Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions.
Q = 500L0.6K0.8,
where Q = annual output measured in pounds,
L = labor measured in person hours,
K = capital measured in machine hours.
The marginal products of labor and capital are:
MPL = 300L-0.4K0.8 MPK = 400L0.6K-0.2
Davy's employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Davy forecasts annual costs of $500,000 per year, measured in real dollars.
a. Determine the firm's optimal capital-labor ratio, given the information above.
b. How much capital and labor should the firm employ, given the $500,000 budget? Calculate the firm's output.
c. Davy is currently negotiating with his workers. The firm's personnel manager indicates that the wage may rise to $22.50 under the proposed contract. Analyze the effect of the higher wage on the optimal capital-labor ratio and the firm's employment of capital and labor. What will happen to the firm's output?