Short Run Production Analysis Quiz

Relationship between TP curve, APL, and MPL in the Short Run

Total Product of Labor (TPL)

Total Product of Labor (TPL) is the production function that shows the total output (Q) in the short run, given the variable input while holding capital constant. It is a measure of how much output can be produced with a certain amount of labor input.

Average Product of Labor (APL)

Average Product of Labor (APL) is the ratio of total output to the number of laborers used to produce it. It is calculated as the total output divided by the number of laborers (Q/L). APL represents the average productivity of labor at a particular level of employment.

Marginal Product of Labor (MPL)

Marginal Product of Labor (MPL) is the extra output produced by adding one more unit of labor input. It is calculated as the change in output (∆Q) divided by the change in labor input (∆L). MPL represents the productivity of the last unit of labor added to the production process.

Relationship between TP, APL, and MPL

The relationship between Total Product (TP), the Average Product of Labor (APL), and the Marginal Product of Labor (MPL) in the short run can be summarized as follows:

1. Increasing Returns to Labor: When the Total Product (TP) increases at an increasing rate, both the Marginal Product of Labor (MPL) and the Average Product of Labor (APL) increase as well.

2. Diminishing Returns to Labor: When the Total Product (TP) increases at a diminishing rate, both the Marginal Product of Labor (MPL) and the Average Product of Labor (APL) decrease.

3. Maximum Output: When the Total Product (TP) reaches its maximum point, both the Marginal Product of Labor (MPL) and the Average Product of Labor (APL) become zero.

4. Negative Marginal Product: When the Total Product (TP) starts decreasing, the Marginal Product of Labor (MPL) becomes negative, while the Average Product of Labor (APL) remains positive.

Marginal Rate of Technical Substitution (MRTS)

The Marginal Rate of Technical Substitution (MRTS) is the ratio of the Marginal Product of Labor (MPL) to the Marginal Product of Capital (MPK). It measures how efficiently a firm can substitute one input for another while maintaining the same level of output. The MRTS is equal to the ratio of the two marginal products, MPL/MPK.

Analysis of a Chair Manufacturer's Production Function

An example of a chair manufacturer's production function in the short run shows how the relationship between TPL, APL, and MPL can be observed. As the number of laborers used in the production process increases, the number of chairs produced changes: 10, 17, 22, 25, 26, 25, 23. This production function exhibits diminishing returns to labor, as the marginal product of labor diminishes as workers are added, and is actually negative for the sixth and seventh workers.

Practical Implications

Understanding the relationship between Total Product (TP), the Average Product of Labor (APL), and the Marginal Product of Labor (MPL) in the short run is crucial for businesses to make informed decisions about their production processes. By analyzing these productivity measures, firms can optimize their resource allocation, minimize costs, and maximize output.