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

The Total Product (TP) curve represents the relationship between the total output produced and the number of units of a variable input (such as labor) when all other inputs (such as capital) are held constant. The general shape of the TP curve is usually upward sloping, indicating that as more units of the variable input are employed, more output is produced. However, as more input is added, the rate of increase in total output begins to decline, ultimately resulting in diminishing returns. This phenomenon is known as the Law of Diminishing Marginal Returns, and it is usually due to the fixed nature or limited availability of other inputs. Therefore, the total product curve has a positive slope, increasing at a decreasing rate, and exhibiting a concave shape.

The Marginal Product (MP) curve represents the relationship between the change in total output produced and the change in the units of a variable input. In other words, it shows the additional output produced when an additional unit of the variable input is employed. The general shape of the MP curve is upward-sloping at first, followed by an inverted U shape, and then downward-sloping. This is because, initially, as more units of the variable input are added, the marginal productivity increases due to specialization and efficiency. However, as more and more units are added, the marginal productivity starts to decrease, reflecting the diminishing marginal returns derived from the additional units of input. At this point, the MP curve has reached its peak and begins to decline, resulting in a downward-sloping curve. In summary, the Total Product curve has a concave shape, with a positive slope that increases at a decreasing rate, while the Marginal Product curve is upward-sloping with an inverted U shape, followed by a downward-sloping segment. These shapes are reflective of the Law of Diminishing Marginal Returns, which states that as more units of a variable input are employed, holding other inputs constant, the marginal return from the additional variable input will eventually decline.