How to Calculate MPK

Marginal product of capital, or MPK, is an economic term that describes the incremental change in production when there is an increase in capital by one unit. If this statement doesn't automatically make sense to you, then you're probably not an economist.

MPK as well as MPL (marginal product of labor) can be valuable for any small business looking to increase production because it shows you whether or not the extra investment will return enough to cover the increased costs.

TL;DR (Too Long; Didn't Read)

MPK can be calculated as the change in total production divided by the change in capital assuming that no other adjustments to production have been made, including changes in labor.

Minding Your Ks and Ls

To understand MPK, it helps to see a company as a system like a machine. If you feed time and money into the company, then the company produces goods or services. The more time and money you put in, the more goods or services the company should produce.

Of course, the time you invest in a company isn't always your own, so it's best to refer to time as labor (L). Similarly, the money you put into a company isn't always your own either. Because you may borrow that money, it's best to refer to money as capital (K).

So, instead of saying that you put time and money into a company to produce goods and services, you can now say that you input capital (K) and labor (L) to get an output of goods or services. Now you're talking more like an economist!

How to Calculate Marginal Product of Capital

Marginal product of capital can be calculated very easily if you know what the change in output will be based on your increased expenditure. In order for this formula to work, there should not be any other changes to production except capital:

MPK = Change in Total Product Output / Change in Capital

or

MPK = Δ P / Δ K

For example, suppose you own a small manufacturing plant that produces 20,000 units every month. You can lease additional equipment for $5,000 each month, resulting in an increased production of 30,000 units. Your change in output is 10,000 units at a cost of $5,000 for the same period:

MPK = (30,000 - 20,000) / $5,000

MPK = 10,000 / $5,000

MPK = 2

In other words, every dollar invested gives you an increased production of two units. If your profit per unit was just one dollar, your investment would be doubled. However, if you were only making 10 cents profit per dollar, then this equipment would hardly be a good investment.

Marginal Product of Labor: MPL Formula

The marginal product of labor is much the same as the marginal product of capital. If you increase the amount of labor in production, assuming you don't make any other changes including changes in capital, then you can determine the incremental change in production based on one unit of labor.

Labor can be expressed as the number of employees, the number of hours put into production or any other unit that makes sense for your circumstances. Thus, the value of marginal product of labor can be expressed as:

MPL = Change in Total Product Output / Change in Capital

or

MPL = Δ TP / Δ L

For example, if you decided to add a second shift to your production facilities consisting of 10 workers and this increases production from 20,000 units per month to 40,000 units, this would work out to be:

MPL = (40,000 - 20,000) / 10

MPL = 20,000 / 10

MPL = 2,000

Whether or not this is worthwhile will depend on the profit you make from each unit compared to the cost of each employee. If each employee costs you more than what you make from 2,000 units, it would not be a wise decision.