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Consider a firm the faces the following production technology: Y = 500K − K2 where Y...

Consider a firm the faces the following production technology:

Y = 500K − K2

where Y denotes output, and K the capital stock.

The price of capital, pk, is 500, the real interest rate, r, is 5%, and the depreciation rate, d, is 15%.

(a) Derive the expected future marginal product of capital, MPKf . How does MPKf vary with K?

(b) What is the user cost of capital and the firm’s desired capital stock? If the initial capital stock K0 is 150, what are net investment and gross investment?

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