Econ 301
Chapter 25
Monopoly Behavior
Skip second degree price discrimination in section 25.3.
The Temptation to Price Discriminate
Consider the monopolist shown below. If the same price must be charged to all buyers, then P0 is the best price.
But the temptation to price discriminate, i.e, to charge
different prices to different buyers, is evident in the figure.
First, buyers in set 1 are all willing to pay more that P0, so it
would be nice to be able to charge them more. Second,
buyers in set 2 are willing to pay more than MC, but less
than P0, so it would be good to be able to make sales to
them as long as we don’t have to reduce prices to everyone
else. These considerations give rise to price discrimination.
Third Degree Price Discrimination
A monopolist sells a single product to two distinct sets of buyers...maybe business travelers and personal travelers,
maybe senior citizens and everyone else, etc. We’ll call them Group 1 and Group 2. The demands are shown
below.
D1 is the demand from sector 1, D2 is the demand from sector 2, and D is the market demand. D is the horizontal
sum of D1 + D2. Note that if the firm charges group 2 buyers more than a2, they will not buy anything. The tricky
Figure 2
part here is the MR that pairs up with the kinked whole-market demand curve D. There is a “trick” to drawing MRs
for linear demand curves that works like this: (See Figure 3.) At any given price and quantity on D, MR lies below
the demand curve by the amount of the difference
between the demand curve intercept and the price.
That is, the magnitude of the two red lines are
equal. (You can put the proof together yourself by
looking at the picture to the left.) Because of the
kink in D in Figure 2, the blue MR curve is disjoint
at Q0.
Figure 3
Now suppose the MC is MC0, if the firm elected to charge everyone the same price, i.e., not price discriminate, then
it would set the price at P* and sell a total quantity of Q*, as you can see in Figure 4. Note that because D is the
Figure 4
horizontal sum of D1 and D2, we know that Q* = q1* + q2*. If MC were higher, it might hit MR twice, in which
case we would have to look at two potential profit maximum points. Never mind that–we’ll look at a simple case.
Also, if MC were above the intercept for D2, the firm would not sell at all to Group 2 buyers, since none of them
are willing or able to a price above MC. Finally, we could draw in an ATC on the right graph of Figure 3 and use
that to find profits or losses.
Let’s ask if charging everyone the same price is a strategy that results in maximum profits. A little logic reveals that
in order to maximize profits, the firm should follow two rules:
1. Set P1 and P2 for the two groups so that MR1 = MR2.
Why? Suppose not. Suppose MR1 > MR2. That couldn’t be a profit maximum, since it would be possible
to cut P1 a little to sell one more unit to Group 1 and at the same time raise P2 a little to sell one less to
Group 2. Since Q stays the same, so do costs. But since MR1 > MR2, there will be a net increase in
revenue, and therefore a net increase in profit. In the same way, if MR1 < MR2, profit cannot be at a
maximum. Since you can’t be at a profit maximum with either MR1 > MR2 or MR1 < MR2, it must be that
at the max, MR1 = MR2.
2. Also, you must have the two MRs = MC.
Look back at Figure 4 and see if you can compare MR1 with MR2 when both firms are charging the same price, P*.
Do you see that MR1 < MR2. The graph below shows why.
Figure 5
When you charge P* to both sets of buyers, Group 1 buys q1*, and MR1 is relatively low, whereas, when you sell
q2* to Group 2, MR2 is relatively high. We could raise profit be selling more to Group 2 (by cutting P2 below P*)
while raising P1 and selling less to Group 1. See if you can picture what the optimum would look like, and then see
the next page.
Figure 6
The prices will now be P1' and P2', and the quantities will be q1' and q2', as above.
What’s the effect of price discrimination?
The firm is better off, since its profits are higher.
Group 2 buyers like it since because they now pay P2' instead of P*.
Group 1 buyers don’t like it because they pay P1' instead of P*.
The total quantity produced will not change, though we will not try to prove that here.
Notes:
1. There is a sort of subsidy going from the Group 1 buyers to the Group 2 buyers.
2. It is possible that the firm could not produce at all unless it were able to price discriminate. This would
happen if total cost exceeded revenues when there was no price discrimination, but were less than revenues
when there was price discrimination.
What has been happening with prescription drugs is that some nations, like Canada, impose price ceilings on drug
sales in their country. How does that work? Let’s look first at how a monopolist would respond to price controls.
Look at Figure 7. If the price were fixed at P4, the firm
would choose to deliver Q4 units of the good...as long as it
could afford to stay in business. The reason for this is that
every unit sold at a price above MC will help increase
profits or reduce loss. So if fixed costs are covered, Q4
makes sense. If there are not enough funds to cover both
fixed and variable costs, then in the long run the firm will
exit or choose to never enter.
Figure 7
Now suppose that Groups 1 and 2 are two different countries. Let Country 2 regulate prices, setting a ceiling at P4,
while the price in the other country is P1'. See Figure 8. Total output is q1' + q2'. What happens in this market in
the long run depends upon TC. If the sum of the two revenues exceeds TC, then the firm will produce the output,
but notice that the buyers in Country 1 are subsidizing the buyers in Country 2, or to say it differently, Country 2 is
“free-riding” on Country 1. In the case of prescription drugs, the buyers in Country 1 are paying the bulk of the
fixed costs, which tend to be mostly up-front development/research costs, while the buyers in Country 2 pay only a
Figure 8
small markup over direct production costs, or what we call variable costs. If TC exceeds revenues from Groups 1
and 2, then the firm will not stay in this market in the long run or will not enter (or do the research) if it is not yet in
the market.
What would happen if buyers in Country 1 were allowed to buy in Country 2?
First Degree (Perfect) Price Discrimination
This will be our final type of price discrimination. It is an ideal case that will never be observed in fact. We assume
that the seller is able to size up the buyer and determine exactly what the buyers reservation price is, and to charge
every buyer exactly that reservation price. To make the analysis as simple as possible, we assume that the
production function is linear and there are no fixed costs. If
that is the case we have the following cost curves:
You can verify that the MC = ATC and that both are flat by
using the usual ray from the origin and tangent derivations
that we learned in the cost curve chapter.
If a monopolist faces these cost curves and charges everyone the same price, then the optimum price will be P0 and
the profits will be the shaded area below:
Now let’s view the demand curve as a step function with each buyer sitting on a step. Those, like A, with high
reservation prices sit on high steps.
If the seller charged everyone the same price, the optimum quantity would be where MRsp (the marginal revenue in
effect when everyone pays the same price) hits MC, and the profit would be the turquoise shaded rectangle. But if
the seller could somehow charge A a very high price, and B a somewhat lower price, etc., it could continue to sell
Q0 to the Set 1 buyers, but take in more money. This would obviously add to profits, and the amount of added
profit would be the green “triangle” shown above. We can also add to profit by making sales to the Set 2 buyers,
sense they are willing to pay more than MC. The added profits from these sales is shown as the pink “triangle.”
The end result is that if we don’t price discriminate, we earn only the turquoise rectangle of profit, but if we do price
discriminate, we earn the a profit given by the turquoise, green and pink areas combined.
How do the buyers feel about this compared with having the firm charge P0? Set 1 buyers don’t like it.
And Set 2 buyers do. Can you see how there is a sort of transfer from the Set 1 to the Set 2 buyers?
Third degree price discrimination. Here we have two groups of customers (group 1 and group 2) buying the same
good from a monopolist.
I’ll prove that the monopolist maximizes profit when
MR1 = MR2
and MR1 = MR2 = MC
Note that if the MR’s are equal, then
where Pi is the price charged to the group i buyers, and ,i is the elasticity of demand for the group i buyers.
Suppose that P1 > P2 at the optimum. Then
It follows that ,1 > ,2. In other words, the group 1 buyers have a relatively inelastic demand compared with group
2, and they get stuck with the higher price...which makes sense.
Entry Fees or two part tariffs Suppose you run an amusement park,
where visitors pay an entry fee, E, and pay P each time they buy a ticket
to a ride. The number of tickets to the rides is y. The cost to provide
rides is c(y) and the inversed demand curve is P = a - by. So profit is
given by
B = P y + E - c(y) = ay-by2 + E - c(y)
How big a fee (E) can you charge? Take the whole consumer’s surplus, which is shaded here. The shaded area is
(1/2)y(a - a + by) = by2/2, so
B = a y - by2/2 - c(y).
To maximize this, find dB/dy and set to zero.
dB/dy = a - by - dc/dy = 0
but a - by is the demand, and dc/dy is the MC,
so the optimum is to set the price at the point
where the Demand curve hits the MC and to
make E the size of the consumer’s surplus. In
a simple world with flat MC, the solution would look like this:
Read section 25.7 and end the chapter with
that.