In economics, the marginal product (also known as marginal physical product) is the increase in output that results from adding one more unit of a particular input, such as labor or capital, while holding all other inputs constant. The average product (also known as average physical product) is the total output divided by the number of units of a particular input used.

To find the marginal product, we can use the following formula:

Marginal product = Change in total output / Change in the number of units of a particular input

For example, suppose a factory produces 100 units of a product with 10 units of labor and 5 units of capital. If the factory adds one more unit of labor and keeps the capital constant, and as a result, the total output increases to 105 units, the marginal product of labor would be:

Marginal product of labor = (105 units - 100 units) / (1 unit) = 5 units

On the other hand, to find the average product, we can use the following formula:

Average product = Total output / Number of units of a particular input

Continuing with the previous example, the average product of labor would be:

Average product of labor = 100 units / 10 units = 10 units

It's important to note that the marginal product curve usually starts at its maximum and then declines as more units of a particular input are added. This happens because there are usually diminishing returns to a particular input, which means that each additional unit of the input adds less output than the previous one. On the other hand, the average product curve starts at a low level and then increases until it reaches a maximum before it starts decreasing.

To understand the relationship between marginal and average product, we can look at the following example:

Suppose a farmer has a piece of land where he grows crops. At first, the farmer uses only a few units of labor and the total output is low. As the farmer adds more units of labor, the total output increases, and so does the marginal product of labor. However, since the total output is still low, the average product of labor is also low. As the farmer keeps adding more units of labor, the total output keeps increasing, and so does the marginal product of labor. At some point, the marginal product of labor starts decreasing, but the total output is still increasing, so the average product of labor keeps increasing. Finally, the marginal product of labor becomes negative, which means that adding one more unit of labor would decrease the total output. At this point, the average product of labor starts decreasing as well.

In conclusion, the marginal product measures the increase in output resulting from adding one more unit of a particular input, while the average product measures the total output divided by the number of units of a particular input used. Understanding these concepts can help managers and policymakers make informed decisions about how to allocate resources and increase productivity.