Economics: Production Function

Production Function

• The production function expresses the relationship between the quantity of productive factor used and the amount of product obtained.
• The first partial derivatives of output with respect to each of the inputs are positive, indicating a positive relationship between output and inputs (X and Y).
• The second partial derivatives of output with respect to each of the inputs are negative, indicating that the production function has a maximum point.

Concepts of Production

• Total Product: the total output in a given period.
• Marginal Product: the increase in total product due to the addition of one more unit of variable factor.
• Average Product: output per unit of input of variable factors.

Short Run and Long Run

• In the short run, the production function depends largely on labor and capital.
• To increase output in the short run, a firm must increase the amount of labor employed.
• The total product curve shows how total product changes with the quantity of labor employed.
• In the long run, the firm can choose the optimal size of the production capacity that minimizes the cost.

Key Assumptions

• The production function assumes a fixed state of technology, efficient use of input combinations, and a given time period.
• The production function can be represented as Q = F(X, Y), where Q is the output, and X and Y are the inputs (labor and capital).

Revenue and Profit

• Total Revenue is the full amount of total sales of goods and services.
• Marginal Revenue is the increase in revenue that results from the sale of one additional unit of output.
• Profit is the difference between Total Revenue and Total Cost.

Quiz Questions

• What equation expresses the relationship between the quantity of productive factor used and the amount of product obtained?
• What are the two factors of production?
• What is the theoretical objective of a firm?
• What is an increase in revenue that results from the sale of one additional unit of output?
• What is the marginal revenue?
• What is the technical relationship that shows the maximum attainable production levels using different combinations of input?
• What is the relationship between one variable factor and output?
• What is the time period over which the firm can change the quantities of all the inputs?

This quiz covers the production function, its relationship with inputs, and the characteristics of the function. Test your understanding of the first and second partial derivatives of output with respect to inputs.