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valuation management
Homework 3 Due at 8:30 PM on Thursday October 18 on Elearning

1. Suppose that a firm’s production function is given by Q =F(K,L) = 3K+2L . What is the marginal rate of technical substitution between capital and labor when K=3 and L=4? (The rate at which the firm can substitute between capital and labor while keeping output constant, with the change in capital in the numerator and the change in labor in the denominator.)

2. The production function for a competitive firm is Q = K1/2L1/2. The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at 25 units and the cost of rental rate of capital is $10 per unit. What is the profit-­‐maximizing quantity of labor?

( recall that for a Cobb-­‐Douglas production function Q =F(K, L)= KaLb , MPK= aKa-­‐1Lb and MPL=bKaLb-­‐1)

3. What is the marginal rate of technical substitution between capital and labor when capital is fixed at 25 units and labor is at the profit-­‐maximizing level found in question 1?

4. At the quantity of labor and capital found in problem 2, is the firm using the cost-­‐
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