Question 1

Suppose firm X utilizes only two inputs, namely labor (L) and capital (K). Firm X hires both inputs in competitive markets, with wages w = 5 for each unit of labor and r = 2 for each unit of capital. (a) Write the equation of a generic isocost given w and r.

(b) Sketch two isocost curves, corresponding to C = 120 and C = 180, respectively.

(c) Provide an economic interpretation of the isocost's slope.

Question 2

Consider the following Cobb-Douglas production function for the bus transportation system in a particular city, Q = L1F2K3,

where L is labor in worker hours, F is the fuel input in gallons, K is capital in number of buses, and Q is output measured in millions of bus kilometers. The parameters (, 1, 2, 3) of this model were estimated using annual data for the past 25 years, and the following results were obtained: = 0.0012,1 = 0.45,2 = 0.20, = 0.30.

(a) What type of returns to scale appears to characterize this transportation system?

(b) Explain why, for a Cobb-Douglas production function, returns to scale depend crucially on the sum of exponentials of the inputs.

(c) How does doubling the amount of inputs affect the marginal rate of technical substitution between capital and labor, MRTSK, L?

For questions 3 and 4, select your answer and motivate it with a short comment.

Question 3

A firm employs 100 workers at a wage of $15/h, and 50 units of capital at the cost

of $30/h. It is known in the industry that the marginal product of labor is 60, while the marginal product of capital is 90. We can thus say that the firm is minimizing costs.

Question 4

A firm can employ L and K to produce its final product. Denote with w the price of L and with r the price of K. In the short and long run, a profit-maximizing firm will always choose its input mix based on MRTS = wr.