100B Economics UCSC
Abhijit Sen Gupta Summer 2006
Answer Key to Problem Set 4 1) Problem 3, Chapter 16 of Blanchard Applying equation (16.5) p. 346: a. 18000/.05+.08 = 138,462 > 100,000 so buy b. 18000/.10+.08 = 100,000 so indifferent c. 18000/.15+.08 = 78,261 < 100,000 so do not buy
2)
Problem 4, Chapter 16 of Blanchard a. Expected Net Present Value of no-school option: [1-.40][40,000 + 40,000/(1+rt) 40,000/((1+rt)(1+ret+1)(1+ret+2))...] for 38 years. However, as the real interest rate is expected to be zero always this simply becomes [1-.4][40,000]38 = 912,000 - Expected Net Present Value of school-then-work option: [1-.40][1.10][40,000/((1+rt)(1+ret+1)) + ....40,000/((1+rt)(1+ret+1)(1+ret+2)) + .....] for 36 years. Again using that the expected real interest rate is always zero this simply becomes [1-.40][1.10][40,000]36 = 950,400 - So willing to pay up to 950,400 - 912,000 = 38,400 to go to school b. Tax rate of .3 implies willing to pay 1,108,800 -1,064,000 = 44,800 to go to school. + 40,000/((1+rt)(1+ret+1)) +
3)
Problem 3, Chapter 17 of Blanchard a) A decrease in expected future real interest rate will increase the present discount value of future earnings. This will increase current consumption and investment and shift the IS curve to the right.
Economics 100B UCSC
Abhijit Sen Gupta Summer 2006
b)
An increase in current money supply will lower current interest rate and increase current output. This will cause the LM curve to shift right. Within the context of IS-LM, with a fixed capital stock, an increase in expected future taxes causes IS to shift left. However, the increase in future taxes (a deficit reduction program) will lead to lower real interest rates and increased investment in the medium run and higher output in the long run. The expected changes in the real interest rate and output tend to cause the IS curve to shift right. The net effect on the IS curve is ambiguous. A decrease in expected future income will lead to a reduction in current consumption and investment and shift the IS curve to the left.
c)
d)
4)
Problem 5, Chapter 17 of Blanchard These answers ignore any effect on capital accumulation and output in the long run. a. In the future, tax cuts will lead to a boom. This leads to higher expected output, lower expected taxes, but a higher expected interest rate in the future. The effect on current output is ambiguous. This means that the Fed will increase the interest rate in the future (shift LM left). The expected interest rate will increase more, but there is still the effect of lower expected taxes on current consumption. The effect today on output is still ambiguous, but more likely to be negative than in part (a). Future output will be higher, the future interest rate will not increase, and future taxes will be lower. The current IS curve definitely shifts right, and current output increases.
b.
c.
5)
Problem 3, Chapter 18 of Blanchard The exchange rate stands at 1$ = 0.75, i.e. E = 0.75 The face value and the prices of the two bonds are given by United States 1-year bond Germany 1-year bond Face Value $10,000 10,000 Price $9615.38 9433.96
(a). The price of the bond and the face value of the bond are related by the following equation Price*(1 + it) = Face Value Thus for the domestic (U.S.) bond we have
Economics 100B UCSC
Abhijit Sen Gupta Summer 2006
9615.38* (1 + it ) = 10, 000 (1 + it ) = it = 4%
We denote foreign variables with a star. So the foreign interest rate is denoted by it . For the foreign (German) bond we have
*
10, 000 = 1.04 9615.38
9433.96 * (1 + i*t ) = 10,000 (1 + i*t ) = i*t = 6% 10,000 = 1.06 9433.96
(b)
The uncovered interest parity condition states
E et +1 - Et it i t - Et
*
i.e. the domestic interest rate must be approximately equal to the foreign interest rate minus the expected depreciation of the domestic currency. Thus we have
E et +1 - 0.75 0.95 e E - 0.75 -0.02 = t +1 0.75 -0.02 * 0.75 = E et +1 - 0.75 0.04 = 0.06 + -0.015 = E e t +1 - 0.75 E e t +1 = 0.735
(c) If we expect the dollar to depreciate relative to the Euro, we should buy the German bond as the return on German bond will be higher, since the Euro will be worth more dollars. (d) The realized rate of return on a German bond is the ex post rate of return. It is given as
Economics 100B UCSC
Abhijit Sen Gupta Summer 2006
E R t +1 - Et i _ Et
* t
0.72 - 0.75 0.75 0.03 0.06 + 0.75 0.06 + 0.04 0.10 = 10% 0.06 -
Thus an U.S. investor would earn 10% return if he was to invest in a German bond. This happens as the German bond pays a nominal interest rate of 5%, and the dollar has depreciated by 4%. On the other hand the realized rate of return on the US bond is the nominal interest rate i.e. 4%. (e) The uncovered interest parity condition talks about the expected exchange rate and not the actual exchange rate in the future. Thus the statement is consistent with the uncovered interest parity condition. 6) Problem 6, Chapter 18 of Blanchard (a) The following graph plots the yes versus dollar exchange rate for the period Jan 1979 to November 2004 on a monthly basis.
Yen Vs. Dollar Exchange Rate 300
250
200 Exchange Rate
150
100
50
0 Jan-79 Jan-81 Jan-83 Jan-85 Jan-87 Jan-89 Jan-91 Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
Period
Economics 100B UCSC
Abhijit Sen Gupta Summer 2006
Here any appreciation (depreciation) of the yen implies a depreciation (appreciation) of the dollar. In the graph above, since early 1985 the shaded regions depict periods when yen appreciated (dollar depreciated) while the unshaded regions depict period when the yen depreciated. The yen dollar exchange rate was quite stable from Jan 1979 to early 1985. The yen started to appreciate from middle of 1985 to mid1995. Thereafter it started depreciating and continued to depreciate till mid-1998. The yen again appreciated for a brief time period from mid-1998 through the end of 1999. It again started depreciating from the beginning of 2000 and continued to do so until the first quarter of 2002. Since then the yen has been steadily appreciating. Looking at the broader picture we find that the has yen appreciated by over 100% in the 21 year period from 1984-2005. (b) It would require a depreciation of the yen to make Japanese goods more attractive to foreign consumers. As a result of this depreciation Japanese goods would become cheaper for the foreign (i.e. US) consumers. (c) In the last few years i.e. since the second quarter of 2002 the yen has appreciated against the dollar. This has made Japanese exports more expensive and imports from the US cheaper. However, the last 12 months has witnessed an appreciation of the dollar.
7)
Problem 1, Chapter 19 of Blanchard a. False According to the National Income Identity NX = S+T-G-I I = S + (T-G)-NX Thus the investment can be financed by private saving (S), public saving (T-G) and international saving (-NX). A negative trade account implies positive capital account. So a trade deficit does not necessarily imply that there is a budget deficit. It means that the private and public savings are not enough to finance investment. b. False According to the National Income Identity NX = S+T-G-I I = S + (T-G)-NX If there is high enough private savings (S is large enough ) then private savings will be able to cover trade deficit as well as finance investment. In that case, the economy does not have to run a trade deficit. c. False A small open economy might find it difficult to stabilize output as the economy is hit by several shocks from other countries. On the other hand in an open economy the policymaker has an additional instrument, the exchange rate to stabilize the economy.
Economics 100B UCSC
Abhijit Sen Gupta Summer 2006
d. e.
False Trade surplus can also be eliminated if there is a reduction in foreign countries' income or a rise in domestic country's income True A fiscal contraction will lead to a fall in interest rate a fall in output. Both these effects would raise net exports. The effect of an increase in net exports would be larger in a small open economy than a large economy. By definition in a small open economy imports and exports and hence net exports form a big share of GDP. So a change in net exports will have a stronger effect on output. True From Figure 19.1 in the chapter we can see that at the point of intersection of the DD and ZZ line trade is in balance and trade deficit is zero. The DD line gives the domestic demand for all goods (C + I + G), while the ZZ line gives the total demand for domestic goods (C + I + G + X 1/ IM ). At the point of intersection we have C + I + G = C + I + G + X 1/ IM X 1/ IM = 0 False As the J curve suggests a real depreciation.does not immediately improves the trade balance. The immediate effect is on the relative price of domestic and foreign goods (real exchange rate). The quantity of imports and exports change after a certain period. As a result following a real depreciation the trade balance worsens before it improves. True/Uncertain. Appreciation of the dollar also played a role. Moreover for several years now investment in US has been much higher than private or public savings
f.
f.
g.
8)
Problem 3, Chapter 19 of Blanchard a. The share of Japanese spending on U.S. goods relative to U.S. GDP is 7%*10%=0.07*0.1=0.007=0.7% b. U.S. GDP falls by 2*5%*1%=2*0.05*0.01=0.001=0.1% c. U.S. GDP falls by 2*5%*10%=2*0.05*0.1=0.01=1% d. This is an overstatement. The numbers above indicated that even if U.S. exports fall by 5%, the effect is to reduce growth by 1%. This is small relative to GDP, but large relative to normal growth ( of around 3%)
9)
Problem 1, Chapter 20 of Blanchard a. Uncertain The multiplier is smaller in the open economy. When there is an increase in government expenditure then part of the expenditure can be on foreign goods. So now the multiplier works in the foreign country. However, in a open economy a fiscal policy will also effect exchange rate (through interest rate) and hence influence net exports which will have an impact on output. b. False A fiscal expansion increases interest rate and output. A rise in interest rate increases the exchange rate (both real and nominal) and assuming
Economics 100B UCSC
Abhijit Sen Gupta Summer 2006
Marshall-Lerner condition holds, lowers net exports. The higher output increases imports and lowers net exports. c. True -- An increase in expected exchange rate implies investors are expecting the domestic currency to be stronger in the future. Thus the domestic bond becomes an attractive option as the foreign bond will yield a lower return (in terms of domestic currency) one year from today. So investors will move out of the foreign bond into the domestic bond. To do this they will have to sell foreign currency and buy domestic currency, which will raise the exchange rate today. d. True -- If investors expect the dollar to depreciate over the coming year, Japanese bonds will become an attractive option. For the interest parity condition to hold, domestic interest rates have to rise so that people hold both foreign and domestic bond. e. False Foreigners will hold Japanese bonds if they expect the dollar to depreciate against the yen. f. False The money stock has to change so that money supply is equal to money demand at a constant interest rate.
10)
Problem 3, Chapter 20 of Blanchard a) A monetary expansion leads to an increase in output and lower interest rate. As a result of higher output, consumption will be higher. On the other hand due to lower interest rate and higher output, investment will also be higher. The lower interest rate will make domestic bonds less attractive and investors will switch away from domestic bonds and into foreign bonds. To do this they will sell domestic currency and purchase foreign currency. Thus the price of the domestic currency in terms of foreign currency (the nominal exchange rate E) will fall. Assuming the ratio of domestic and foreign prices is equal to one, this will cause the real exchange rate to fall. Assuming, Marshall-Lerner condition holds, the net exports will rise. However, the rise in output will cause imports to rise and therefore net exports will fall. Thus the overall effect on net exports is ambiguous.
b)