# What Is a Marginal Physical Product in Economics?

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Marginal Physical Product, or Marginal Product as it is sometimes called, is a central component of modern economics, particularly as it relates to microeconomics. In a nutshell, Marginal Physical Product or MPP, tells you how efficient it is to add additional labor to any production system. MPP relates to any business making any physical goods, ranging from an automobile manufacturer to a part-time home business silk-screening T-shirts. Understanding how to calculate MPP using a basic formula will help to ensure that your business is optimizing production, rather than losing money on unnecessary labor costs.

## What Does Marginal Physical Product Mean?

In any production system, whenever you change the input, the output is affected. When you increase one variable in the input by one unit, while all other variables remain constant, the resulting change in the number of units produced is called Marginal Physical Product.

In most cases, MPP involves labor. For example, if you add one person to a production line, or increase labor by a single hour, the resulting change in how many items were produced would be the MPP. If you added two or three people to an assembly line, or increased labor by two or more hours, you would not be able to accurately determine the MPP for the last person or hour added to the production line. If you added additional equipment to a production line while adding an extra employee, you would not be able to calculate the MPP for that employee because the investment in equipment would also be affecting the formula.

Another economics term, Marginal Revenue Product, is used to describe the change in revenue per item when something in the input is increased. Economists often simplify Marginal Physical Product by calling it Marginal Product. The full term Marginal Physical Product is used, so it's not confused with Marginal Revenue Product.

It’s important to remember that a marginal change only refers to the last change in the production’s input. That is to say, If you add two workers to a production line of ten people, the MPP only measures the change by the twelfth worker. It does not describe the change in production caused by the eleventh person, nor the original first ten workers.

## How MPP Relates to Other Measurements

Marginal Physical Product is related to three other important measurements: Total Physical Product, Average Physical Product and Marginal Revenue Product.

Total Physical Product or Total Product is the total amount of units produced by any production system based on a specific quantity of inputs. If you don’t know the Total Physical Product, you can’t calculate the MPP.

Average Physical Product or Average Product is the average number of units produced by a system as it relates to the number of labor units. You can calculate the Average Physical Product by dividing the Total Physical Product by the number of workers, or by the number of hours if that is what is being measured to determine the MPP.

If you want to determine how much money you will earn by increasing the amount of labor in a production system, you can use the MPP to calculate the Marginal Revenue Product, simply by multiplying the MPP by the amount of money each item sells for. Once you know the Marginal Revenue Product, you can then calculate how profitable the additional labor is by subtracting your costs per unit from the revenue per unit and multiplying that by the MPP.

## Diminishing Marginal Product

In theory, there may be times when increasing the amount of labor will increase the amount of production by the same margin, regardless of how many new units of labor you add. An example of this could be a telemarketing service, provided everyone worked from home where you would not be hampered by limited resources, like a fixed number of cubicles, telephones and computers. In this case, if one person makes 10 sales per day, then having 100 people could increase sales to 1,000 per day and having 200 people could give you sales of 2,000 per day. However, telemarketing sales are not physical products.

When dealing with physical products like widgets, automobiles or sandwiches, several factors beyond labor can affect the number of products being produced. These can include available workspace, capital, equipment and raw materials. Consequently, most MPP changes are described by economists as diminishing marginal returns, or diminishing marginal product. Adding additional labor to any system may increase marginal product at first, but the more you add, the more likely the returns will decline with each additional unit added.

Regardless of what system you use to create a product, as you add more people to that system, employees will eventually be bumping into each other, waiting around to use equipment, waiting for more raw materials to be brought in or waiting for trucks to move the product out of the way. Eventually, MPP may become negative if too much labor is added to a production system, which means the additional worker is reducing output rather than helping to increase it.

## What Is the Marginal Physical Product Formula?

Before you can calculate the MPP, you must first know what the total physical product was before you changed the input and what the total was afterward. Subtracting the initial production from the current production will give you the change in the total physical product produced. You can then divide this by the change in the input to get the marginal physical product:

MPP = (change in total product) / (change in input)

## Marginal Physical Product Example

If you had 10 people working on a production line and increased that to 12 people, basic math might suggest that you should be able to produce 20 percent more of the same product. In reality, however, this is seldom what happens. In most cases, Total Physical Product will increase with each additional worker you add, however, it won't increase by the same amount.

Suppose you own a take-out sandwich shop. Every weekday, lunch hour is your busiest time, and you have a line of customers going out the door and down the street as they wait to order their sandwiches. You currently have three employees working behind the counter making the sandwiches and working the till. Each lunch hour, you sell an average of 84 sandwiches. You want to know if you can increase production if you add another employee to the line.

At one time, you had only two workers behind the counter, and you made, on average, 62 sandwiches at lunch hour. Using the formula for MPP, you determine that making an additional 12 sandwiches with a third employee has given you 12 additional sandwiches – simply by dividing the change in production of 12 by the change in employees, which is one.

MPP = (change in total product) / (change in input)

MPP = 12/1

MPP = 12

So you decide to hire an additional employee for the lunch hour, suspecting that having a fourth employee will increase your production by another 12 units. However, at the end of the week, you find that your average production per day is 92, rather than 96, which is an MPP of eight (MPP = 8/1).

There may be any number of reasons, or a combination of reasons, why your new MPP is lower than the last. Perhaps your new employee is not as motivated as your others, or she has not been adequately trained. Maybe having only one cash register has limited the number of sandwiches you can produce in one hour. There may no longer be enough room behind the counter for all of the employees to service the customers. Perhaps some of the other employees are working more slowly because they are taking advantage of the extra pair of hands.

After watching your employees working for a few more days, you wonder if having an even number of employees was the problem. When there were three, you noticed that two worked as a team while the third worked the cash register. With four employees, you suspect that their timing is off now. So you decide to try having five people behind the counter and the lunch counter increases its productivity to an average of 99 each lunch hour, an increase of seven sandwiches. This makes the MPP of your newest employee seven units (MPP = 7/1).

If you were to plot the change in MPP as you add more employees, you would see that it creates a downward slope, with the MPP of each subsequent employee being less than the one before:

• third employee: 12
• fourth employee: 8
• fifth employee: 7

Because you charge \$8.50 for every sandwich, you can easily calculate the MPP as \$59.50 (\$8.50 x 7) Depending on your profit margin; it may be worthwhile to keep the fifth employee on staff. However, adding a sixth employee will likely not be worthwhile. Other alternatives, like adding a second cash register, moving to a larger location or introducing a pay-by-phone service may be better ways to increase production at this point.

If you were to add additional employees, without changing anything else about your lunch counter setup, you would likely find that each new employee will result in a lower MPP, looking something like this:

• third employee: MPP = 12
• fourth employee: MPP= 8
• fifth employee: MPP = 7
• sixth employee: MPP = 6
• seventh employee: MPP = 4

Note that in each case, your Total Physical Product increases by the marginal rate. You were making 99 sandwiches each day with five employees, so adding a sixth employee would increase that to 105 while adding a seventh employee would increase your Total Physical Product to 109.

As your MPP declines, so does your Average Physical Product. When you divide your Total Physical Product by the number of workers, the Average Physical Product looks like this:

• three employees:  84/3 = 28
• fourth employee: 92/4 = 23
• fifth employee: 99/5 = 19.8
• sixth employee: 105/6 = 17.5
• seventh employee: 109/7 = 15.6

## Projecting Data to Other Scenarios

Increasing labor to a total of 20 employees would likely give you no measurable increase in the MPP, and may even decrease the MPP, due to the congestion and confusion in your restaurant.

If you were to lay off all of your employees except two, or if they all quit because they were overworked, you can use this data to estimate how far your production would fall – most likely to an Average Total Production between 20 and 25, making a total of 40-to-50 sandwiches each lunch hour.

In most cases, adding additional labor into a production system is not the only solution you should consider. Optimizing the current system by updating or replacing equipment, changing the workspace layout or otherwise increasing worker efficiency are often good ways to increase production while also increasing revenue and profits.