Economics Basics: Lesson 2

Marginal Cost & the Output Rate under Competition

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 shows how, in theory, a business firm in a competitive industry can use the marginal cost concept developed in the previous tutorial to decide how much to produce and sell.

We’ll also get into how a competition progresses over time.

We will learn a marginal decision rule that applies to firms in competitive industries.

A “Competitive Industry, in economics jargon, “is an industry in which each firm must sell at the going price, take it or leave it”. In the economist’s theoretical idea of a competitive industry, there are so many firms that the market price does not go up if any one firm sells less output, nor does the price go down if the one firm sells more output. Farming is a good example.

The marginal decision rule theory also applies to any firm that is a “price taker,” NOT a “price maker.”

A health care provider is a “price taker” if it must sell its services at a price fixed by the government, or other major payor. For example, a hospital that takes Medicare patients has to take the price that the U.S. Centers for Medicare and Medicaid Services sets. All the hospital can do is decide how much service capacity to have.

The marginal decision rule theory assumes that the firm’s only goal is maximum profit. A health care organization with a community service orientation has other goals, but we ignore them for the time being.

We’ll be working again with the imaginary Joan’s Home Care Co., using the same cost numbers as in the preceding tutorial. We’ll assume that Joan’s is a price taker, so the only decision to be made is how many patients to treat per year, based on whatever the going price is.

The Marginal Decision Rule:

The marginal decision rule is: Expand production if and only if the price is greater than the marginal cost. The idea here is simple, once you get used to the jargon. Increasing production makes both total cost and total revenue go up. If the revenue goes up more than the cost, profit goes up. (Profit = total revenue – total cost.)

Marginal cost is how much cost goes up from making one more. The price is how much revenue goes up from selling one more. (This is where the price-taker assumption comes in — you don’t have to cut your price to sell more.) If the price is bigger than the marginal cost, then what you gain in revenue is greater than what you lose in added cost. That makes your profit higher, so you should go ahead and expand production.

On the other hand, if price is less than marginal cost, increasing production costs you more than the revenue you gain. You should not expand production.

Let’s see how this works. Here is Joan’s cost table, showing the Total Cost and the Marginal Cost for each number of patients. Assume as before that patients sign one year contracts, so we don’t have to bother with fractions of patients:

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
0 $ 1000
1 $ 4500 $ 3500
2 $ 7500 $ 3000
3 $ 10000 $ 2500
4 $ 12000 $ 2000
5 $ 14500 $ 2500
6 $ 17500 $ 3000
7 $ 21000 $ 3500
8 $ 25000 $ 4000
9 $ 30000 $ 5000

In each row of this table, the marginal cost number is how much total cost increases when going up to that rate of production. You can think of the Marginal Cost here as meaning “the marginal cost of adding this patient.” For example, the $3500 for marginal cost in the row for 1 patient means that serving 1 patient costs $3500 more than serving 0 patients.

Here’s the top of that cost table again:

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
0 $ 1000
1 $ 4500 $ 3500

Suppose the going price is $3700. At that price, you can get patients to sign contracts for your service.

We’re going to work our way up to finding the number of patients that gives you the most profit, starting from 0 patients.

To start, assume you are currently treating 0 patients — no patients at all. Would adding 1 patient make you better off? The going price is $3700, so that one patient would pay you $3700. Answer in “Yes” or “No”

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“Wait a second,” you might say, “the table says my total cost of seeing one patient is $4500. The patient is paying me only $3700, so I’m losing $800! Shouldn’t I see 0 patients?”

Is 0 a better choice? Answer in “Yes” or “No”

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Let’s look at the second and third rows of the cost table:

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
1 $ 4500 $ 3500
2 $ 7500 $ 3000

The price is still $3700. You are currently treating one patient.

Should you add a second? Answer in “Yes” or “No”

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So far, we have figured out that we want to contract with at least 2 patients.

We got this far solely by comparing the marginal cost with the price. We haven’t had to do any other calculating to decide whether or not to expand output. We haven’t needed the total cost numbers.

Nevertheless, I’m going to leave the total cost column in the table, just to see if I can confuse you.

Here is the cost table again. We already know that we want to have at least two patients, so I’ll start with row 2.

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
2 $ 7500 $ 3000
3 $ 10000 $ 2500
4 $ 12000 $ 2000
5 $ 14500 $ 2500
6 $ 17500 $ 3000
7 $ 21000 $ 3500
8 $ 25000 $ 4000
9 $ 30000 $ 5000

Looking over the above table, what is the highest number of patients for which the $3700 price is greater than marginal cost?

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Therefore, what is the profit-maximizing number of patients if the price is $3700?

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We have found the number of patients that gives us the greatest profit, just by comparing the price with the numbers in the marginal cost column. No arithmetic is needed.

Now I’ll do the arithmetic for you, to verify that this answer is correct.
Total Revenue = $3700 times the Number of Patients.
Profit = Total Revenue minus Total Cost.

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
Total Revenue for n patients Profit
(Total Revenue minus
Total Cost)
0 $ 1000 $ 0 – $ 1000
1 $ 4500 $ 3500 $ 3700 -$ 800
2 $ 7500 $ 3000 $ 7400 -$ 100
3 $ 10000 $ 2500 $ 11100 $ 1100
4 $ 12000 $ 2000 $ 14800 $ 2800
5 $ 14500 $ 2500 $ 18500 $ 4000
6 $ 17500 $ 3000 $ 22200 $ 4700
7 $ 21000 $ 3500 $ 25900 $ 4900
8 $ 25000 $ 4000 $ 29600 $ 4600
9 $ 30000 $ 5000 $ 33300 $ 3300

Sure enough, profit is greatest when you serve 7 patients. The marginal decision rule told you that without having to calculate out the whole table.

On the other hand, the marginal decision rule didn’t tell you how much profit (or loss) you have if you server 7 patients. For that you do need the calculations, and we see that profit at 7 patients is $4900.

Answer the following in “True” or “false”:

The marginal decision rule says you should set your price to be equal to your marginal cost.

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Competition:

Now let’s introduce some competition. I called this price-taker market “competitive” at the beginning, but so far Joan’s competitors have been invisible.

They’ll stay invisible, actually. But here’s what they do: New competitors enter the market. Why do they do this? Because there is profit to be made in this industry. Joan’s is making $4900 a year. Others can figure that out, and start their own companies just like Joan’s.

The result is that supply expands for the whole industry. If the industry demand curve doesn’t change, the equilibrium price will fall.

In a market where the government sets the price, this won’t happen automatically, but the government may catch on that it can cut the price and still get the service provided. Something like this happened with Medicare and real home health agencies in 1999.

Suppose the price falls to $3300. How many patients does Joan’s serve now? We’ll figure this out by starting where we are now (at 7 patients per year) and using the marginal decision rule.

Here are the relevant lines in the cost table:

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
6 $ 17500 $ 3000
7 $ 21000 $ 3500

Should Joan’s continue to serve 7 patients, if the price is $3300? Answer in “Yes” or “No”

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If the going price drops from $3700 to $3300, the old output rate of 7 is too high, if we want the greatest profit. Let’s look at one line up in the Joan’s cost table.

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
5 $ 14500 $ 2500
6 $ 17500 $ 3000

How about 6? Should Joan’s serve 6 patients if the price is $3300? Answer in “Yes” or “No”

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We now have the new profit-maximizing output rate.

Let’s figure out how much profit Joan’s makes now:
Total revenue is 6 times $3300, which equals $19800.
Total cost from the table above is $17500.
Profit is $19800 – $17500 = $2300.
This is less profit than before, but it’s the most Joan’s can make at the current price.

The Effect of Entry:

As each firm, assuming they are all like Joan’s, cuts back on the number of patients it takes, the total industry supply will shrink and the price may go part way back up.

At the same time, though, there will still be more firms entering this industry, because there is still some profit to be made in this business. As the new firms enter, supply will expand some more and the price will fall again.

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
5 $ 14500 $ 2500
6 $ 17500 $ 3000

Suppose the price now falls to $2900. Will Joan’s still want to serve 6 patients? Answer in “Yes” or “No”

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Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
4 $ 12000 $ 2000
5 $ 14500 $ 2500
6 $ 17500 $ 3000
7 $ 21000 $ 3500
8 $ 25000 $ 4000

If the price is $2900, how many patients will Joan’s serve?

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How much profit is Joan’s making now?

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Joan is not too happy now, unless she is paying herself a handsome salary out of overhead (fixed cost), which Medicare and Medicaid allow.

If we assume that there is no profit masquerading as cost, then the incentive to enter this industry is gone. No more firms would enter, so the price would stop falling.

At this point, competition has forced the price down to its minimum. All excess profit is squeezed out. The firms have been forced to be just the right size to minimize cost. The customer gets the most possible value per dollar spent.

This example works as happily as it does because we assume that there are diminishing returns to scale, so Joan’s marginal cost rises when her output rate is high. If Joan’s costs fell as her firm got bigger, competition would force her firm to grow and grow.

Getting back the circumstance we have, what can Joan’s do about her $0 profit? One possibility is to innovate, to change how she operates. She can hire cheaper personnel, lowering marginal cost but raising fixed cost due to the need for more supervision.

Joan’s can also buy new equipment that allows the visiting nurse or technician to tend to each patient in less time. This also lowers marginal cost but raises fixed cost.

With less qualified personnel spending less time with each patient, Joan’s may hire an economist to do a study showing that her quality is not significantly worse than before and may be better in some ways. The study’s cost adds to fixed cost, but may help stimulate some demand.

Here’s Joan’s new cost table. Fixed cost is higher. Marginal cost is generally lower than before:

Number of Patients Total Cost
of n patients
Marginal Cost
of the nth patient
0 $ 2000
1 $ 5600 $ 2900
2 $ 8500 $ 2900
3 $ 10700 $ 2200
4 $ 12200 $ 1500
5 $ 14000 $ 1800
6 $ 16100 $ 2100
7 $ 18500 $ 2400
8 $ 21200 $ 2700
9 $ 24700 $ 3500

Now how many patients does Joan’s serve if the price is $2900?

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Joan’s is making profit again. This starts the competition cycle again, though, as other firms enter the market and start driving prices down again.

We’re almost done. Just one more point to make.

A different application of the marginal decision rule

The idea of comparing marginal cost with the price can be applied to cost-effectiveness analysis. For example, here are figures from a study about how often women should get Pap tests.

The study is Eddy, D.M., “Screening for Cervical Cancer,” Annals of Internal Medicine, August 1, 1990, 113(3), pp. 214-226.
The study showed that the more often the test is done, the more lives are saved. However, the more often the test is done, the higher is the cost per year of life saved. The Law of Diminishing Returns is at work.

Pap test every
this many years
Marginal cost per year of life saved
4 $10,000 compared with no testing at all
3 $180,000 compared with testing every 4 years
2 $260,000 compared with testing every 3 years
1 $1,200,000 compared with testing every 2 years

Suppose we put a price on life. We decide that a year of life saved is worth $200,000. (How we decide that is a whole other discussion!) Testing once every four years is definitely better than no testing at all. Testing once every four years adds $10,000 to total medical care costs to save a year of life, which is worth much more than $10,000.

Using that logic, how often should we have Pap tests — every how many years?

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

Copyright © 1985-2000 Samuel L. Baker

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