A firm's output (Y) depends on how much capital (K) it has, according to the equation: Y = 20K - K2. The real interest rate is 6% per year, the depreciation rate of capital is 14% per year and the price of a unit of capital is $80, and each unit of output sells for $1.(a)For capital levels of 0 to 6, how much is output?(b)For capital levels from 1 to 6, calculate the marginal product of capital.(c)How many units of capital does the firm desire?(d)If the real interest rate was 1% per year, how many units of capital would the firm desire?
What will be an ideal response?
(a) & (b)
| Capital | Output | MPK |
| 0 | 0 | --- |
| 1 | 19 | 19 |
| 2 | 36 | 17 |
| 3 | 51 | 15 |
| 4 | 64 | 13 |
| 5 | 75 | 11 |
| 6 | 84 | 9 |
| (c) | uc = (r + d)pK = (0.06 + 0.14) × 80 = 16, so the firm would like 2 units of capital; a 3rd unit of |
| (d) | uc = (r + d)pK = (0.01 + 0.14) × 80 = 12, so the firm would like 4 units of capital; a 5th unit of |
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