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Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for...

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.

Construct the isocost equation.
Draw isocost lines when budgets are $500,000 and $600,000. (Y-Axis is Capital and X-Axis is Labor)
Determine the firm's optimal capital-labor ratio (K/L), given the information above.
How much capital and labor should the firm employ, given the $500,000 budget?
Calculate the firm's output.
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. 1) Analyze the effect of the higher union wage on the optimal capital-labor ratio and the firm's employment of capital and labor. 2) What will happen to the firm's output?

Expert Solution

The production function would be as .

(a) The isocost equation would be as or .

(b) The isocost lines for the stated costs would have the equation or . The graph would be as below.

(c) The optimal capital labor ratio would be where or or or or .

(d) For the isocost be and the optimal capital labor ratio as or , we have or or , and since , we have or or .

These are the required optimal input combination for the given budget.

(e) The output would be as or or units.

(f) (1) The capital labor ratio would be as where or or or or or . As can be seen, the optimal capital per labor required increased.

(f) (2) Putting this in the isocost line, we have or or or and or or . The output in this case would be or or units.

As can be seen, the output has decreased due to increase in the wages.

Rahul Sunny answered 6 months ago

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