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Defining and Calculating Marginal Physical Product (MPP) and Marginal Revenue Product (MRP)

Here are some important terms to know:
Marginal Physical Product (MPP)-The physical output that is due to the addition of one more unit of a variable factor of production.  The change in total product occurring when a variable input is increased and all other inputs are held constant.  (Also known as marginal product)
Law of diminishing marginal product: The observation that after some point, successive equal-sized increases in a variable factor of production, such as labor, added to fixed factors of production will result in smaller increases in output.
Marginal Revenue Product (MRP): The marginal physical product (MPP) times marginal revenue (MR) obtained from a one-unit change in labor input.

Now let’s put these terms into use by solving some sample problems…
Sample Problem: Calculating Marginal Physical Product (MPP)
A bakery owner is considering how many bakers it needs each day.  If there are no bakers working, then 0 donuts will be produced that day.  If one baker is working, then 20 donuts will be produced that day.  If two bakers are working, then 50 donuts will be produced that day.  If three bakers are working, then 75 donuts will be produced that day.  Calculate the marginal physical product of each quantity of labor (bakers, in this case).
Remember that the marginal physical product is the change in output due to the increase in one variable factor of production, which are bakers in this example.
To calculate the MPP of Baker 1, we need to know that the previous output was 0 and now the new output is 20 donuts.
MPP of Baker 1 = 20 – 0 = 20
To calculate the MPP of Baker 2, we need to know that the previous output was 20 donuts and is now 50 donuts with the addition of the second baker.
MPP of Baker 2 = 50 – 20 = 30
Using the same methodology for the third baker:
MPP of Baker 3 = 75 – 50 = 25

Notice that the MPP of baker 3 is experiencing diminishing returns, since the MPP has fallen from 30 to 25 when adding the 3rd baker.

Sample Problem: Calculating Marginal Revenue Product (MRP)
Using the problem above, let’s say that the donuts sell for $2 each.  To calculate the MRP for each input level (number of bakers), we take the MPP we calculated above and multiply it by the marginal revenue.  The marginal revenue is the price that the donuts sell for.
MRP of Baker 1 = MPP x MR = 20 x 2 = 40
MRP of Baker 2 = 30 x 2 = 60
MRP of Baker 3 = 25 x 2 = 50
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