A firm has current and future marginal productivity of capital given by MPK = 10,000 - 2K + N, and marginal productivity of labour 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 is $15.

Question

Quizplus · Accepted Answer

The Answer is a. uc = (r + d)pK = .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 =-8750 - 2K or 2N = -17,500 + 4K. Setting = 17,500 - 4K = 35 - K gives 3K = 17,535 which yields K = 5845. Then N =2940.

A Firm Has Current and Future Marginal Productivity of Capital