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# Determine the quantity of labor

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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.

https://brainmass.com/economics/output-and-costs/determine-the-quantity-of-labor-25628

#### Solution Preview

In the short run K=160,000,
then q = 2.5L^(1/4)*( 160,000) ^(1/2) = 2.5L^(1/4)*400 = 1000 L^(1/4)
the firm's profit function is ...

#### Solution Summary

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.

\$2.49