Answer to Homework for chapter 4

Review questions:

6. The two components of the user cost of capital are the interest cost and the depreciation cost. The depreciation cost is the value lost as the capital wears out during the period. The interest cost represents the opportunity cost of not using the funds that purchased the capital in some other way; an example would be if the money was invested in bonds rather than buying capital goods.

7. The desired capital stock is the amount of capital that allows the firm to earn the largest possible profit. The higher the expected future marginal product of capital, the higher the desired capital stock, since any given amount of capital will be more productive in the future. The higher the user cost of capital, the lower the desired capital stock, since a higher user cost yields lower profits on each unit of capital. The higher the effective tax rate, the lower the desired capital stock, again because the firm gets lower profits on each unit of capital.

Numerical questions:

2. (a) This chart shows the MPKf as the increase in output from adding another fabricator

# Fabricators / Output / MPKf
0 / 0 / —
1 / 100 / 100
2 / 150 / 50
3 / 180 / 30
4 / 195 / 15
5 / 205 / 10
6 / 210 / 5

(b) uc = $32. HHHHC should buy two fabricators.

6. (a) Sd = Y – Cd – G

= –4800 + 2000r + 0.9Y

(b) (1) Using Eq. (4.7): Y = Cd + Id + G

Y = 6000 – 6000r + 0.1Y

So 0.9Y = 6000 – 6000r

At full employment, Y = 6000. We get r = 0.10.

(2) Using Eq. (4.8):

Sd = Id

–4800 + 2000r + 0.9Y = 1200 – 4000r

0.9Y = 6000 – 6000r

When Y = 6000, r = 0.10. So we can use either Eq. (4.7) or (4.8) to get to the same result.

(c) When G = 1440, desired saving becomes Sd = Y – Cd – G = –5040 + 2000r + 0.9Y. Sd is now 240 less for any given r and Y; this shows up as a shift in the Sd line from S1 to S2 in Figure 4.3.

Figure 4.3

Setting Sd = Id, we get:

–5040 + 2000r + 0.9Y = 1200 – 4000r

At Y = 6000, r = 0.14. The market-clearing real interest rate increases from 10% to 14%.