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 = 500L^0.6K^0.8,
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:
MP_L = 300L^-0.4K^0.8 MP_K = 400L^0.6K^-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 a newly organized union. The firm's personnel manager indicates that the wage may rise to $22.50 under the proposed union contract. Analyze the effect of the higher union wage on the optimal capital-labor ratio and the firm's employment of capital and labor. What will happen to the firm's output?

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The Answer of 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 = 500L^0.6K^0.8, 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: MP_L = 300L^-0.4K^0.8 MP_K = 400L^0.6K^-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 a newly organized union. The firm's personnel manager indicates that the wage may rise to $22.50 under the proposed union contract. Analyze the effect of the higher union wage on the optimal capital-labor ratio and the firm's employment of capital and labor. What will happen to the firm's output?

Davy Metal Company Produces Brass Fittings