK per year: G =

Macroeconomics Exercise 3

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7. The business cycle 2: A very simple Keynesian model

7.4. Assume that the following applies to the closed economies, Asien and Besien.

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Both Asien BesienC0 = 400 tSEK per year t = 25 percent t = 50 percentMPC = 0,8 T = 625 tSEK per year T = 1250 tSEK per yearI = 100 tSEK per yearG = 0 tSEK per year

Here C0 is autonomous consumption, MPC is the marginal propensity to consume, I is the real investment in equilibrium, G is public consumption, t is the rate of income tax, and T are transfers from central government to households.


(a) When GDP = GDP equilibrium (and inventory investments are zero), we know that Y is equal to MPC [(1−t)Y +T]+C0 +G+I. Show this with the help of a picture of the circular flow.

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(b) Calculate equilibrium GDP for each country.

𝑌𝑌 = 𝑀𝑀𝑀𝑀𝑀𝑀 1 − 𝑡𝑡 𝑌𝑌 + 𝑇𝑇 + 𝑀𝑀0 + 𝐺𝐺 + 𝐼𝐼

𝑌𝑌 = 𝑀𝑀𝑀𝑀𝑀𝑀∗𝑇𝑇+𝑀𝑀0+𝐺𝐺+𝐼𝐼1−𝑀𝑀𝑀𝑀𝑀𝑀(1−𝑡𝑡)

𝑌𝑌𝐴𝐴 = 0.8∗625+400+0+1001−0.8∗(1−0.25)

= 2500 tSEK/year

𝑌𝑌𝐵𝐵 = 0.8∗1250+400+0+1001−0.8∗(1−0.5)

= 2500 tSEK/year

(c) Calculate the multiplier for each country.

The multiplier is 11−𝑀𝑀𝑀𝑀𝑀𝑀(1−𝑡𝑡)

2.5 in Asien and 1.67 in Besien.

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Assume that both countries initially have a GDP level that is equal to GDP equilibrium and then they are affected by a disturbance in aggregate demand such that C0 decreases temporarily (for one year) by 50 thousand SEK.(d) What will be the total decline in GDP as a result of the disruption, in each country?• To calculate the total decline, take the multiplier and multiply it by the size of the shock. • The result is 2.5*50 = 125 tSEK in Asien and 1.67*50 = 83.5 tSEK in Besien.(e) Explain the meaning of automatic stabilizers. Does a large public sector lead to larger or smaller economic fluctuations?• When the government spending is a significant proportion of aggregate demand, and if that

spending is constant over the business cycle, then it will tend to speed up recovery from shocks and therefore stabilize the economy, without the need for active decisions. For instance, assume a negative shock. If G is large and constant then when firms reduce production in response to the shock, AD goes down by less than the production drop, which hastens recovery. If G is countercyclical (This means that when the business cycle turns down, G goes up) then the effect is even stronger. Some elements of G — such as welfare payments and unemployment benefit are countercyclical!

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7.5. (a) Explain why investment I normally falls more (in percentage terms) than consumption C during a downturn in economic activity.• When firms plan to cut production, they need fewer workers and fewer

machines. If a firm cuts production by 10 percent from one year to the next then it is reasonable to suppose that it needs 10 percent fewer of each. This implies a 10 percent reduction in the workforce. But what about investment? If the depreciation rate is 10 percent per year, then investment in that firm should decrease to zero!

(b) Compare to what happens in an economy without money when households become worried about the future and reduce their consumption.• In an economy without money, when households become worried about

the future and reduce their consumption they put their efforts into investment instead: investment rises!

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7.6.* Assume an economy with 100 workers. Each worker needs one machine in order to be productive. The workers are employed by competitive firms, each of which owns 10 machines and employs 10 workers. Eight of the firms produce consumption goods, and 2 produce new machines. These two firms, with 10 employees each, produce 5 machines each per year (10 machines per year altogether). At the end of each year, 10 percent of machines break down irreparably (depreciation). In a normal year that means that 10 machines depreciate, and therefore 10 new machines must be bought at the start of the following year, and the economy is in long-run equilibrium.Now assume that year 1 was a normal year, but in year 2 consumers reduce their purchases of consumption goods by 2 percent. This means that producers of consumption goods decide to reduce their production in year 3 by 2 percent, and they lay off 2 percent of their workers.(a) How many machines (made in year 0) do the producers of consumption goods buy at the start of year 1? And how many do the producers of machines keep back from their own production?• Producers of consumption goods had 80 machines in year 0 of which 10% breaks down irreparably so they

buy 8 machines at the start of year 1. • The producers of machines had 20 machines in year 0 of which 10% breaks down irreparably so they keep

back 2 machines at the start of year 1.

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(b) How many machines (made in year 1) do the producers of consumption goods buy at the start of year 2? And how many do the producers of machines keep back from their own production?• Nothing changes, yet. In year 2 producers of consumption goods buy 8 machines. • The producers of machines keep back 2. (c) How many machines (made in year 2) do the producers of consumption goods buy at the start of year 3? And how many do the machine producers have left altogether, to use in year 3?• In year 3 producers of consumption goods want to reduce machines by 2%. Therefore

they buy 6.4 machines. • The machine producers had 20 machines in year 2 of which 10% depreciates. Including

the unsold 3.6 machines, they have left 21.6 machines at the beginning of year 3.

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(d) How many machines do the producers of machines make in year 3, assuming that they expect demand for machines in future years to be equal to demand in year 3, and that they want to have sufficient capacity to meet that demand? Of those they make, how many do they keep?• They make 6.4 machines and to make this they use 12.8 machines of which 10%

percent depreciates. So at the end of year 3 they will have (21.6-1.28 = ) 20.32 machines. They keep back nothing.

(e) By what percentage does investment fall in year 3? • Investment decreased from 10 to 6.4 which is a 36% fall.

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7.7. Assume an economy with households, firms, a financial sector, a central bank, and a government. The government taxes income and uses the money to pay for services such as health care and education. The role of the central bank is to determine the interest rate in the economy.Households become worried about the future and cut their consumption.(a) Explain how this can lead to an economic downturn.• If investment remains the same, firms do not sell all their goods. Firms

therefore cut production, and cut investment. This causes household income to fall, which causes households to further reduce their consumption if their worries remain; even if their worries are over their consumption will be below normal, because of their low income. The effect therefore lives on in the economy.

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(b) Discuss what the government and central bank can do to speed up recovery from the downturn.• The government can use fiscal policy to boost the economy, the

central bank can use monetary policy. Expansionary fiscal policy may include lowering taxes, or raising government spending. The result in the short run for the government is that its deficit increases. Expansionary monetary policy, in modern economies, means lowering the interest rate.

• This makes investment more attractive while also lowering the opportunity cost of consumption for consumers, thus encouraging them to consume.

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(c) In real economies, monetary policy is used much more actively than fiscal policy to manage the business cycle. Why?• Monetary policy is used much more actively than fiscal policy for two

major reasons. The first is that (in most cases) it addresses the underlying problem directly, which is that the drop in consumption does not feed through into a rise in investment. The second is that monetary policy is much easier and quicker to adjust in the short run; governments don’t open schools or hospitals to help the economy out of a downturn, because the lags on such decisions are so long that the effects would most likely be felt far too late, perhaps boosting the next upturn instead. Note however that in a very major downturn—an economic crisis or depression—then fiscal policy may be a powerful instrument.

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7.8. Assume an economy with four individuals of different ages. Each individual works for 30 years and is then a pensioner for 30 years. At birth, agents borrow money, buy a house and start work. At retirement, agents have paid off their loan and accumulated some financial assets. They sell the house and move to a flat, subsequently living off their savings. GDP per capita is 625 SEK per year.The current situation is as follows. The ages of the four individuals are 0, 15, 30, and 45 respectively. The new-born worker has just bought a house for 1000 SEK, and has a debt of 1000 SEK with the bank. The 15-year-old has an identical house, and a remaining debt of 250 SEK. The 30-year-old has just bought a flat for 500 SEK, and has financial assets worth 1000 SEK. And the 45-year-old has an identical flat and savings of 250 SEK.(a) What is the total level of household debt in the economy, as a proportion of total GDP?𝑌𝑌 = 625 ∗ 4 = 2500 𝑆𝑆𝑆𝑆𝑆𝑆 𝑝𝑝𝑝𝑝𝑝𝑝 𝑦𝑦𝑝𝑝𝑦𝑦𝑝𝑝𝐷𝐷𝑝𝑝𝐷𝐷𝑡𝑡 = 1000 + 250Debt as percentage of GDP 1250

2500= 50%

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(b) Assume that the interest rate declines. What is the effect on consumption C in this economy? Explain.• When interest rate decreases the individuals with negative balance

get richer and want to consume more, and the individuals with positive balance get poorer and want to consume less. The net effect on wealth and consumption cancels out. However, the opportunity cost of consumption (which is saving) decreases and therefore consumption will increases.

(c) Assume that households become more optimistic about future incomes. What is the effect on C? Explain.• Consumption increases.

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8. The business cycle 3: A model of the medium term with inflation

8.1. Assume an economy with a single product, widgets, produced using labor alone. There are 100 working-age adults in the economy, each of whom can produce one widget per day, and everyone works in widget production. (All adults are in the labor force, and there is no unemployment.) There are also 50 retirees in the economy, and workers save a proportion of their wages to build up savings, while retirees live off their savings. The economy starts in a long-run equilibrium with zero net savings, zero investment, and zero inflation.Now assume that the short-run supply curve is similar to that illustrated in Figure 3, and that the citizens of the economy become more optimistic about the future and decide to save less and consume more. Describe what happens over time according to the AD–AS model assuming that wages are sticky, that is that they change slowly in response to changed circumstances.

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Figure 3: AD–AS model with booms: (a) the economy is in equilibrium; (b) recession. The black dots show the price level and GDP, where AD and SAS meet.


• The AD curves shifts up, whereas SAS stays put. This means that wages stay the same but prices rise, and Y rises. This implies that returns to capital increase whereas average returns to labor decrease; firms make profits, and competition for labor increases. This competition for labor drives up wages, pushing the SAS curve up while reducing returns to capital. In the long run we have a new stable equilibrium with higher prices, while Y is at its long-run level (as is unemployment).

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Y

P

AD2

AD1

SAS1

SAS2

LAS


8.2. Assume an economy in equilibrium which is suddenly hit by a negative demand shock, such that the demand curve shifts to the left. Use AD–AS model to answer the following questions.(a) Show the short-term impact on GDP (and hence unemployment) and inflation.• Shift the SAS curve such that Y goes down whereas prices are unchanged.(b) Show the effect in the medium term if the state does nothing and the high unemployment leads to a downward pressure on wages.• If wages fall then the SAS curve shifts down and we have a new long-run equilibrium with lower prices and wages, but trend Y (and

unemployment).(c) Show the effect in the medium term if the state tries to neutralize the shock with expansionary policy.• Now the SAS curve moves back and (in the best case) we have a new long-run equilibrium with prices at the same level as before.

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8.3. (a) An economy, A, has long had stable inflation at 2 percent per year. Suddenly the government implements a more expansionary policy that leads to a sharp increase in AD. Explain the effect on inflation, GDP and unemployment in the short and medium term.

• The expansionary policy is not expected by the market, and the consequence is that it has large real effects; i.e. that there will be a relatively long period of high GDP and low unemployment before the market adjustments and the inflation rate rises instead, while unemployment returns to its structural level and GDP returns to potential GDP.

(b) Another economy, B, has long had high and volatile inflation, which is, however, currently at 2 percent per year. Suddenly the government implements a more expansionary policy that leads to a sharp increase in AD. Explain the effect on inflation, GDP and unemployment in the short and medium term, compared to in economy A.

• Now the real effects are smaller and more short-lived, because the market is largely prepared for such fluctuations. Preparedness means for instance that wage agreements expire in a relatively short time.

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8.4. Assume a country where technological development means that labour productivity rises. Illustrate what happens with LAS curve with time. Explain briefly!• The LAS curve moves outwards (to the right) over time when productivity

increases. Equilibrium (structural) GDP increases when technology improves.

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Y

P

AD2AD1

SAS1 SAS2

LAS1 LAS2


8.5. Assume an economy with zero growth (there is no technological progress) in which prices and wages both grow at 2 percent per year, while unemployment is stable at 5 percent. The government is not happy; it wants higher GDP and lower unemployment. To achieve this it decides to reduce interest rates and raise spending. Furthermore, it is determined to achieve its goals.

Describe, step-by-step, what is likely to happen. Use economic reasoning (such as a model economy), and cite evidence from real economies.

• We can represent such an economy with the help of a graph showing aggregate demand and aggregate supply, as in the left-hand graph. The short-run supply curve slopes upwards beyond a certain point, as marginal costs of production increase. When aggregate demand increases as in the second graph, GDP increases and unemployment falls. Furthermore, firms make excess profits and competition for labour pushes up wages, which pushes up the short-run supply curve. The result is higher prices, while GDP and unemployment fall back to their long-run levels and profits return to normal (third graph).

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• If the government is determined to achieve its goals, it will respond with further measures to raise AD. If it catches the market by surprise again, then there will again be a period of high GDP and low unemployment. However, if the market is expecting these further measures then the wage increases that they ultimately cause will already be planned, i.e. they will occur immediately. Then the result of the measures will be still higher inflation, while unemployment remains at 5 percent and GDP remains at its long-run level.

• If the government tries again, pushing up AD even faster, again there may be a temporary effect if the market is caught by surprise. However, it should be clear that the market will soon learn what the government is up to, and it will therefore plan wage increases in advance such that GDP and unemployment are at their long-run levels. Meanwhile, inflation accelerates and the economy heads towards hyperinflation and total breakdown.

• There are many examples of the long-run link between fiscal and monetary policy and inflation. One simple example is the hyperinflation in Zimbabwe in the 1990s, where the government paid its bills (in particular the army) by printing its own money. At first the result might be happy soldiers, but soon the flood of money—and resulting increasing aggregate demand—drove up prices and wages. The government responded by printing even more money to pay its bills, and so on . . .

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8.6. Assume an economy in which the government controls both monetary policy (the interest rate) and fiscal policy (the government budget). The government claims that it hates inflation, but market agents are not convinced; they think that the government hates unemployment, and isn’t too bothered about inflation as long as it is no higher than 10 percent. The inflation rate is currently 10 percent, and the interest rate is 13 percent.

(a) What is likely to happen if the government announces that from now on inflation will be 2 percent, and consequently that it plans to reduce interest rates to 5 percent so that the real interest rate remains at 3 percent? Explain carefully.

• We are told that the market does not believe the government. Let us assume that the market is right. Then the government won’t actually do anything about inflation, which will remain at around 10 percent, while the interest rate remains at 13 percent. Since this is expected by the market, wages will rise in line with inflation, and GDP and unemployment will be as normal.

• Let us now assume that the market is wrong, and the government acts. Since it wants to push inflation down, it must drive AD down in order to create downward pressure on wages and prices. (More accurately, it must slow the rate of increase in AD, which is currently at 10 percent per year.) It does so by raising interest rates and tightening fiscal policy. This catches the market by surprise, and therefore leads to a recession with low GDP and high unemployment. No wonder the government preferred the first option!

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(b) What is likely to happen if the government announces that it has created an independent central bank whose sole aim, set down in law, is to keep the rate of inflation as close as possible to 2 percent? Explain the difference.• If the government announces the creation of an independent central bank this immediately

changes the expectations of the market, towards lower inflation. Wage increases are likely to be moderated, in the best case without the need for raising interest rates! As wage and price increases slow down, the interest rate can be reduced, and within a few years inflation is close to 2 percent, while the interest rate is 5 percent (giving a real interest rate of 3 percent, as previously).

• The key difference is that the creation of an independent central bank fundamentally changes market expectations, and when low inflation is expected then it tends to arise of its own accord, without the need for drastic measures triggering an economic slowdown.

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8.7. The central bank controls the short-run interest rate. This question is about how the long-run interest rate is determined.

The date is May 29. Assume you hold, among other assets, 10 000 bonds giving 50 EUR in payment at the end of each year, in perpetuity (a bond or other security with no fixed maturity date). You are happy with your investments at the moment. However, you are suddenly convinced that the central bank is going to lower the short-run interest rate on June 1, and moreover that it will signal a lower interest rate path in the future than the one previously announced. These events are not expected by the financial markets.

(a) What do you do with your bonds, or any of your other assets, when you get your new beliefs? Explain!

• If you are right and the central bank unexpectedly lowers the base rate and signals lower rates for the future, then the long-run interest rate will fall on June 1, implying that the value of your bonds (which give a fixed return) will rise. This rise in value will give you a one-off profit. You therefore retain your bonds. Furthermore, if you have other assets (such as foreign assets) whose value is note affected by the base-rate change in the same way then you sell these assets and buy more domestic bonds.

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(b) Assume instead that you are not alone in your insight: the entire market has the same insight as you, on 29 May. What happens?If everyone else has the same insight at the same time as you, then the result will be that the bond price will rise immediately (before you or anyone else actually buys any extra bonds). You therefore have no opportunity to profit from your insight.

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8.8. Assume that you own a hundredth of a business, and the market believes that the company – if it is well run — will deliver benefits totaling 100 000 SEK annually in perpetuity to their owners. You are thinking of selling your share when you retire and living on it.(a) What is the value of your share of the company if the interest rate is fixed at 5 percent per year in perpetuity?

If the interest rate is 5 percent, and your share of the annual benefits if 1000 SEK, then the value of your share V is such that

0.05V = 1000,i.e. if you sell your share and put the money in the bank, your annual income should be unaffected. Hence

V = 20 000 SEK.

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(b) What is the value if interest rates rise to 10 percent?0.1V = 1000V = 10 000 SEK.

(c) What is the impact of such a rate increase on your prioritization between consumption and saving? Explain!• When the interest rate rises, the value of your assets falls. This means that your

wealth has decreased; hence you consume less and save more. Put differently, the opportunity cost of consumption is higher; hence you consume less and save more.

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8.9. – We cannot promise spending when there is no money, said Finance Minister Anders.

Prime Minister Fredrik however is confused. Should the government not run a deficit during a recession? Help him sort this out! Is Anders right? Is Fredrik right? What should Fredrik do?

• The basic rule for any government is that it should balance its budget over the economic cycle. That means running a deficit during recessions (due to automatic stabilizers and possibly deliberately expansive fiscal policy), and running a surplus during good times. In Sweden there is even a goal to run a long-run surplus, överskottsmålet (surplus target): the government should run a surplus of 1 per cent per year averaged over the economic cycle. Thus, both are right: the government run a deficit during a recession, but within limits!

• During times of crisis, the equation becomes even more difficult as it becomes more difficult to predict the future. For example if the government chooses expansive fiscal policy and the crisis continues, it risks running huge deficits and building up an unsustainable public debt. On the other hand, if the government cuts spending during a crisis this will tend to make the crisis worsen, further reducing government income, and once again increasing the debt!

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9. Unemployment: Definitions and Data

9.1. Two countries, A and B, have 100 working-age adults each. Their economies are in long-run equilibrium, and the occupations of the working-age adults are distributed as below.

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(a) i. What is the level of unemployment in each country, as a percentage? Definition:

• The number of unemployed: All the people who do not have a job and are actively seeking work.• The labor force: All those who want to work, i.e. the sum of the unemployed and all those who do have jobs.• The unemployment rate: The number of unemployed as a percentage of the labor force.

• Unemployment rate in Land A 880

= 10%

• Unemployment rate in Land B 460

= 6.7%

ii. Every person who is employed produces goods with a value of 1000 SEK per year. What is the level of GDP per capita in each country?

• In land A, 𝐺𝐺𝐷𝐷𝑀𝑀 = 72 ∗ 1000 = 72000, 𝐺𝐺𝐷𝐷𝑀𝑀 𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑦𝑦𝑝𝑝𝑐𝑐𝑡𝑡𝑦𝑦 = 72000100

= 720 𝑆𝑆𝑆𝑆𝑆𝑆 𝑝𝑝𝑝𝑝𝑝𝑝 𝑦𝑦𝑝𝑝𝑦𝑦𝑝𝑝

• In land B, 𝐺𝐺𝐷𝐷𝑀𝑀 = 56 ∗ 1000 = 56000, 𝐺𝐺𝐷𝐷𝑀𝑀 𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑦𝑦𝑝𝑝𝑐𝑐𝑡𝑡𝑦𝑦 = 56000100

= 560 𝑆𝑆𝑆𝑆𝑆𝑆 𝑝𝑝𝑝𝑝𝑝𝑝 𝑦𝑦𝑝𝑝𝑦𝑦𝑝𝑝

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(b) Discuss briefly the following statement: ‘The labor market in Country A works better than in Country B, because more jobs are created in A than in B.’• It’s not possible to know in which country the labour market works better,

because we have too little information.• But if we assume that the proportion outside the labor force has nothing to do

with how well the labour market works, then we can conclude that the labor market functions better in the country B, since in B there are only 6.7 percent unemployed instead of 10 percent. But if many of the 40 who are outside the labor force in the country B are discouraged workers, then there is much hidden unemployment in country B, so it could be that the labor market functions worse there.

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Documents

Macroeconomics Exercise 2 · Besien. C 0 = 400 tSEK per year: t = 25 percent. t = 50 percent: MPC = 0,8. T = 625 tSEK per year: T = 1250 tSEK per year. I = 100 tSEK per year: G =