1. Suppose the one-year T-bill rate was 10% on 1/1/92, 8% on 1/1/93, and 6% on 1/1/94. Suppose also that the GDP deflator (1986 dollars) was 160 on 1/1/92, 169 on 1/1/93, 175.4 on 1/1/94, and 183.6 on 1/1/95. The tax rate on interest income is 25%.
(a) Calculate the after-tax nominal rate of return for 1992, 1993, and 1994.
(b) If you began with 1000 on 1/1/92 and invested in T-bills each year (paying taxes at the end of each year), how much would you have in nominal terms on 1/1/95? How much would you have in real terms (1986 dollars)?
(c) What are your nominal and real interest earnings over the three year period?
2. A firm has current and future marginal productivity of capital given by MPK=10,000-2K + N, and marginal productivity of labor given by MPN = 50 - 2N + K. The price of capital is $5,000, the real interest rate is 10%, and capital depreciates at a 15% rate. The real wage rate is $15.
(a) Calculate the user cost of capital.
(b) Find the firm's optimal amount of employment and the size of the capital stock.
3. Consider a Keynesian consumption function with desired consumption equal to 0.9Y, where Y is income. Government purchases are $1000$, net exports are zero, and desired investment varies with the real interest rate according to the following schedule:
r I(desired)
5 3000
4 3500
3 4000
2 4500
Assume the interest rate adjusts so that the economy is in equilibrium. Equilibrium output at `full employment' is 50,000. Find the equilibrium values of consumption, investment, and the real interest rate.
4. Use a saving-investment diagram to explain what happens to saving, investment, and the real interest rate in each of the following scenarios:
(a) Current output rises due to a temporary productivity increase.
(b) The tax code changes so that business firms face higher tax rates on their revenue (offset by other lump-sum tax changes so there's no overall change in tax revenue).
(c) The government increases spending temporarily for a one-year project.
(d) The average education level rises, inducing an increase in the future marginal productivity of capital.
5. Suppose a country has the following balance of payments data:
Merchandise exports 1000 Merchandise imports 1300 Service exports 600 Service imports 500 Investment income 750 Investment payments 1000 Transfers abroad 150 Increase in home 1300 assets abroad Increase in foreign 1900 assets at home
(a) Calculate the current account balance.
(b) Calculate the capital account balance.
(c) Calculate the trade balance.
(d) Calculate net factor payments.
6. A large open economy has desired national saving of S(d) = 20 +200 r(w) and desired national investment of I(d) = 30 - 200 r(w). The foreign economy has desired national saving of S(d)For = 40 +100 r(w), and desired national investment of I(d)For = 75 - 400 r(w)
(a) Calculate the equlibrium values of r(w), CA, CA(For), S, I, S(For), and I(For).
(b) Suppose S(d) rises by 45, so that now S(d) = 65 +200 r(w). Calculate the equlibrium values of r(w), CA, CA(For), S, I, S(For), and I(For).
(c) Suppose, with S(d) as in part a, that I(d) rises by 45, to I(d) = 75 - 200 r(w). Calculate the equlibrium values of r(w), CA, CA(For), S, I, S(For), and I(For).
7. The government of a small open economy announces a tax cut of $100 this year, combined with a tax increases of $110 next year, when the interest rate is 10%. What are the effects of this change on the world real interest rate, national saving, investment, and the current account balance in equilibrium when
(a) Ricardian equivalance holds?
(b) Ricardian equivalance does not hold?
8. Consider a large open economy in equilibrium with zero current account balance. What are the effects on world real interest rate, national saving, investment, and the current account balance in equilibrium if:
(a) future income rises?
(b) business taxes rise?
(c) government purchases decline temporarily?
(d) the future marginal product of capital rises?
1. (a) 7.5%; 6%; 4.5%
(b) $1190.78; $648.73
(c) $190.78; $23.73
2. (a) uc = (r+d)p(k) = 0.25(5000)= 1250.
(b) Setting w = MPN gives 15 = 50-2N+K, or 2N = 35+K. Setting uc = MPK gives 1250 = 10,000 - 2K +N, or N = -8,750 + 2K, or 2N = -17,000+4K. Setting -17,500 + 4K = 35 + K gives 3K = 17,535, which yields K = 5845. Then N = 2940.
3. r=3%; I=4000; C=45,000.
4. (a) The rise in output raises desired saving, shifting the S(d) curve to the right: in equilibrium, this reduces the real interest rate, increasing investment as well.
(b) The rise in taxes reduces desired investment, shifting the I(d) curve to the left; in equilibrium, this reduces the real interest rate, reducing saving as wellj as investment.
(c) The rise in government purchases reduces desired saving, shifting the S(d) curve to the left; in equilibrium, this raises the real interest rate, reducing investment as well as saving.
(d) The rise in future marginal productivity of capital raises desired investment, shifting the I(d) curve to the right; in equilibrium, this raises the real interest rate, increasing saving as well as investment.
5. (a) -600 (b) 600 (c) -300 (d) -250
6. (a) In equilibrium, S(d) + S(d})(For) = I(d) + I(d)(For), so that 60 + 300 r(w) = 105 - 600 r(w), or 900r(w) = 45, so r(w) = 0.05. Using this in the formulas, we get S= 30, I=20, CA=10, S(For) = 45, I(For) = 55, and CA(For) = -10.
(b) Now 900 r(w) = 0, so r(w) = 0.0. Using this in the formulas, we get we get S= 65, I=30, CA=35, S(For) = 40, I(For) = 75, and CA(For) = -35.
(c) Now 900 r(w)= 90, so r(w) = 0.10. Using this in the formulas, we get S= 40, I=55, CA=-15, S(For) = 50, I(For) = 35, and CA(For) = 15.
7. (a) No effect on any of the variables.
(b) Real world interest rate unchanged, national saving declines (private saving rises, but not as much as government saving declines), investment is unchanged, and the current account balance declines.
8. (a) r(w) rises, S falls, I falls, CA falls.
(b) r(w) falls, S falls, I falls, CA rises.
(c) r(w) falls, S rises, I rises, CA rises.
(d) r(w) rises, S rises, I rises, CA falls.