Question

The auto maker Carbon Motors produces cars using capital (K) and labor (L) according to the production function f(K, L) =K^3/4L^1/4. A different car company, Emissions Inc, produces cars according to the production function f(K, L) =K^1/2L^1/2. The wage rate paid to workers is w and the price of capital is r.

(a) Find the cost minimizing input choices of Carbon and Emissions subject to producing q cars. (These will be functions of w ,r, and q.) For the same level of output, which company employs more workers?

(b) Use the input demand functions from part (a) to obtain each company’s cost as a function of the number of cars produced.

(c) The manufacturing facilities of Emissions Inc happen to be located in a country with ample labor, which has led to a lower wage rate. The wage rate faced by Emissions is $10per hour while the wage rate faced by Carbon is $20 per hour. Both face a rental rate of capital of $5. Use these values in the cost function you found in part (b). Find the average and marginal cost functions for each company.

(d) What are the input choices of Carbon and Emissions if each were producing ten cars? What is the cost of each firm of producing ten cars? In separate graphs, draw the isocost curve and isoquant curve for each firm at the cost minimizing input mix.

(e) If the wage rate faced by Carbon were to fall to $10 per hour, use your graph from part (d) to show how Carbon’s choice of L and K is affected.

Answer 1

TC for CM = 124.08

For EI = 141.42

Graph

For CM

For EI