Suppose the Production Function for a Coffee Shop Is

question 120

Essay

Suppose the production function for a coffee shop is:
Q = 2K + 5L
where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. Use calculus to:
a. determine a function for the marginal product of labor.
b. determine a function for the marginal product of capital.
c. find the marginal rate of technical substitution.
d. discuss how MRTS_LK changes as the firm uses more labor, holding output constant.

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Definitions:

Average Cost

This is the total cost divided by the number of goods produced, representing the cost on average for each unit produced.

Marginal Cost

The financial commitment for producing one more unit of a product or service.

Franchise

A type of license that grants a franchisee access to a franchisor’s proprietary knowledge, processes, and trademarks, allowing them to sell a product or service under the business's name.

Supply Curve

A graph showing the relationship between the price of a good and the amount of the good that producers are willing to supply.