Homework 2(A)

Macroeconomics Homework Assignment2Due on Oct16,Week7
1.(25marks)Suppose that the money demand function takes the form
(M/P)d=L(i,Y)=Y 5i
(a)If output grows at rate g,at what rate will the demand for real balances grow (assuming constant nominal interest rates)?
(b)What is the velocity of money in this economy?
(c)If inflation and nominal interest rates are constant,at what rate,if any,will velocity grow?
(d)How will a permanent(once-and-for-all)increase in the level of interest rates affect the level of velocity?How will it affect the subsequent growth rate of velocity?
Answers:
(a)(6marks)If output Y grows at rate g,then real money balances(M/P)d must also grow at rate g,given that the nominal interest rate i is a constant.
(b)(7marks)According to the quantity equation MV=P Y,the velocity of
money:
V=
Y
M/P
=
Y
Y/5i
=5i.
(c)(6marks)If the nominal interest rate is constant,then the velocity of money must be constant.
(d)(6marks)A one-time increase in the nominal interest rate will cause a one-time increase in the velocity of money.There will be no further changes in the velocity of money.
2.(25marks)Suppose that consumption depends on the level of real money balances(on the grounds that real money balances are part of wealth).Show that if real money balances depend on the nominal interest rate,then an increase in the rate of money growth affects consumption,investment,and the real interest rate. Does the nominal interest rate adjust more than one-for-one or less than one-for-one to expected inflation?
This deviation from the classical dichotomy and the Fisher effect is called the Mundell-Tobin effect.How might you decide whether the Mundell-Tobin effect is important in practice?
Answers:
An increase in the rate of money growth leads to an increase in the rate of inflation.Inflation,in turn,causes the nominal interest rate to rise,which means
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Macroeconomics Homework Assignment2Due on Oct16,Week7 that the opportunity cost of holding money increases.As a result,real money balances fall.Since money is part of wealth,real wealth also falls.A fall in wealth reduces consumption,and,therefore,increases saving.The increase in saving leads to a rightward shift of the saving schedule,as in Figure2.This leads to a lower real interest rate and an increase in the level of investment.
Figure2
The classical dichotomy states that a change in a nominal variable such as inflation does not affect real variables.In this case,the classical dichotomy does not hold;the increase in the rate of inflation leads to a decrease in the real interest rate.The Fisher effect states that i=r+π.In this case,since the real interest rate r falls,a1percent increase in inflation increases the nominal interest rate i by less than1percent.
Most economists believe that this Mundell-Tobin effect is not important be-cause real money balances are a small fraction of wealth.Hence,the impact on saving as illustrated in Figure2is small.
3.(25marks)Use the model of the small open economy and drawfigures to predict what would happen to the trade balance,the real exchange rate,and the nominal exchange rate in response to each of the following events.
(a)A fall in consumer confidence about the future induces consumers to spend less and save more.
(b)The introduction of a stylish line of Toyotas makes some consumers prefer foreign cars over domestic cars.
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Macroeconomics Homework Assignment2Due on Oct16,Week7
(c)The introduction of automatic teller machines(ATM)reduces the demand for money.
Answers:
(a)(8marks)An increase in saving shifts the(S−I)schedule to the right, increasing the supply of dollars available to be invested abroad,as in Figure3(a). The increased supply of dollars causes the equilibrium real exchange rate to fall fromϵ1toϵ2.Because the dollar becomes less valuable,domestic goods become less expensive relative to foreign goods,so exports rise and imports fall.This means that the trade balance increases.The nominal exchange rate falls following the movement of the real exchange rate,because prices do not change in response to this shock.
Figure3(a)
(b)(8marks)The introduction of a stylish line of Toyotas that makes some consumers prefer foreign cars over domestic cars has no effect on saving or invest-ment,but it shifts the NX(ϵ)schedule inward,as in Figure3(b).The trade balance does not change,but the real exchange rate falls fromϵ1toϵ2.Because prices are not affected,the nominal exchange rate follows the real exchange rate.
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Macroeconomics Homework Assignment2Due on Oct16,Week7
Figure3(b)
(c)(9marks)In the model we considered in this lecture,the introduction of ATMs has no effect on any real variables.The amounts of capital and labor de-termine output¯Y.The world interest rate r determines investment I(r∗).The dif-ference between domestic saving and domestic investment(S−I)determines net exports.Finally,the intersection of the NX(ϵ)schedule and the(S−I)schedule determines the real exchange rate,as in Figure3(c).
Figure3(c)
The introduction of ATMs,by reducing money demand,does affect the nom-inal exchange rate through its effect on the velocity and hence the domestic price
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Macroeconomics Homework Assignment2Due on Oct16,Week7 level.The price level adjusts to equilibrate the demand and supply of real balances, so that M/P=(M/P)d.
If M isfixed,then a fall in(M/P)d causes an increase in the price level:this reduces the supply of real balances M/P and restores equilibrium in the money market.
Now recall the formula for the nominal exchange rate:e=ϵ(P∗/P).We know that the real exchange rate remains constant,and we assume that the foreign price level P∗isfixed.When the domestic price level P increases,the nominal exchange rate e depreciates.
4.(25marks)You read in a newspaper that the nominal interest rate is12 percent per year in Canada and8percent per year in the United States.Suppose that the real interest rates are equalized in the two countries and that purchasing-power parity holds.
(a)Using the Fisher equation(discussed in Chapter4),what can you infer about expected inflation in Canada and in the United States?
(b)What can you infer about the expected change in the exchange rate between the Canadian dollar and the U.S.dollar?
(c)A friend proposes a get-rich-quick scheme:borrow from a U.S.bank at8 percent,deposit the money in a Canadian bank at12percent,and make a4percent profit.Whats wrong with this scheme?
Answers:
(a)(8marks)According to the Fisher equation i=r+πe,the expected inflation rates in US and Canada are:
πe Can=12−r;
πe US=8−r.
Since the real interest rate r is the same in both countries,we have:
πe Can−πe US=4.
(b)(8marks)The nominal exchange rate is e=ϵ×(P Can/P US),thus we can write the change in nominal exchange rate as:
%change in e=%change inϵ+(πCan−πUS).
If purchasing-power parity holds,then a dollar must have the same purchas-ing power in every country.This implies that the percent change in the real ex-change rateϵis zero because purchasing-power parity implies that the real ex-change rate isfixed.Thus,changes in the nominal exchange rate result from differ-ences in the inflation rates in the United States and Canada.Because people know
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Macroeconomics Homework Assignment2Due on Oct16,Week7 that purchasing-power parity holds,they expect this relationship to hold.In other words,the expected change in the nominal exchange rate equals the expected in-flation rate in Canada minus the expected inflation rate in the United States,which according to part(a),is4percent.
Expected%change in e=(πCan−πUS)=4.
(c)(9marks)The problem with this scheme is that it does not take into account the change in the nominal exchange rate e between the U.S.and Canadian dol-lars.Given that the real interest rate isfixed and identical in the United States and Canada,and given purchasing-power parity,we know that the difference in nom-inal interest rates accounts for the expected change in the nominal exchange rate between U.S.and Canadian dollars.In this example,the Canadian nominal inter-est rate is12percent,while the U.S.nominal interest rate is8percent.We con-clude from this that the expected change in the nominal exchange rate is4percent. Therefore,
e this year=1C$/US$;
e next year=1.04C$/US$.
Assume that your friend borrows1U.S.dollar from an American bank at8 percent,exchanges it for1Canadian dollar,and puts it in a Canadian Bank.At the end of the year your friend will have$1.12in Canadian dollars.But to repay the American bank,the Canadian dollars must be converted back into U.S.dollars. The$1.12(Canadian)becomes$1.08(American),which is the amount owed to the U.S.bank.So in the end,your friend breaks even.In fact,after paying for transaction costs,your friend loses money.
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