|
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
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.
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.
Answer in “Yes” or
“No”…….
If your answer is “Yes”, you
are
Correct! The $3700 price the patient pays is more
than
the $3500 marginal cost. You gain $200 profit from the first patient.
If your answer is “No”, you are
Wrong! - Compare the gain from treating
the first patient with how much the first patient adds to your
cost. Which is greater?
"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”…….
If your answer is “No”, you are
Correct! You are losing money,
but you lose $200 less if you
take 1 patient. We assume you can't get out of your $1000 fixed cost.
If your answer is “Yes”, you
are
Wrong! Sometimes maximizing profits
means minimizing losses. We assume that you can't get out of your fixed
cost.
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
|
The price is still
$3700. You are
currently treating one patient. Should you add a second?
Answer in “Yes” or
“No”…….
If your answer is “Yes”, you
are
Correct! The $3700 price you get from
the second patient is bigger than the second patient's $3000 marginal
cost. You gain $700 profit from taking
the second patient.
If your answer is “No”, you are
Wrong! Compare the gain from adding the
second patient with how much the second patient adds to your
cost. Which is greater?
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?
If
your answer is “7”, you are
Correct!
At
7 and below, marginal cost is
less than $3700.
Above 7, marginal cost is greater
than $3700.
Therefore, what is
the
profit-maximizing number of patients if the price is $3700?
Here again, If your answer is
“7”, you are Correct!
7
satisfies the marginal decision
rule. It's the most we can expand production before the marginal cost
becomes
greater than the price
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.
Answer the following in “True”
or
“false”:
The marginal
decision rule says you should set your price to be equal to your
marginal cost.
If your answer is “True”, you
are
Wrong! ; As a price-taker, you don't
control your price. All you control is how much to make.
You expand how much you make
until the marginal cost rises to equal the going price.
If your answer is “False”, you
are Correct! The marginal decision rule tells
you what output rate to set, not what price to set. In this kind
of market, you take the
market price as given and do your best
with it.
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
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?
Answer
in “Yes” or “No”……
If your answer is “Yes”, you
are
Wrong! What's the marginal cost of the
7th patient?
How
does that compare with the
new price of $3300?
Does Joan's gain or lose on the
7th patient?
If your answer is “No”, you are
Correct! The marginal cost of the 7th
patient is more than the new price.
Joan's
now loses money on the 7th
patient.
Joan's should therefore serve
less than 7 patients.
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?
Answer in “Yes” or
“No”……
If your answer is “Yes”, you
are
Correct!
The marginal cost of the 6th
patient is less than $3300.
Joan's
makes money on the 6th
patient, but loses on the 7th.
Joan's should therefore serve 6
patients.
If your answer is “No”, you are
Wrong! What's the marginal cost of the
6th patient?
How
does that compare with the
new price of $3300?
Does Joan's gain or lose on the
6th patient?
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
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?
Answer in “Yes” or
“No”…….
If your answer is “No”, you are
Correct! The marginal cost of the 6th
patient is above the new price. Joan's
loses $100 on the 6th patient, so she'll cut back.
If your answer is “Yes”, you
are
Wrong! Compare the marginal cost of the
6th patient with the revenue the 6th patient brings in ($2900).
Which
is greater?
What does that imply?
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?
If your answer is 5, You are Correct! The 5th
patient's marginal cost is less than $2900.
The
6th patient's marginal cost
is greater than $2900.
5 is therefore the most
profitable number of patients.
How much profit is
Joan's making
now?
To
answer: calculate
the total revenue,
which is the number of patients Joan's will serve times the $2900 price
per
patient and
subtract the total cost shown
in the table above for that number of patients.
If your answer is 0, You are Correct! $0 profit.
Revenue is 5 times $2900 =
$14500, the same as the total cost of 5 patients. Average cost at 5
patients is
$14500/5 = $2900, same as the price.
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
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?
If your answer is “8”, you are
Correct!
The 8th patient's marginal cost is less
than $2900.
The
9th patient's marginal cost
is greater than $2900.
8 is therefore the most
profitable number of patients.
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?
If your answer is “8”, you are
Correct! The added cost per year of
life saved from testing every 3 years, rather than every 4, is less
than
$200,000.
Going
to every 2 years, however,
would cost more per life year saved
than the value we've put on it.
***That's all for now. Thanks for
participating!***
|
