Biology Forums - Study Force

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 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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