Answer for Homework 5: Modern Macroeconomics I

1. Answer the following question.
(a) Explain three functions of money.
Answer Three functions of money are:i. A store of value: Money can be used to transfer purchasing power fromthe present to future.
ii. A unit of account: Money provides the yardstick with which we measure
the value of our transaction.
iii. A medium of exchange: Money is tool with which we use to buy or sellgoods.
(b) Suppose that currencies are 200 million yen and deposits are 300 million yen andreserves are 100 million yen. Derive a money multiplier in this economy.
Answer The de…nition of money multiplier is
Money multiplier=

C=D + 1
C=D + R=D

where C is currency, D is deposits, and R is reserves. Then, we obtain:
C=D + 1
C=D + R=D200+1300= 200+ 100
300
300
5=3

Money multiplier =(c) Explain how the Bank of Japan controls money supply.
Answer There are three instruments:
i. Open-Market Operations: Bank of Japan can sell or buy government
bonds. When it buys bonds in the market, it pays yen for the bonds.
Therefore, monetary base goes up. On the other hand, when it sells, it
receives yen. Hence monetary base goes down.
I thank to Hiroshi Kitamura and Wataru Tamura who made these sample answers.

1ii. Operations at Exchange Market: Bank of Japan can sell or buy
dollars. When it buy dollars on the market, it pays yen for the dollars.
Therefore, monetary base goes up. On the other hand, when it sells, itreceives yen. Hence, monetary base goes down.
iii. Change in the Discount Rate: When commercial banks …nd that they
do not have enough reserves, they can ask Bank of Japan to discount theirbills. When Bank of Japan reduce the discount rate, commercial bankcan easily borrow money from Bank of Japan and it increases monetarybase.
2. Assume that population and asset is normalized to be 1. Consider the following aggregate supply and aggregate demand model and answer the following questions.
y =(he (w))
0w =(he (w))=(he (w)) whe (w)y = c+i+g
ms= k( )yP
Suppose that(he ) = (he )1kk( ) =;;where y is GDP per capita, w is wage rate, is interest rate, he is labor, g is government
expenditure, c is consumption, i is investment, ms is money supply, P is price de‡ator.
We assume that = 0:3 and k = 0:1.
(a) Suppose that government increases government expenditure, g, by 200 billion yen.
How much does it a¤ect GDP, the interest rate, wage, investment, consumption
and aggregate price? Brie‡y explain your results.
Answer In the long run, y, w, and are determined by supply side. Therefore,
an increase in g does not a¤ect y, w, and . However, the increase in g a¤ects
consumption c and investment i. Since we know that y is constant in the longrun and we have y = c + i + g, the increase in g by 200 billion yen decreases
c + i by 200 billion yen.
(b) Suppose that Bank of Japan increases money supply, ms , by 4 %. How much doesit a¤ect GDP, the interest rate, the wage, investment, consumption and aggregate
price? Brie‡y explain your results.
Answer In the long run, y, w, and are determined by supply side. Therefore,
an increase in ms does not a¤ect y, w, and . However, the increase in msa¤ects aggregate price P . Since we know that k ( ) y is constant in the longsrun and we have mP = k ( ) y, the increase in ms by 4% increases P by 4%.
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3. Answer the following question.
(a) Suppose that real interest rate is 2 percent. Currently many Japanese believethat in‡ation rate is 2 percent. How much is the nominal interest rate?
Answer The real interest rate is de…ned as nominal interest rate minus the expected in‡ation rate
r= n gPe
where r is the real interest rate, n is the nominal interest rate and gPe isthe expected in‡ation rate. According to this de…nition, the nominal interest
rate isn= r + gPe= 2+2= 4:(b) Suppose that Bank of Japan set the growth rate of money supply, M s , by 2 %.
How does it a¤ect GDP, the interest rate, the wage, investment, consumption andaggregate price in the long run? Brie‡y explain your results.
Answer Let ms money supply, g government expenditure, y GDP, w wage,
interest rate, c consumption, and P price. Given (ms ; g), the long run marketequilibrium is summarized by (Y; w; i; C; P ), which satis…esi. Supply side conditions determine (y; w; ):y =w ==(he (w))(he (w))(he (w)) whe (w)0ii. Demand side conditions determine (i; P ).
y = c+i+g
ms= k( )yP
First, in the long run, GDP, the interest rate, and wage are determinedby the supply side. Therefore, they do not change whereas money supplyincreases. Second, the consumption and the investment are determinedby the interest rate, GDP, and government expenditure. Since interest
rate is constant, the investment is constant. In addition, since y = c+i+g
and we know y, i, and g are constant, c is also constant. Therefore, theinvestment and the consumption do not change. However, the aggregate3sprice depends on the money supply: P = k(m )y andPP
P==

msk( )ymsk( )ymsk( )yms

msms;

where P is the aggregate price when ms increases to ms . Therefore, anincrease in the money supply raise the aggregate price by 2 percent in thelong run.

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