# How to Calculate the Point of Diminishing Returns

psphotograph/iStock/Getty Images
Share It

The law of diminishing returns is an economist's way of saying that sometimes, you can have too much of a good thing. This is true about most things in life, not just in business. If you're hungry, a cookie may be very satisfying, but by the time you get to the bottom of the bag, it's likely that you will find that your pleasure in eating has been diminished.

In business, you have two main resources: time and money. A key part of being successful is knowing how much time (or labor) and money to invest in a project without either being wasted, and that is identifying the precise point of diminishing returns.

## Law of Diminishing Returns Equations

Unfortunately, there is no magic diminishing returns formula that will tell you how much you should increase your resources without hitting the point of diminishing returns. However, once you understand how production functions work, you can apply their principles to your own production.

A production function shows you the relationship between money and labor and how they affect the output of production or services. These can be very simple formulas, or they can be quite complex depending on how many different variables are involved.

## Simple Production Functions

A simple production function maps production only to labor or capital. If someone can stuff 100 envelopes an hour, the quantity (Q) becomes a function of the units of labor (L), measured in hours:

Q = 100 L

If you had two people working, then they would produce 200 every hour, while one person working two hours would also produce 200 finished envelopes. If you were to plot this on a graph, you would get a straight line since every increase in labor results in a proportional increase in production.

A linear production function does not give you a point of diminishing returns. However, it is a good way to quickly estimate production based on changes in labor or capital.

## Multifactor Production Functions

A more realistic production function is multifactor in that it maps production to two or more variables, like labor and capital (K). Additionally, the function takes into account that increasing one factor will not increase production proportionately.

If you were stuffing envelopes for two hours, for example, it's likely that you could double your production compared to one hour, but what would happen if you planned to work 18 hours each day? Fatigue would eventually set in, and your production would drop. Similarly, putting two people in the same room to work could double production, but this doesn't mean that putting 100 people in that room would give you 100 times the production — far from it.

Consequently, it's more realistic to use a multiplier, or component, on each variable in your equation, such as this:

Q = 100 K aL b

The multipliers "a" and "b" should be fractions. However, what these fractions might be will depend on the situation. Note that if you increase only one variable in a multifactor equation, your production will immediately diminish, while if you increase both variables proportionately, production will increase at a linear rate.

## Calculating the Point of Diminishing Returns: Example

To calculate a point of diminishing returns, imagine that you have a team of four workers packing boxes on a conveyor belt. You want to increase the number of workers to increase production without going beyond the point of diminishing returns.

## Identify the Most Limiting Variable

In any system, there is always one variable that will put a ceiling on production regardless of what other changes you make. In this example, it could be that only 10 workers could physically stand alongside the conveyor belt at any one time. Your point of diminishing returns will therefore be 10 workers or less.

## Record Your Production

With four workers, record their production rate. In this example, let's assume that after a week, they average 100 packed boxes per hour, or 25 per worker.

## Increase the Variables Incrementally

Add another worker to the production line and after she goes through her learning curve, record the production. If production is still 25 boxes per hour per worker, you can increase the labor variable again by putting six people on the line.

As soon as production slips below 25 boxes per worker, you have reached the point of diminishing returns. If you added more labor to the line, each additional person will give you less production per person per hour.

At this point, in order to efficiently increase production, you would have to start increasing capital by adding a second conveyor belt, leasing a second plant, etc.

#### About the Author

A published author, David Weedmark has advised businesses on technology, media and marketing for more than 20 years and used to teach computer science at Algonquin College. He is currently the owner of Mad Hat Labs, a web design and media consultancy business. David has written hundreds of articles for newspapers, magazines and websites including American Express, Samsung, Re/Max and the New York Times' About.com.

#### Photo Credits

• psphotograph/iStock/Getty Images