11/28/10
CHAPTER 13: DIRECT PRICE DISCRIMINATION 145
I. INTRODUCTION
This is Luke Froeb, author with Brian McCann of Managerial Economics: a
problem-solving approach, and this short video is designed to accompany chapter
13, “Direct Price Discrimination.”
In chapter 6, we presented a simple model presented of a single firm setting a
single price on a single product. In Chapter 12, we relaxed one of those
assumptions by examining how a single firm would set prices on multiple
products. In this chapter, we relaxed another of the assumptions and consider
the case of a single firm charging different prices for the same product, like the
prices depicted in this picture of a sign from an archeological site in India.
Here citizens of India pay an admission fee of 10 rupees (about 25 cents)
and "other citizens" pay ten times as much.
<<INSERT SIGN PICTURE, USE FULL SCREEN, AND CIRCLE THE TWO
DIFFERENT PRICES>>
In fact, there are at least four different prices on this photo. Kids get in free
<CIRCLE THIS PRICE>> and it costs 25 rupees if you want to use a video
camera <<CIRCLE THIS PRICE>>. This picture is taken from Mark
Perry’s terrific blog, Carpe Diem.
I. WHY DISCRIMINATE?
To see why this kind of pricing is profitable, let’s return to the simple
pricing example from Chapter 6, where we constructed a demand curve
from ten different consumers who placed different values on an item. We
constructed a demand curve by lining them up, from the highest value to
the lowest value, and then used marginal analysis to determine how many
to sell, or equivalently which price to charge. <<SIMPLY RERUN THE
CLIP FROM CHAPTER SIX WHERE WE SHOWED THAT THE OPTIMAL
PRICE WAS $7 and at the optimal price the firm sold 4 units.>>
Price
$10
$9
$8
$7
$6
$5
$4
$3
$2
$1
Quantiity Revenue MR
MC
Profit
1
$10
$10
$3.50
$6.50
2
$18
$8
$3.50
$11.00
3
$24
$6
$3.50
$13.50
4
$28
$4
$3.50
$14.00
5
$30
$2
$3.50
$12.50
6
$30
$0
$3.50
$9.00
7
$28
($2)
$3.50
$3.50
8
$24
($4)
$3.50
-$4.00
9
$18
($6)
$3.50
-$13.50
10
$10
($8)
$3.50
-$25.00
Notice that at the best price of $7 <<HIGHLIGHT THIS ROW>>, there are
still three consumers—those with values of $6, $5 and $4 <<HIGHLIGHT
THESE ROWS>> willing to pay more than the marginal cost of the good. If
we could (1) identify these consumers, and (2) figure out a way to charge
them a separate price, and (3) prevent them from re-selling to the high
value consumers who were buying at $7, then we could construct a second
demand curve, and set a second price.
In the table below, we compute the most profitable price for the low value
consumers. We use marginal analysis to show that we could profitably sell
two extra goods at a price of $5 to these low value consumers and earn an
extra $3 in profit.
Price
$6
$5
$4
$3
$2
$1
Quantiity Revenue MR
1
$6
2
$10
3
$12
4
$12
5
$10
6
$6
MC
$6
$4
$2
$0
($2)
($4)
$3.50
$3.50
$3.50
$3.50
$3.50
$3.50
Profit
$2.50
$3.00
$1.50
-$2.00
-$7.50
-$15.00
<<ILLUSTRATE the EXTRA SALES BY HIGHLIGHTING THE
RELEVANT ROWS>>. By price discriminating, or by reducing the price to
the low-value consumers, we can make more money.
Now, let’s get concrete and imagine that these low value customers are all
over 65 years of age. And imagine that this is a movie theatre and that the
second lower price is offered as a discount to senior citizens. This price
discrimination scheme allows us to identify the low value customers by
making them present proof that they are over 65, and you prevent them
from re-selling their tickets outside the movie theatre by checking the age of
anyone using a discounted ticket.
II. WHAT EXACTLY IS PRICE DISCRIMINATION?
Any time a firm has two different types of consumers, with different elasticities of
demand, and it <<LIST “3 CONDITIONS FOR DIRECT PRICE
DISCRIMINATION” IN A LIST>> (1) can identify them, (2) charge different
prices to each group, and (3) prevent the low-price group from re-selling to the
high-price group, then it becomes profitable to discriminate.
Recall from chapter six, that the optimal price is where MR=MC, which is
equivalent to (P-MC)/P=1/|elasticity|. We called the left side of the equation the
“actual margin”, and the right side of the equation the “desired margin.”
So imagine that one group of consumers has a price elasticity of demand equal to
-2 which implies a desired margin of 50% and the other has a price elasticity of
demand equal to -3 which implies a desired margin of 33%. If your marginal cost
is $4, then set of prices of $8 and $6 to the two groups.
<<SHOW EQUATIONS ($8-$4)/$8=1/|2| “for the low elasticity group”>>
<<SHOW EQUATIONS ($6-$4)/$6=1/|3| “for the high elasticity group”>>
And this makes intuitive sense: charge a higher price to the group that is less
sensitive to price and a lower price to the group that is more sensitive to price.
So price discrimination is the practice of charging different prices to different
consumers based on differences in demand, not on differences in marginal costs.
However, sometimes it is difficult to tell what is causing the difference.
One example is airline fares. Business travelers and leisure travelers have very
different demands. Business travelers want to fly at very specific times, e.g., “I
have to be in Cleveland on July 18, at 10am” whereas leisure travelers are more
flexible about time and destination. In other words, leisure travelers have more
substitutes. But perhaps the biggest difference is that business travelers do not
pay for their own tickets; instead, the company pays for their travel. Both of
these factors make business demand less elastic than leisure demand, so it makes
sense that business travelers pay more for airline tickets than leisure travelers.
However, some of the price difference between business and leisure travelers
may be driven by the higher cost of serving business customers. Business
meetings are scheduled and cancelled at the last minute, so serving business
demand often means that seats go unsold. These unsold seats are costly, so the
marginal cost of selling business seats is higher than the marginal cost of selling
leisure seats. So there may be a cost element that could explain some of the price
difference between business and leisure fares. But even with higher marginal
costs, if margins are higher for business travel, then prices are determined, at
least in part, by differences in demand elasticities, which is price discrimination.
III. IMPLEMENTING PRICE DISCRIMINATION SCHEMES
Once you understand how price discrimination works, you will start to notice
examples all around you. For example, most business schools offer financial aid
to students with stronger academic records. These students typically have more
options than weaker students, which is just another way of saying that they have
more substitutes, which makes their demand more elastic. As a consequence,
most schools reduce the price of tuition for these students. Financial aid is the
way they charge different prices to different students based on differences in
demand.
Another example comes from the Indian archaeological site. As in many places
around the world, tourists are often charged higher prices than locals, because
they have less elastic demands. This may be due to higher income or it may also
be due to the better information of locals: they are more likely to be aware of
lower-priced substitutes which tends to make their demand more elastic.
In the sign, there are also discounts for children and a premium for using a video
camera. Families with children probably have more elastic demand due to less
disposable income, so this is likely a price discrimination scheme; and consumers
who want to use video cameras probably have less elastic demands because they
are likely to have higher incomes.
Drug companies charge higher prices to consumers living in higher income
countries. This creates incentives for consumers to travel to lower income
countries to buy drugs and bring them back. In the US, older consumers, who
typically consume more drugs, will sometimes travel on busses to Mexico to buy
drugs and bring them back to the US for consumption. This is called a “grey
market” as opposed to a “black market” because it violates company policy, not
necessarily a country’s law. <<GRAPHIC OF OLD PEOPLE ON BUSSES TRAVELLING
TO MEXICO TO BUY DRUGS AND BRING BACK?>> If enough consumers do this,
they reduce the incentive of companies to discriminate. So many drugs sold in
Mexico end up in the US that the drug companies have raised prices to Mexican
consumers.
If you are going to price discriminate, it is usually best to keep the practice as
secret because no one likes to pay higher prices than someone else. In fact, if
consumers become aware that others are getting better prices, they may even
refuse to purchase.
Now that we have taught you how to discriminate, I want to warn you that in
many parts of the world, price discrimination is illegal. In the US, it is illegal to
price discriminate if you are selling intermediate goods (to another business).
Price discrimination in services and to final consumers is OK. It is also OK to
reduce price in order to respond to competition.
IV. Competition and Price Discrimination
Thus far, we have been talking about price discrimination by a single firm, which
prices high to consumers with less elastic demands and prices low to consumers
with more elastic demands. But what happens when competitors enter a
market? While the empirical evidence is mixed, a competitor would find it
relatively easy, and very profitable, to sell to the consumers who are paying the
higher prices or being discriminated against.
In the graph below, taken from an article written by Kristopher Gerardi and Adam
Shapir, we see the dispersion of prices charged by United Airlines on its
Philadelphia to Chicago route. Airlines sell tickets at many different prices, and
the distribution of prices is plotted against time from 1993 to 2006. Each line
represents a different “decile” of the price distribution. The bottom most line
represents the lowest 10% of prices, sold primarily to leisure travelers who buy
two weeks in advance, stay over a Saturday night, and fly at unpopular times. The
highest line represents the 10% most expensive tickets, which are sold primarily
to business travelers with no advance purchase, travelling at popular times.
The interesting thing about the graph is that the price dispersion collapses
following the entry of low cost airlines. Before Midway entered the route in
1994, United ticket prices ranged from $100-$300. After Midway entered,
denoted by green dots, average ticket prices declined, which is what you would
expect with more competition, but the range of prices also declined: to between
$75-$150. <<POINT TO THE GREEN DOTS>>
Following the entry of Southwest in 2005, denoted by pink dots, <<POINT TO PINK
DOTS>> you see a similar collapse in the spread of United’s pricing from between
$150-300 to between $90-$150. In this industry at least, it appears that price
discrimination becomes much harder when competitors enter the market.
Curiously, entry by ATA (denoted blue dots) <<POINT TO BLUE DOTS>> had a
much smaller effect on United prices than Midway or Southwest entry.
Perhaps they were not as strong of a competitor or entered only with a
limited number of flights per day.