BE Homework 5

Which of the following cost functions exhibits cost complementarity?

−4Q1Q2 + 8Q1

Suppose that production for good X is characterized by the following production function, Q = K^0.5L^0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $15 and the per-unit wage, w, is $5, then the average fixed cost of using 16 units of capital and 25 units of labor is:

$12

For the cost function C(Q) = 1000 + 14Q + 9Q^2 + 3Q^3, what is the marginal cost of producing the fourth unit of output?

$230

Suppose the production function is given by Q = 3K + 4L. What is the average product of capital when 5 units of capital and 10 units of labor are employed?

11

Suppose the production function is given by Q = 4K + 3L. What is the average product of labor when 10 units of capital and 5 units of labor are employed?

11

Which of the following statements is incorrect?

Fixed costs are always greater than sunk costs

Which of the following sets of economic data is minimizing the cost of producing a given level of output?

MPL = 20, MPK = 40, w = $16, r = $32

The first-order conditions for maximizing profits, π = P × F(K, L) - wL − rK, are:

a. P × MPK − r = 0 and P × MPL − w = 0. b. (picture) c. VMPK = r and VMPL = w. d. All of the answers are correct

Suppose the cost function is C(Q) = 50 + Q − 10Q^2 + 2Q^3. At 10 units of output, the average cost curve is:

in the increasing stage

You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w = $40, r = $100, MPL = 4, and MPK = 40 the firm:

should use more K and less L to cost minimize.