If the short run total product curve is a linear function of the variable input over some range of values. Describe the shape of the marginal product and average product functions.

I am guessing that the marginal product is constant, which a horizonal line. What about the average product, what does it look like?

The shape of the average product curve cannot be determined given the info you provided. It depends on whether the marginal product curve was rising or falling on production points before examining this special, short run section.

then what will it look like if MP is rising? and falling?
thanks.

What do Product curves reflect?

Product curves, such as the total product, marginal product, and average product curves, reflect the relationship between the quantity of input (usually labor) and the level of output produced in the short run. They showcase how changes in input affect the productivity of the production process.

Specifically:

1. Total Product (TP) Curve: This curve shows the total output produced by varying levels of input. It represents the overall productivity of the production process. The shape of the TP curve depends on the specific production technology and can vary, but it generally has an upward-sloping section that eventually becomes flatter due to diminishing returns.

2. Marginal Product (MP) Curve: It represents the additional output produced by adding one more unit of input. Mathematically, it is calculated as the derivative of the total product curve with respect to input. If the short-run total product curve is a linear function, the MP curve would be a horizontal line since the slope of a linear function is constant at any point.

3. Average Product (AP) Curve: It shows the average output produced per unit of input. It is calculated as the total product divided by the corresponding quantity of input. The shape of the AP curve depends on the relationship between the TP and MP curves.

- If the MP curve is rising, the AP curve will be increasing. This is because the additional input is contributing more output than the average, leading to an improvement in average productivity.
- If the MP curve is falling, the AP curve will be decreasing. In this scenario, the additional input is contributing less output than the average, causing a decline in average productivity.

Therefore, without additional information about the behavior of the MP curve, we cannot determine the shape of the AP curve.