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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Definitions:

Deep Discount

The sale of an asset or product at a price significantly below its usual or intrinsic value.

Coupon Payments

Periodic interest payments made to bondholders, typically on a semi-annual basis, based on the coupon rate of the bond.

Municipal

Relating to a city or town or its governing body.

Sinking Fund

A reserve fund established by a company to set aside revenue over time for the purpose of paying off debt or replacing a major asset in the future.