# Average Cost #### Formerly at hspm.sph.sc.edu/ECON/ACost/ACost.html

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 you have a toy factory.

Your an annual fixed cost is \$10000. This fixed cost covers loan interest, utilities, property taxes, etc.

Suppose the marginal cost of producing each toy is \$1. This is labor and materials.

If you need it, there is a tutorial that explains marginal cost.

What is the average cost per toy if you make just 1 toy a year?

Do not type a \$ sign or a comma with your number. (Sorry!)
If you need a hint, just click the button.

Assume that you can make any number of toys at the same \$1 marginal cost per toy.

What is the average cost per year of producing 2 toys per year?

Do not type a \$ sign or a comma with your number. (Sorry!)
If you need a hint, just click the button.

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.

Suppose someone asks, "What is the cost of producing a toy?" He or she might want the average cost or he or she might want the marginal cost. You have to guess which from the context of the question.

### A more elaborate example 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 ...

Type a number from the bottom row of the table. Do not type a \$ sign or a comma with your number.

The average cost help you see whether you are breaking even, or making money, or losing money. Try this True or False question:

Suppose that Joan's charges all of its patients the same price. Then Joan's is making a profit if, and only if, the average cost is less than the price.
That is true.
That is false.

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.

What is the lowest output rate at which Joan's at least breaks even?

Type a number from the Number of Patients row of the table.

What is the highest output rate that is profitable for Joan's?

Type a number from the Number of Patients row of the table.

Leaving space until the above question is answered correctly.

### The Break Even Point

The break even point is the lowest output level at which total revenue exceeds total cost.

You could argue that there are two break-even points for Joan's. Joan's loses money if she signs up too few or too many patients. In practice, selling too few is a way more common problem than selling too many. We therefore define the "break even point" as the minimum you have to do to make your enterprise viable.

By this definition, the break even point for Joan's is 4.

This table shows in boldface the profitable output rates for Joan's if the price is \$3200:

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.

There are two ways to do a break even analysis.

1. You can compare total revenue with total cost at a range of output rates, or
2. You can compare the price with the average cost at a range of output rates
Method 2 requires that all your customers pay the same price. Method 1 is more flexible -- there can be a non-linear relationship between output rate and revenue. In this tutorial, we assume that all customers do pay the same price, so we can talk about "the price" and use either method to determine the break even point.

### The break even point when competition increases

Let us see what happens 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

What is Joan's break even point, based on that price and the costs above?

Type a number from the Number of Patients row of the table.

Where does Joan's average cost bottom out? At what output rate is Joan's average cost minimized?

Type a number from the Number of Patients row of the table.

True or false: A firm should always choose the output level at which its average cost is the least.
True. False.

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?

Type a number from the Number of Patients row of the table.

I am deliberately switching back and forth between marginal cost and average cost, to better bring out what each is good for.

• Average cost tells you if you are making or losing money overall.
• Marginal cost tells 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?

Type a number from the Number of Patients row of the table.

Leaving space until the above question is answered correctly.

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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