6.7 : Relation between Total Product, Marginal Product and Average Product

In the short run, a firm manufactures a product using a fixed amount of capital and varying numbers of workers. Its total product (TP) shows how much output can be produced in a specific period for each combination of labor and capital. Since capital is constant, the output varies with labor. Marginal product (MP) measures the additional output produced by adding one more unit of labor. It is calculated as the change in output divided by the change in labor quantity (ΔTP/ΔL). Average product (AP) represents the output per unit of labor. It is calculated by dividing TP by the total units of labor employed (TP/L).

The production process typically exhibits three stages. In the first stage, characterized by increasing marginal returns, the positively sloped TP curve ascends sharply and is convex to the origin. In this stage, the MP curve also rises, reaching its peak at the end of stage one. When the MP curve is greater than the AP curve, this raises the AP curve as the variable input is increased.

In the second stage of diminishing marginal returns, the TP curve continues to rise as the variable input is increased, but at a diminishing rate, causing the TP curve to become concave. As the MP curve falls, it eventually becomes equal with the AP curve, causing the AP curve to reach its peak. As the MP curve continues to decline, it eventually becomes zero and the end of stage two.

In the third stage, marked by negative marginal returns, the TP curve has already peaked and is now decreasing because the MP curve is negative throughout this stage. The AP curve continues its decline.

Key relationships between these concepts include: when MP exceeds AP, AP is rising; when MP is less than AP, AP is falling. The MP curve intersects the AP curve at the AP's maximum point. These relationships are crucial for firms to understand as they optimize production decisions and resource allocation in the short run.