Problem set 7 money growth and inflation PDF

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Problem set 7 with solutions ...

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Alba Andújar Arjona

Problem set 7: Money Growth and Inflation 1. Suppose that this year’s money supply is 500 billion, nominal GDP is 10 trillion and real GDP is 5 trillion. In order to solve this exercise, it is necessary to use the quantity equation, which is à M*V=P*Y We have available the following information: - M = $500 billion - nominal GDP à P*Y = $10 trillion - real GDP à Y = $5 trillion a) What is the price level? What is the velocity of money? We can obtain the price level by à P*Y=10 ; P* =10 ; P=10/5 = $2 trillion. The velocity of money will be à M*V=10,000 ; 500*V=10,000 ; V=10,000/500 = $20 billions. b) Suppose that velocity is constant and the economy’s output of goods and services rises by 5 per cent each year. What will happen to nominal GDP and the price level next year if the central bank keeps the money supply constant? If M and V remains constant, and there is an increase of the 5% on Y, then following the quantity equation, P has to fall by 5%. And in order to make on side of the equation constant, we also have to make the other side constant so, the nominal GDP will remain unchanged. c) What money supply should the central bank set next year if it wants to keep the price level stable? In this case, we have that V and P will remain constant, meaning that if Y increases by 5%, M has to increase the same as Y in order to keep the price level stable. d) What money supply should the central bank set next year if it wants inflation of 10 per cent? In order to have an inflation of the 10%, it is necessary to increase M by 15% so the nominal GDP also rises 15%. So, P increases 10% and real GDP 5%.

2. Suppose that changes in bank regulations expand the availability of credit cards, so that people need to hold less cash. a. How does this event affect the demand for money? When bank regulations increase credit card availability, people tend to carry less cash, so that demand for money will decrease (shift to the left) as both individuals and companies need to have less cash with themselves in order to satisfy their transactions. b. If the central bank does not respond to this event, what will happen to the price level? If there is no change in the supply of money and the demand for money curve has decrease, this means that the value of money declines, so the price level rises.

c. If the central bank wants to keep the price level stable, what should it do? In order to keep the price level stable, it is necessary to shift the money supply to the left the same amount that the demand for money shifted, so that the money value and the price level does not change as it is represented in the graph.

3. It is often suggested that central banks should try to achieve 0 inflation. If we assume that velocity is constant, does this zero inflation goal require that the rate of money growth equal zero? If yes, explain why. If no, explain what the rate of money growth should be equal. The quantity equation M*V=P*Y determines that when velocity (V) and quantity of output (Y) remain constant, if the inflation rate is reduced to zero, it would be necessary for the money growth to be equal to the growth rate of output in order to keep the same proportion.

4. Let’s consider the effects of inflation in an economy composed only for two people: Michael, a bean farmer, and Dorothy, a rice farmer. Michael and Dorothy both always consume equal amounts of rice and beans. In year 2018 the price of beans was 1 and the price of rice was 3. In order to solve this exercise, it is necessary to use the inflation formula à Inflation = ((New price – Old price)/Old price) * 100 a. Suppose that in 2019 the price of beans was 2 and the price of rice was 6. What was inflation? Was Michael better off, worse off or unaffected by the changes in prices? What about Dorothy? Price 2018 Price 2019

Beans (Michael) 1 2

Rice (Dorothy) 3 6

TOTAL 4 8

Inflation = ((8-4)/4)*100 = 100% As the inflation rate is equal to 100% because the price of the goods have doubled, both Michael and Dorothy receive a 100% increase in their incomes, so no one of them is affected. b. Now suppose that in 2019 the price of beans was 2 and the price of rice was 4. What was inflation? Was Michael better off, worse off or unaffected by the changes in prices? What about Dorothy? Price 2018 Price 2019

Beans (Michael) 1 2

Rice (Dorothy) 3 4

TOTAL 4 6

Inflation = ((6-4)/4)*100 = 50% In this case, Dorothy is worse off because the inflation is 50% meaning that the prices of the goods she buys rose faster than the price of the goods she sells which are only 33%. However, Michael is better off because his revenues increased 100% while inflation is only 50%.

c. Now suppose that in 2019 the price of beans was 2 and the price of rice was 1.5. What was inflation? Was Michael better off, worse off or unaffected by the changes in prices? What about Dorothy? Price 2018 Price 2019

Beans (Michael) 1 2

Rice (Dorothy) 3 1.5

TOTAL 4 3.5

Inflation = ((3.5-4)/4)*100 = -12.5% In this case, Michael is better off too, because his revenues increased 100% while prices overall fell 12.5% but Dorothy is worse off because the prices of the goods she buys don’t fall as fast as the price of the rice she sells. d. What matters more to Michael and Dorothy the overall inflation rate or the relative price of rice and beans? The inflation rate of rice and beans matters more to them than the overall inflation rate because it is what determines that they are better or worse off. If the price of the good rises more than inflation it would lead to a better off situation. However, if the price of the good rises less than the inflation it would be worse off.

5. If the tax rate is 40% compute the before-tax real interest rate and the after-tax real interest rate in each of the following cases. In order to solve this exercise, it is necessary to use the before-tax and after-tax interest rate formulas à Before-tax interest rate = nominal interest rate – inflation rate After-tax interest rate = 60%*nominal interest rate – inflation rate a. The nominal interest rate is 10% and inflation rate 5% Before-tax interest rate = 10 – 5 = 5% After-tax interest rate = 60%*10 – 5 = 1% b. The nominal interest rate is 6% and inflation rate 2% Before-tax interest rate = 6 – 2 = 4% After-tax interest rate = 60%*6 – 2 = 1.6% c. The nominal interest rate is 4% and inflation rate 1% Before-tax interest rate = 4 – 1 = 3% After-tax interest rate = 60%*4 – 1 = 1.4%

6. Suppose that people expect inflation to equal 3% but in fact prices rise by 5%. Describe how this unexpected high inflation help or hurt the following: a- The government In this scenario, the high inflation helps the government collect tax revenue as well as to reduce the value of the outstanding debt.

b. a homeowner with a fixed-rate mortgage The increase in inflation helps a homeowner with a fixed-rate mortgage as the person only has to pay the interest rate that was depended on expected inflation and thus the persona can pay a lesser real interest rate than was predicted. c. a union worker in the second year of a labor contract The increase in inflation in that case does not help to a union worker in the second year of contract because they receive a less real wage than expected since the contract is based on the nominal wage. d. a retired person who has invested their savings in government bonds. The increase harms the retired people that has invested their savings in government bonds. It means that they are receiving a lower interest rate than they had planned.

7. Explain whether the following statements are true, false or uncertain a. Inflation hurts borrowers and helps lenders, because borrowers must pay a higher rate of interest. The statement is false. When inflation is unexpected, the borrower has to pay more on interest payments, but the lender receives low real interest rate. So, the borrower will be better off and the lender worse off. b. If prices change in a way that leaves the overall price level unchanged then no one is made better or worse off. The statement is false. Changes in relative prices can make some people better off and others worse off, even though the overall price level does not change. c. Inflation does not reduce the purchasing power of most workers. The statement is true. As inflation occurs, wages of the workers increased too, so the people’s real income does not fall....