1. Hula hoop fabricators cost $100 each. The Hi-Ho hula Hoop Company is trying to decide how many of these machines to buy. HHHHC expects to produce the following numbers of hoops each year for each level of capital stock shown.

                Number of Fabricators                                                                 Number of Hoops

Produced per Year

0                                                                                                                                                                     0

1                                                                                                                                                                     100

2                                                                                                                                                                     150

3                                                                                                                                                                     180

4                                                                                                                                                                     195

5                                                                                                                                                                     205

6                                                                                                                                                                     210

Hula hoops have a real value of $1 each. HHHHC has no other costs besides the cost of fabricators.

a.       Find the expected future marginal product of capital (in terms of dollars) for each level of capital. The MPK^f for the third fabricator, for example, is the real value of the extra output obtained when the third fabricator is added

b.      If the real interest rate is 12% per year and the depreciation rate of capital is 20% per year, find the user cost of capital (in dollars per fabricator per year). How many fabricators should HHHHC buy?

c.       Repeat Part (b) for a real interest rate of 8% per year

d.      Repeat Part (b) for a 40% tax on HHHHC’s sales revenues.

e.       A technical innovation doubles the number of hoops a fabricator can produce. How many fabricators should HHHHC buy when the real interest rate is 12% per year? 8% per year? Assume that there are no taxes and that the depreciation rate is still 20% per year.

2. An economy has full-employment output of 6000. Government purchases, G, are 1200. Desired consumptions and desired investment are

                                C^d =3600 – 2000r + 0.10Y, and

                                I^d = 1200 – 4000r,

Where Y is output and r is the real interest rate.

a.       Find an equation relating desired national saving, S^d, to r and Y

b.      Using both versions of the goods market equilibrium conditions, Eqs. (4.7) and (4.8), find the real interest rate that clears the good market. Assume that output equals full-employment output.

c.       Government purchases rise to 1440. How does this increase change the equation describing desired national saving? Show the change graphically. What happens to the market-clearing real interest rate?

3. Suppose that the economywide expected future marginal product of capital is MPK^f = 20 – 0.02K, where K is the future capital stock. The depreciation rate of capital, d, is 20% per period. The current capital stock is 900 units of capital. The price of a unit of capital is 1 unit of output. Firms pay taxes equal to 50% of their output. The consumption function in the economy is C= 100 + 0.5Y-200r, where C is consumption, Y is output, and r is the real interest rate. Government purchases equal 200, and full-employment output is 1000.

                a. suppose that the real interest rate is 10% per period. What are the values of the tax-adjusted user cost of capital, the desired future capital stock, and the desired level of investment?

                b. Now consider the real interest rate determined by goods market equilibrium. This part of the problem will guide you to this interest rate.

                                i. Write the tax-adjusted user cost of capital as a function of the real interest rate r. also write the desired future capital stock and desired investment as functions of r.

                                ii. Use the investment function derived in Part (i) along with the consumption function and government purchases, to calculate the real interest rate that clears the goods market. What are the goods market-clearing values of consumption, saving, and investment? What are the tax-adjusted user cost of capital and the desired capital stock in this equilibrium?

4.  Use the saving-investment diagram to analyze the effects of the following on national saving, investment, and the real interest rate. Explain your reasoning.

a.       Consumers become more future-oriented and thus decide to save more.

b.      The government announces a large, one-time bonus payment to veterans returning from a war. The bonus will be financed by additional taxes levied on the general population over the next five years.

c.       The government introduces an investment tax credit (offset by other types of taxes, so total tax collections remain unchanged).

d.      A large number of accessible oil deposits are discovered, which increases the expected future marginal product of oil rigs and pipelines. It also causes an increases in expected future income.

5.  A country loses much of its capital stock to a war.

e.      What effects should this event have on the country’s current employment, output, and real wage?

f.        What effect will the loss of capital have on desired investment

g.       The effects of desired national saving of the wartime losses are ambiguous. Give one reason for desired saving to rise and one reason for it to fall.

h.      Assume that desired saving doesn’t change. What effect does the loss of capital have on the country’s real interest rate and the quantity of investment?

6.  In a small open economy, output (gross domestic product) is $25 billion, government purchases are $6 billion, and net factor payments from abroad are zero. Desired consumption and desired investment are related to the world real interest rate in the following manner:

World Real Interest Rate                     Desired Consumption                   Desired Investment

5%                                                          $12 billion                                            $3 billion

4%                                                          $13 billion                                            $4 billion

3%                                                          $14 billion                                            $5 billion

2%                                                          $15 billion                                            $6 billion

                For each value of the world real interest rate, find national saving, foreign lending, and absorption. Calculate net exports as the difference between output and absorption. What is the relationship between net exports and foreign lending?