A Firm Has the Production Function Q = K⁰

question 22

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 for the following:
a. to derive the demand for capital
b. to confirm that the demand for capital satisfies the law of demand
c. What is the optimal level of capital if the rental rate on capital is $25?

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Definitions:

Marketing Research

The process of gathering, analyzing, and interpreting information about a market, about a product or service to be offered for sale in that market, and about past, present, and potential customers for the product or service.

Sampling

The process of selecting a subset of individuals, items, or data from a larger population or set to estimate characteristics or outcomes of the whole group.

Representative Elements

Chemical elements found in groups 1, 2, and 13-18 of the periodic table, characterized by their wide range of physical and chemical properties.

Population

The total number of people within a specific area or region.