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A firm has a technology described by the production function:

q = 2.5 L1/4K1/2

where L is the number of labor units per period and K is the number of square feet of floor space and machines per period, and q represents firm output. The firm faces the following output and input prices on the market, and these are fixed to this firm:

Output price: $100.0/unit
Wage rate: $25.00/labor unit
Capital cost/unit: $2.50/sq. ft.

1. In the short run this firm has 160,000 square feet of floor space, all of which is to be used for production. Determine the quantity of labor demanded by the firm, the K/L ratio, output produced and profit to the firm.

2. If the firm holds its short run production level but can vary the amounts of labor and capital it uses, determine the quantity of labor demanded by the firm, the cost minimizing K/L ratio, and profit to the firm.

3. Determine the quantity of labor demanded by the firm, the cost minimizing K/L ratio, output produced and profit to the firm in the long run, when capital, labor and output can all be varied.

4. Determine the output and usage of capital and labor if the wage rate increases by nine per cent. Using this information and that obtained in question 3. above (assume p=$100.00 and v=$2.50), determine the amount of the change in labor usage due solely to the change in the wage rate. Then determine the amount of change in labor usage due solely to the change in the output level. In other words, determine the substitution and output effects of the wage increase.

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Solution Summary

Determine the quantity of labor demanded by the firm, the cost minimizing K/L ratio, output produced and profit to the firm in the long run, when capital, labor and output can all be varied.

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2. If the firm holds its short run production level but can vary the amounts of labor and capital it uses, determine the quantity of labor demanded by the firm, the cost minimizing K/L ratio, and profit to the firm.

This is a cost-minimization question:
The firm will produce at the output level Q = 10,000 by varying K and L.
The cost-minimization condition is:
MPk / r = MPl/w
or MPk / ...

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