University of South Carolina, Norman J. Arnold School of Public Health, Dept. of Health Administration, Economics Interactive Tutorials, October 30, 2000

Economics Interactive Tutorial (Instructions)

Average Cost

The Average Cost is the Total Cost divided by the rate of output.

This tutorial

discusses average cost, and
gives some typical uses of the average cost concept, and
shows the distinction between average cost and marginal cost.

Average cost example

Imagine that your factory has an annual fixed cost of $1 million ($1,000,000), for interest, utilities, taxes, etc. Your factory makes plastic toys.
Suppose the marginal cost of producing one toy is $1. Enable Java on your computer to use this applet.
What is the average cost per toy if you make just 1 toy a year?
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Once you have that one right, try this one:
For that same factory, what is the average cost of producing 2 toys per year?
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It's easy to confuse average cost with marginal cost. Marginal cost is the cost of adding or subtracting one unit of output.

The average cost includes a portion of the fixed cost, as well as variable cost. The marginal cost includes only variable cost.

Table Representation of Average Cost

I'll use the Joan's Home Care numerical example from the preceding interactive tutorials.

In the table below, I put the marginal cost between the columns, because it is calculated by comparing two output rates. Average cost goes directly in the columns. Average cost is is calculated from cost information at one output rate. You divide the total cost of that output rate by the amount produced.

Number of Patients per Year:
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333

The average cost of serving 3 patients, for example, is ...

The average cost can tell you whether you are breaking even -- whether your total revenue is covering your total cost. Try this True or False question:
Suppose that the firm charges all of its patients the same price. True or False: The firm is making a profit if, and only if, the average cost is less than this price.

Let's do a numerical example that shows this. The example also illustrates break even analysis.

Number of Patients:
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Total Revenue: = number of patients times the price, $3200
$ 0 3200 6400 9600 12800 16000 19200 22400 25600 28800

This table shows Joan's costs and revenues if patients pay $3200 each.
Joan's breaks even or makes a profit at some output rates,
that is, at some numbers of patients served per year.
Your question is: What is the lowest output rate at which Joan's at least breaks even? (Click for definitions of revenue, cost, and profit.)
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And, what is the highest output rate that's profitable for Joan's?
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If you had trouble with those, better check your definitions of Revenue, Cost, and Profit.

Revenue
Total Revenue is the total amount of money received at any given output rate. It is the price multiplied by the quantity of output.
Cost
Total Cost is the cost of maintaining any given output rate. This generally comes from a table or a calculation, because it is the sum of the fixed cost and the variable cost.
Profit
Profit is total revenue minus total cost.
(If you jumped down here to get these definitions, click here to jump back to your question.)

The Break Even Point

The break even point is, in the usual usage, the lowest output level at which total revenue exceeds total cost. That's because most new business fail by selling too little, not by selling too much. The break even point tells you the minimum you have to do to make your enterprise viable.

We have already seen that the break even point for Joan's is 4, and that profitable output rates range from 4 to 8. The numbers for those output rates are in boldface in this table:

Number of Patients per Year:
0 1 2 3 4 5 6 7 8 9

Total Revenue: = number of patients times price patients pay ($3200)
$ 0 3200 6400 9600 12800 16000 19200 22400 25600 28800

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Profit (= Revenue minus Cost)
$-1000 -1300 -1100 -400 800 1500 1700 1400 600 -1200

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333
Average cost less than $3200.

Profit is positive if and only if average cost is less than the price patients pay. Thus, we can judge whether the firm breaks even either by looking at total revenue and total cost or by looking at price and average cost.

That means you have two ways that you can present a break even analysis.

You can compare revenue with cost at a range of output rates, or
You can compare price with average cost at a range of output rates

We can apply this principle to show what happens to the break even point in a competitive industry if more and more firms enter the market and drive the price down.

Here is the cost table, again:

Number of Patients per Year
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333

Let's start our example with a high price: $4200.

What is Joan's break even point, based on that price and the costs above?
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Here is the cost table, yet again:

Number of Patients per Year
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333

Where does Joan's average cost bottom out? At what output rate is Joan's average cost minimized?
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True or false: A firm should always choose the output level at which its average cost is the least.

The cost table yet again:

Number of Patients per Year
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333

What is the number of patients that gives Joan's the most profit, if the price patients pay is $4200?
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I'm deliberately switching back and forth between marginal cost and average cost, to better bring out the distinction between them.

Average cost tells you if you are making or losing money.
Marginal cost doesn't tell you that, but it does tell you how to increase or decrease your profit.

Effect of new entry into the market

Suppose that new firms, attracted by the easy profit, enter the home care industry in Joan's area. More firms try to serve more patients. Suppose this drives price per patient down to $3200. (Home care markets don't always respond to changes in supply, because Medicaid, with its politically-set prices, can dominate on the demand side. Let's suppose, for the sake of this illustration, that there is price competition anyway.)

The cost table again:

Number of Patients per Year
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333

Now what is Joan's break even number of patients, after the price has fallen to $3200?
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Number of Patients:
     0      1      2      3      4      5      6      7      8      9
                                 |-----Profitable range-->?
Total Cost:
$ 1000   4500   7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333

What is the top end of the profitable range, the most patients Joan's can serve and still make a profit, if the price patients pay is $3200?
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The profitable output range shrinks as the price falls. When the price was
$4200, profitable output rates were 2 through 9. As the price falls, Joan's leeway is reduced.

Number of Patients:
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333

What would be a price for which the break-even or make-profit output rate range would be just 5 to 6 patients per year?

There is a range of correct answers. I'll accept as correct any number in that range.

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As new firms flood into the home care market, the price patients have to pay will be bid down further and further.

What price is so low that the best Joan's can do is just break even?

Number of Patients:
0 1 2 3 4 5 6 7 8 9

Total Cost:
$ 1000 4500 7500 10000 12000 14500 17500 21000 25000 30000

Marginal Cost: = difference in Total Cost
$ 3500 3000 2500 2000 2500 3000 3500 4000 5000

Average Cost: = Total Cost ÷ Number of Patients
$ ---- 4500 3750 3333 3000 2900 2917 3000 3125 3333
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If competition in the industry drives the price down this low, this will squeeze the profit out of the industry, assuming that Joan's costs are typical.

If the price falls this low, and profits disappear, new firms will stop entering this market, and some established ones may fold.; This will make the supply stop growing and the price stop falling.

In an ideal theoretical competitive market, the freedom to set up a new business firm guarantees that the consumers' demands for products and services will be met at the lowest possible costs and prices.

Those prices will be at (or just above) the minimum level of average cost.

This is called consumer sovereignty.

Innovation to stay ahead, temporarily

There's another way that Joan's might deal with a low price for her product. That would be to reduce her minimum average cost below $2900. A typical way to do that would be to buy labor-saving equipment. Her fixed cost would go up (paying off the loan that enabled her to buy the equipment), but variable cost would go down (less labor means less paying less in total wages.)

Below is what Joan's costs might look like now:
Can Joan's now make profit if the price is $2900?

Number of Patients: 0 1 2 3 4 5 6 7 8 9

Total Cost: $ 2000 5600 8500 10700 12200 14000 16100 18500 21200 24700

Marginal Cost: = difference in Total Cost $ 3600 2900 2200 1500 1800 2100 2400 2700 3500

Average Cost: = Total Cost ÷ Number of Patients $ ---- 5600 4250 3567 3050 2800 2683 2643 2650 2744

Can Joan's now make profit if the price is $2900?

How many patients should Joan's serve to maximize profit at the $2900 price?

With the old technology, Joan's treated 5 patients and just broke even, when the price was $2900.
With the new cost-cutting technology, Joan's expands her output rate to 8.

If all the firms in the industry adopt the new technology, so that all the firms have costs just like Joan's, then every firm will try to expand its output just as Joan's did. Which way will the price go?

My analysis assumes that there is price competition in this market. By contrast, Brown, M.L., Kessler, L.G., Reuter, F.G., "Is the Supply of Mammography Machines Outstripping Need and Demand?" Annals of Internal Medicine, October, 1, 1990, 113(7), pp. 547-552, found that prices of screening mammograms stayed high despite a great increase in supply, because there was no price competition. I am assuming a textbook type of perfect competition in the market that Joan's is in.

Suppose, though, that competition doesn't work, and the price stays up at $2900. In that case, the firms will want to treat 8 patients each, but there won't be enough patients to go around. Many will have to settle for fewer than 8 patients. What is Joan's minimum break even output rate?

Number of Patients: 0 1 2 3 4 5 6 7 8 9

Total Cost: $ 2000 5600 8500 10700 12200 14000 16100 18500 21200 24700

Marginal Cost: = difference in Total Cost $ 3600 2900 2200 1500 1800 2100 2400 2700 3500

Average Cost: = Total Cost ÷ Number of Patients $ ---- 5600 4250 3567 3050 2800 2683 2643 2650 2744

That should be plenty on the break even output rate and the profit maximizing output rate! Thanks for participating!

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