Price Discrimination
John Eckalbar
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 Figure 1.
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. We will look at two types of price
discrimination: third degree price discrimination and perfect
price discrimination.
Figure 1
Third Degree Price Discrimination
Assume that 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 group 1, D2 is the demand from group 2.
Figure 2
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.
Assuming that MC is flat, as is MC0 below, the optimal prices are P1' and P2'and the quantities will be q1' and q2',
as shown below. It is easy to see that when q1' and q2' are sold, MR1 = MR2 = MC, as we argued on the previous
page.
It could be shown that if the firm had to charge everyone the same price, call it P*, we would have P1' > P* > P2'.
A proof of this is available on the web in my Econ 101 folder, but you don’t need to know this.
Figure 3
What are the effects of this type 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*.
Notes:
1. There is a sort of subsidy or transfer 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.
Now let’s look at what happens when there are price controls in one of the markets.
What has been happening with prescription drugs is that some nations, like Canada, impose price ceilings on drug
sales in their country. (Canadian drug prices are about 40% lower than US prices of US produced drugs.)
How does that work? Let’s look first at how a monopolist
would respond to price controls.
Look at Figure 4. 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. But note that 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. This can be
important.
Figure 4
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 5. Total output is q1' + q2'. What happens in this market in
Figure 5
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
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? The answer is obvious...the
demand in country 1 would collapse and the demand in country 2 would grow. Nearly all sales would then be at the
regulated country 2 price, and revenues would fall. If the markup over MC is too small to fund fixed research and
development costs, then new drug programs suffer.
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?