Chapter Exercises

tions.These conditions indicate that returns to scale are constant.Do you agree? Explain. 5.33An increase in the size of a company’s labor force resulted in an increase in the average product of labor.For this to happen,the firm’s total output must have increased.Do you agree? Explain. 5.34An increase in the size of a company’s labor force will result in a shift of the average product of labor curve up and to the right.This indicates that the company is experiencing increasing returns to scale.Do you agree? Explain. 5.35Suppose that output is a function of labor and capital input and exhibits constant returns to scale.If a firm doubles its use of both labor and capital,the total product of labor curve will become steeper.Do you agree? Explain.

CHAPTER EXERCISES

5.1Suppose that the production function of a firm is given by the equation

where Q represents units of output, K units of capital,and L units of labor. What is the marginal product of labor and the marginal product of capital at K = 40 and L = 10? 5.2A firm’s production function is given by the equation

where Q represents units of output, K units of capital,and L units of labor. a.Does this production function exhibit increasing,decreasing,or constant returns to scale? b.Suppose that Q = 1,000.What is the equation of the corresponding isoquant in terms of labor? c.Demonstrate that this isoquant is convex with respect to the origin. 5.3Determine whether each of the following production functions exhibits increasing,decreasing,or constant returns to scale for K = L = 1 and K = L = 2. a. Q = 10 + 2L2 + K3 b. Q = 5 + 10K + 20L + KL Q KL = 2 5 5. .

Q K L = 100 03 08 . .

c. Q = 500K0.7L0.1 d. Q = K + L + 5LK 5.4Suppose that a firm’s production function has been estimated as

Q K L = 5 05 05 . .