Economics Basics: Lesson 3

Average Cost & Break Even Analysis

ConcreteBasics.org thanks Dr. Samuel L. Baker, Ph.D., Department of Health Services Policy and Management,University of South Carolina, U.S.A for granting the permission to publish this article. Click Here to access complete list of articles under “Economics Basics for Civil Engineers” 

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

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. 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 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 Total Cost Marginal Cost= difference in Total Cost Average Cost= Total Cost ÷ Number of Patients
0 1000
3500
1 4500 4500
3000
2 7500 3750
2500
3 10000 3333
2000
4 12000 3000
2500
5 14500 2900
3000
6 17500 2917
3500
7 21000 3000
4000
8 25000 3125
5000
9 30000 3333

The average cost of serving 3 patients, for example, is 3333

The average cost can tell you whether you are breaking even — whether your total revenue is covering your total cost.

Suppose that the firm charges all of its patients the same price.

Try this True or False question: The firm is making a profit if, and only if, the average cost is less than this price: Answer in “True” or “False”

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

Number of Patients per Year Total Cost Total Revenue = number of patients times the price, $3200 Average Cost= Total Cost ÷ Number of Patients
0 1000
1 4500 3200 4500
2 7500 6400 3750
3 10000 9600 3333
4 12000 12800 3000
5 14500 16000 2900
6 17500 19200 2917
7 21000 22400 3000
8 25000 25600 3125
9 30000 26800 3333

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?

The answer is 4 ;  the lowest output rate at which Joan’s makes a profit is 4 patients per year.

And, what is the highest output rate that’s profitable for Joan’s?

The answer is 8; the highest output rate at which Joan’s makes a profit is 8 patients per year.

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.

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 – as can be seen in this table:

Number of Patients per Year Total Cost Total Revenue = number of patients times the price, $3200 Profit= Total Revenue-Total Cost Average Cost= Total Cost ÷ Number of Patients
0 1000 0 -1000
1 4500 3200 -1300 4500
2 7500 6400 -1100 3750
3 10000 9600 -400 3333
4 12000 12800 800 3000
5 14500 16000 1500 2900
6 17500 19200 1700 2917
7 21000 22400 1400 3000
8 25000 25600 600 3125
9 30000 26800 -1200 3333

Profit is positive if and only if average cost is less than the price patients pay (i.e. if average cost is less than $ 3200) 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 Total Cost Marginal Cost= difference in Total Cost Average Cost= Total Cost ÷ Number of Patients
0 1000
3500
1 4500 4500
3000
2 7500 3750
2500
3 10000 3333
2000
4 12000 3000
2500
5 14500 2900
3000
6 17500 2917
3500
7 21000 3000
4000
8 25000 3125
5000
9 30000 3333

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

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

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Question: 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.

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Question: 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 Total Cost Marginal Cost= difference in Total Cost Average Cost= Total Cost ÷ Number of Patients
0 1000
3500
1 4500 4500
3000
2 7500 3750
2500
3 10000 3333
2000
4 12000 3000
2500
5 14500 2900
3000
6 17500 2917
3500
7 21000 3000
4000
8 25000 3125
5000
9 30000 3333

Question: Now what is Joan’s break even number of patients, after the price has fallen to $3200?

Answer: 4; 4 is the smallest number of patients for which average cost is less than $3200.

Joan’s makes only an average of $200 per patient, but that’s a profit. Notice that Joan’s break even point is now higher than it was before. It’s 4, rather than 2.

Question: 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

Answer: 8; 8 is the largest number of patients for which average cost is less than $3200. Notice that this top end is now lower it was before. It’s 8, rather than 9.

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.

Question: 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?

Answer: $ 2917-$ 3000; For any price from $2917 up to $3000, output rates of 5 and 6, and only those, are profitable or break even. Joan’s output decision is narrowly constrained if the price is in this $2917-$3000 range.

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

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

Answer: 2900; At this price, Joan’s has no choice but to see 5 patients per year, and the firm just breaks even.

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:

Number of Patients per Year Total Cost Marginal Cost= difference in Total Cost Average Cost= Total Cost ÷ Number of Patients
0 2000
3600
1 5600 5600
2900
2 8500 4250
2200
3 10700 3567
1500
4 12200 3050
1800
5 14000 2800
2100
6 16100 2683
2400
7 18500 2643
2700
8 21200 2650
3500
9 24700 2744

Question: Can Joan’s now make profit if the price is $2900?

Answer: Yes; Some average costs are lower than before. There are several output rates at which the average cost is less than $2900.

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

Answer: 8; With these lower costs, Joan’s makes the most profit at an output rate of 8. It’s the highest output rate before the marginal cost gets higher than $2900.

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.

Question: 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?

Answer: The supply expansion, and consequent competition among the sellers, should force the price down.

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.

Question: 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?

Answer: 5; 5 is the smallest number of patients for which average cost is less than $2900. Joan’s break even point is higher than it was at the old price and the old technology, which had less fixed cost.

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

  ***That’s all for now. Thanks for participating!***

Copyright © 1985-2000 Samuel L. Baker

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