Question

What shapes would you generally expect a total product curve and a marginal product curve to have?

Short answer

The general shape of the total product curve can be described in three stages: (1) increasing at an increasing rate and concave up due to increasing returns to scale, (2) increasing at a decreasing rate with a concave shape due to diminishing returns to labor, and (3) negatively sloped when the total product declines as a result of too much labor used. The marginal product curve also has three stages: (1) starting with a downward slope due to increasing returns to scale and labor productivity, (2) declining at a slower rate reflecting diminishing returns to labor, and (3) becoming negative when more labor causes a decrease in total output.

Step-by-step solution

1. Total Product Curve

The total product curve represents the relationship between the total output produced and the quantity of a single input, typically labor, used in production. The general shape of the total product curve can be described in three stages: Stage 1: The total product curve increases at an increasing rate as more units of labor are added. This part of the curve is concave up, due to increasing returns to scale. Stage 2: The total product curve continues to increase but at a decreasing rate, as more units of labor are added. This stage ends when the total product reaches its maximum value. The curve becomes less steep and starts bending downwards, indicating diminishing returns to labor, and is described as having a concave shape. Stage 3: The total product curve starts to decline as more units of labor are added. In this stage, the curve becomes negatively sloped because the marginal product of labor becomes negative. This is a result of too much labor being used relative to the available resources (e.g., capital, space).

2. Marginal Product Curve

The marginal product curve represents the additional production obtained from using one more unit of labor. It can be derived from the total product curve by calculating the first derivative of total product with respect to the number of labor units. The general shape of the marginal product curve can also be described in three stages: Stage 1: The marginal product curve starts at a high level and declines as more units of labor are added, due to increasing returns to scale and the increasing productivity of labor. The curve is downward sloping in this stage. Stage 2: The marginal product curve continues to decline, but at a slower rate compared to the first stage, reflecting diminishing returns to labor (productivity decreases, but the output is still increasing). The slope of the curve becomes less steep. Stage 3: The marginal product curve eventually becomes negative when the value of the marginal product of labor decreases with the increase in labor units. At this point, adding more labor causes a decrease in total output, reflecting negative marginal product of labor. In summary, the typical total product curve has a concave up shape in the first part, becoming concave down as it reaches its maximum and then declining in the third part. The typical marginal product curve starts with a downward slope and becomes less steep before eventually turning negative.