CORRECTLY DRAWING THE ZERO ECONOMIC PROFIT
GRAPH FOR A MONOPOLISTICALLY COMPETITIVE FIRM
Cyril Morong
San Antonio College
ABSTRACT
Many principles of economics texts do not correctly draw the graph
showing zero economic profit for a monopolistically competitive firm. The
average total cost curve and the marginal cost curve are not consistent with each
other. That is, they are not derived from the same total cost curve (as shown by
numerical inspection of these curves). Also, the marginal revenue line is often not
twice as steep as the demand line.
Using a total cost curve of the form TC = fixed cost + aQ3 – bQ2 + cQ
and a linear demand line, I find the general form equation for calculating the
slope and intercept of both demand and marginal revenue for a chosen quantity.
That quantity is such that P = ATC, MR = MC, the slope of marginal revenue is
twice as steep as the demand line and both the ATC and MC lines are derived
from the same total cost curve. These equations are used to generate the correct
graph in a spreadsheet program.
INTRODUCTION
Principles of economics books usually contain a graph of a typical firm in monopolistic
competition earning above economic profit. Then nearby or right next to it, there is a graph of
the firm earning normal profit. As the story goes, the above normal profit caused more firms to
enter the industry (which easily happens since free entry is assumed). For the typical firm this
means that their demand curve shifts to the left as far as is necessary for profit to be driven down
to zero or normal (meaning P = ATC). Sometimes demand is said to move down and part of this
process could also involve demand getting more elastic. Once profit is zero, no more firms enter.
But rarely do the textbook graphs list any numbers, so it is not easy to see if they are
realistic. That is, the ATC curve may not be consistent with the MC curve. If they were
consistent with each other, they would both be derived from the same total cost (TC) curve.
There is usually not any indication that they are. The ATC in these graphs can be approximated
at various quantities using a ruler or grid placed over the graph. Then multiplying this ATC times
Q leaves TC which then allows for MC to be calculated. In many textbook graphs, the
approximate numbers on the MC line are not consistent with or close to the numbers found in the
TC approximation. That is how the ATC and MC lines are not consistent with each other. Other
apparent problems include the MR line not being twice as steep as the demand line and ATC and
MC being in different places in the above normal profit graph than they are in the normal profit
graph.
Even in the initial work by Chamberlin and Robinson, it does not appear that ATC and
MC lines are consistent with each other. It also looks that way in the recent book The
Monopolistic Competition Revolution in Retrospect.
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ILLUSTRATION OF THE PROBLEM
In Figure 1 below, as in many textbook cases, the case of zero profit is shown, but it is
not clear if the graph is drawn correctly. There is no way to tell if ATC and MC are consistent
with each other.
FIGURE 1
P,C
MC
ATC
P = ATC
D
MR
Q
Q
There are no numbers to verify what MC and ATC actually are at various quantities.
There is no table showing these numbers. But this is normally how it is done in the textbooks. So
how do we know that if MC and ATC are consistent with each other, and MR is twice is steep as
demand, ATC will be tangent to demand at the same Q where MC = MR? The next section uses
a set of equations representing the typical firm which allows us to know the precise slope and
intercept of demand and MR if we have MC and ATC curves that are derived from the same TC
curve given a certain quantity. At that Q, profit will be zero.
FINDING THE SOLUTION
Suppose we have a TC function of the form
(1) TC = F + aQ3 – bQ2 + cQ
Where F is fixed costs. This function can lead to a TC curve that looks like the following in
Figure 2 below:
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FIGURE 2
C
40
35
TC
30
25
20
15
10
5
0
0
2
4
8
6
10
12
Q
So the ATC will be
(2) ATC = (F + aQ3 – bQ2 + cQ)/Q
MC will be the derivative of TC, equation (1)
(3) MC = 3aQ2 – 2bQ + C
Then equations (4) and (5) are demand and MR:
(4) P = I – SQ
(5) MR = I – 2SQ
That means that P – MR = I – SQ – (I – 2SQ) = SQ. Knowing this will be helpful in finding the
solution. If we look at Figure 1 again, we can see that when profit is zero ATC – MC = P – MR
is true. Then
SQ = ATC – MC
That means that
(6) S = (ATC – MC)/Q
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If we pick a Q, we can calculate MC and ATC. Plugging that into equation (6) would give us S.
Let’s call the calculated S, S*. So we have the slope of demand. Re-arranging equation (4) leaves
(7) I = P + SQ
But since we will know S (what we called S*), we have
(7a) I = P + S*Q
We will also know that P = ATC. Whatever value we found for ATC can be used for P. That
means that equation (7a) will give us the intercept of demand.
Below is a numerical example
(8) TC = 11 + 0.05Q3 - 0.5Q2 + 4Q
Then
(9) MC = 0.15Q2 - Q + 4
Suppose we pick Q = 4. If we plug that into ATC (5.55) and then MC (2.4), and then those
numbers get plugged into equation (6), S* = 0.7875. Then we can assume that P = 5.55 since P
must equal ATC to have a zero profit. Then the values for S*, P, and Q get plugged in to
equation (7a) to find I. This is 8.7. Given all the values so far, both MC and MR = 2.4. So at Q =
4, ATC = P and MC = MR.
Figure 3 illustrates this. By now the curves and lines should need no labels. The vertical line is a
visual aid to see where MC crosses MR and ATC is tangent to demand.
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Figure 3
12
10
8
6
4
2
0
0
2
4
6
8
5
10
12
14
16
REFERENCES
Brackman, S & Heijdra, B.J. (Eds.) (2004). The Monopolistic Competition Revolution in
Retrospect. New York: Cambridge University Press.
Chamberlin, E.H. (1969, 8e). The Theory of Monopolistic Competition. Cambridge: Harvard
University Press.
Robinson, J. (1938). The Economics of Imperfect Competition. London: MacMillan.
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