A Firm Has the Production Function Q = K⁰

question 90

Essay

A firm has the production function Q = K^0.1L^0.9, where Q measures output, K represents machine hours, and L measures labor hours. Suppose that the wage rate is $45, and the firm wants to produce 100,000 units of output. Use calculus to:
a. derive the demand for capital.
b. confirm that the demand for capital satisfies the law of demand.
c. determine the optimal level of capital if the rental rate on capital is $25.

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