Question

The auto maker Carbon Motors produces cars using capital (K) and labor (L) according to theproduction functionf(K, L) =K3/4L1/4. A different car company, Emissions Inc, producescars according to the production functionf(K, L) =K1/2L1/2. The wage rate paid to workersiswand the price of capital isr.(a) Find the cost minimizing input choices of Carbon and Emissions subject to producingqcars. (These will be functions ofw,r, andq.) For the same level of output, which companyemploys more workers?(b) Use the input demand functions from part (a) to obtain each company’s cost as a functionof the number of cars produced.(c) The manufacturing facilities of Emissions Inc happen to be located in a country withample 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 rateof capital of $5. Use these values in the cost function you found in part (b). Find theaverage 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 isocostcurve 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 ofLandKis affected.

Answer 1