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.
The marginal decision rule theory also applies to any firm that is a "price taker," not a "price maker."
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.
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
n |
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.
Just to be sure you are with me, please answer this: What is the marginal
cost of the 8th patient? (Scroll up to see the cost table, if you need to.)
Here's the top of that cost table again:
| Number of Patients
n |
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.
"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?"
Let's look at the second and third rows of the cost table:
| Number of Patients
n |
Total Cost
of n patients |
Marginal Cost
of the nth patient |
| 1 | $4500 | $3500 |
| 2 | $7500 | $3000 |
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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
n |
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?
Therefore, what is the profit-maximizing number of patients
if the price is $3700?
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 n |
Total
Cost of n |
Marginal Cost
of the nth patient |
Total
Revenue for n |
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.
True or false:
The marginal decision rule says you should set your price to be equal
to your marginal cost.
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.
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
n |
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?
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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
n |
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?
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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.
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
n |
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?
| Number of Patients
n |
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?
How much profit is Joan's making now? To answer:
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.
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
n |
Total Cost
of n patients |
Marginal Cost
of the nth patient |
| 0 | $2000 | -- |
| 1 | $5600 | $3600 |
| 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?
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.
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?