A GUIDE TO THE PITFALLS OF IDENTIFYING PRICE DISCRIMINATION
JOHN R. LOTT, JR. and RUSSELL D. ROBERTS*
TWs paper demonstrates that plausible cost-based explanations exist for what are
commonly perceived to be cases of
price
discrimination. We explain such commonly
discussed problems as the price spreads of
retail
gasoline products, the "high" price
of dinners at restaurants, the "high" price of
popcorn
at movie theaters, and
the
fact
that airline ticket prices vary with how long the ticket is purchased
before
thefiight's
departure. Our explanations benefit from not relying on consumer
ignorance
or implicit
collusion among numerous sellers.
I. INTRODUCTION
Many economists explain pricing
anomalies by invoking "monopoly
power." To paraphrase H. L. Mencken,
such answers are all too frequently simple,
neat, and wrong. By examining specific
pricing anomalies, we show that cases of
alleged price discrimination may simply
involve unrecognized costs. We examine
the pricing of retail gasoline products, the
"high" price of dinners at restaurants, the
"high" price of popcorn at movie theaters,
and the fact that airline ticket prices vary
with how long the ticket is purchased be-
fore the flight's departure. While hardly a
comprehensive selection, each case in-
volves what has been perceived as an "ob-
vious"
case of price discrimination.
When two products appear identical
and sell for different prices, price discrim-
ination is often invoked instead of seeking
unobserved cost or quality differences.
Colleagues have assured us that because
some colas are priced below some seltzers,
* Anderson Graduate School of Management, Uni-
versity of California-Los Angeles and Olin School of
Business, Washington University. We wish to thank
Armen Alchian, Thomas Borcherding, David Butz,
Gertrud Fremling, William Gale, Neal Geary at
Amoco, Russ Gibson at Chevron, David Hirshliefer,
Ben Klein, Bob Kovacovitch at Shell, Sharon Kupfer,
Earl Thompson, Michael Waldman, Ralph Winter, a
particularly diligent anonymous referee from this jour-
nal,
and participants at the 1988 Western Economic
Association Meetings for helpful comments and dis-
cussions, and Kavita Vora and Ed Quigley for research
assistance. Any remaining errors are our own.
there must be monopoly power because
the colas have the seltzer cost plus the ad-
ditional cost of the flavoring. This expla-
nation ignores the possibility that water
quality and carbonation may have to be
higher when pure seltzer is not masked
with cola flavor. We have had colleagues
tell us that Michelin produces tires for
Sears identical to its own but charges dif-
ferent prices for the two brands to price
discriminate. While Michelin does pro-
duce tires for Sears, we have no reason to
believe that the quality is identical in both
cases.
Consumer Reports
[1973], for exam-
ple,
finds Michelin tires are more expen-
sive than Sears tires, but they are also of
higher quality.
Quality differences such as the above
often explain alleged cases of price dis-
crimination. Our focus here is on cost dif-
ferences. Allegations of price discrimina-
tion often ignore differences in costs be-
yond the marginal cost of production. The
examples that follow show how opportu-
nity
costs,
such as inventory and overhead
costs,
are sufficiently large to explain price
differentials in a competitive world of in-
formed consumers.
II.
EXPLANATIONS OF GASOLINE PRICING
Two puzzles have been noted with re-
gard to retail gasoline pricing. First, the
absolute price spread between full-service
and self-service gasolines is smallest for
14
Economic Inquiry
VoL
XXDC,
January 1991,14-23
Western Economic Association International
LOTT & ROBERTS: A GUIDE TO PRICE DISCRIMINATION
15
super unleaded compared to regular un-
leaded and regular leaded gasoline. The
second puzzle is that while the production
costs of leaded and unleaded gasoline dif-
fer by approximately a penny, the price of
regular leaded gasoline is more than a
penny lower.
Two answers based on price discrimina-
tion have been supplied to explain the
price differential between leaded and un-
leaded. The first is that leaded gasoline is
the "fighting grade"—the low leaded
price is posted to lure unsuspecting un-
leaded customers into the station who suc-
cumb to the higher price rather than
search elsewhere. This explanation re-
quires a very short term memory for con-
sumers who are repeatedly fooled, and la-
ziness on the part of competing gasoline
stations (which may only be across the
street from one another) that fail to lower
information costs by advertising. The sec-
ond explanation is that gasoline stations
have monopoly power. Unleaded
customers are hypothesized to have
higher search costs than leaded customers.
Stations then exploit unleaded customers
by charging them higher prices.
1
An Alternative
Explanation
The production cost is only one compo-
nent of the cost of supplying gasoline to
consumers. The cost of selling leaded and
unleaded gasoline need not be the same.
One difference is the size of the transac-
tion. It is cheaper to sell a single 15 gallon
purchase than two purchases of 7.5 gal-
1.
These monopoly explanations were attributed
to Nick Nichols in the "Puzzles" section of the
Journal
of Economic Perspectives. We have heard both of these
explanations many times from others as well. As ev-
idence of monopoly power, Barry Nalebuff in "Puz-
zles"
cites Mixon and Uri [1987] who find that states
with a higher ratio of cars using unleaded gasoline to
cars using leaded have a larger difference, on average,
between the price of unleaded and leaded gasoline.
They argue that the ratio of cars using unleaded to
cars using leaded is a proxy for the elasticity of de-
mand. It seems a rather poor proxy. None of the ex-
planations that posit monopoly power show that it is
large enough to explain the size of the differential.
Ions each because of the fixed costs asso-
ciated with a transaction—making
change, noting the number of gallons,
turning the pump off and on, etc. In addi-
tion, a larger number of smaller transac-
tions makes for more traffic and conges-
tion in the station, reducing total sales or
requiring a larger station. Another cost
difference between grades is the slower
flow rate from the nozzle of the unleaded
pump relative to the leaded nozzle. It
would be cheaper to serve a leaded custo-
mer than an unleaded one because the
leaded customer ties up the pump for a
shorter period of time.
2
Under perfect competition, the seller
sets the unleaded price,
P
u
,
so on average,
revenue, which equals
P
u
times
G
u
(the av-
erage number of gallons purchased of un-
leaded), must cover the costs of serving
the customer and w, the wholesale price
of gasoline. The cost of serving the custo-
mer is approximated by the number of
minutes it takes to make the transaction
multiplied by the per minute rental rate, r,
sufficient to cover the overhead of land
rent, depreciation of capital, and labor
costs.
This is the implicit rental rate that
covers these costs. There are two aspects
to the time cost. One is the time to physi-
cally pump the gasoline,
t
u
G
u
,
where t
u
is
the time (in minutes) to pump a gallon.
The second is the time a transaction takes
in addition to pumping gasoline: the time
it takes to get out of the car, make pay-
ment, and pull out of the station. This time
per transaction, which we will assume is
the same for leaded and unleaded con-
sumers, is denoted by F and is measured
in minutes. So:
(1)
or
(2)
p
u
G
u =
= \r¥/G J
+
(w
+
rt
u
) .
2.
California, and perhaps other states, places a
legal maximum on the pumping speed, which may
affect this differential.
16
ECONOMIC INQUIRY
The leaded price, PL, assuming that the
wholesale price is smaller by
$.01,
is given
by
(3) P
L
= [rF/Gj}
+
(w-
.01 +
rt
L
).
The expected differential is then:
(4)
P
u
~
PL
-
K*«
-
*O
There are three parts to the differential.
The last term is the wholesale difference.
The second term is the difference in cost
due to the fixed cost per transaction—if
the average leaded purchase exceeds the
average unleaded, then the fixed cost is
spread over more gallons, reducing the
price of leaded. The first term captures the
difference in the time to pump a gallon of
leaded and unleaded. It is a per gallon
rental of the pump. The implicit per min-
ute rental rate on the pump, r, also affects
the absolute differential. For example, re-
gions with higher land rents should have
a larger differential if the first and second
terms are not trivial.
Cars using leaded gasoline have, on av-
erage, larger gas tanks than cars using un-
leaded gasoline. The increase in gasoline
prices in the 1970s caused substitution to-
wards smaller, more fuel efficient cars dur-
ing the time unleaded gasoline became re-
quired in new cars. The size of the tanks
fell at the same time.
3
If the average trans-
action is larger for leaded gasoline, the
fixed cost per transaction will be spread
out over a larger number of gallons. We
predict that self-service leaded transac-
tions involve larger average purchases
than self-service unleaded transactions.
4
Since the middle of 1981, the real price of
gasoline has fallen and new cars have got-
ten larger. The resulting increase in gas
tanks and average transactions for un-
leaded cars implies a narrowing differen-
tial. The average unleaded/leaded differ-
ential in the United States was 4.4<t in 1978
and peaked in real terms in 1983. It has
fallen nearly steadily since 1983 and is
even negligible in some markets today.
In a competitive world, equation (4) is
valid in the absence of other costs that are
not constant per gallon. Assume it takes
three seconds (.05 minutes) longer to
pump a gallon of unleaded and two addi-
tional minutes to purchase gasoline out-
side of the pumping, F. Assume an aver-
age unleaded transaction is eight gallons
and an average leaded transaction is 12.5.
Equation (4) becomes
(5)
K-05)
+
[2*045)] + .01
.14 r
+
.01.
To
create a differential of $.06, the per min-
ute rental rate must be $.05/.14 which
equals $.35, or $21 per hour. Assume that
the island is in demand eight hours per
day. Then the daily rental is $168 and the
monthly is $5040. A four-island self-ser-
vice station would be predicted to have a
rental of $20,160. In the Los Angeles area,
according to conversations with oil com-
pany executives, the monthly payment
from a dealer to the oil company leasing
the station with its pumps and storage
tanks might be as high as $10,000. When
labor costs are included, the $20,160 figure
is plausible.
3.
Peter Hartley
of
Rice University tells
us
that
in
Australia, where new cars were
not
required
to use
unleaded gasoline until relatively recently, there is
no
price spread between leaded and unleaded gasoline.
4.
Even though the gas tanks
of
cars using leaded
gasoline
are
larger than those using unleaded, which
average transaction
is
larger
is an
empirical question.
The direction
of
the self-service premium predicts that
leaded transactions
are
larger
on
average. Below
we
discuss why
the
average purchase
of
full-service
un-
leaded may be smaller. Our point here is to show how
price
is a
function
of
cost.
LOTT & ROBERTS: A GUIDE TO PRICE DISCRIMINATION
17
Unfortunately, stations we examined
only keep track of total gallons sold and
not the number of customers or average
size of transaction. So we are unable to
provide direct evidence of the impact of
transaction size. We found further indirect
evidence by looking at the price differen-
tial between full- and self-service gasoline
by grade of gasoline. The fixed cost per
transaction for full-service gasoline is
larger than that for self-service. This is an
obvious reason for why full-serve is more
expensive than self-serve. We might ex-
pect these costs to be the same across
grades of gasoline. It takes an attendant
just as long to check the oil and air pres-
sure and clean the windows for cars that
use super unleaded as it does for cars
using standard unleaded. But in fact, the
differential is typically larger for regular
unleaded or leaded than for super.
We can use the logic of equation (4) to
derive the full-serve/self-serve differen-
tial for leaded gasoline:
(6)
~
p
L ~
- [rF/Gj).
The subscript FL refers to full-service
leaded, Gi is self-serve, s is the extra time
(in minutes) to provide full-service, in-
cluding the extra time at the pump, and
e is the extra labor cost (per minute) to
provide full-service. If purchasers of every
grade used the same extra amount of time,
s, and bought the same amount, the dif-
ferential across grades would be a con-
stant. But as equation (6) shows, as full-
serve purchases decrease relative to the
size of self-serve purchases, the differen-
tial increases. The intuition is the same as
before—smaller purchases mean that the
fixed cost (in this case the extra cost of
labor services and time to provide full ser-
vice) is spread over a smaller number of
gallons, so the differential is larger.
We assume that the opportunity cost of
time for those who use super unleaded is
higher than for those who use other
grades of full service. Both full- and
self-
serve super unleaded customers are more
likely to wait until their tanks are almost
empty and then fill them completely.
Customers demanding leaded gasoline
and, to a lesser extent, regular unleaded
are likely to be poorer and have lower time
costs than those using super unleaded.
When they use full service, they are more
likely to purchase a small amount to ob-
tain the service and bear the additional
time cost of filling up the rest of the tank
later. In a competitive market, stations
charge a premium to cover the cost of this
behavior.
A survey of sixty-six American cities in
1983 (National Petroleum News Factbook
[1984]) found that in the sixty-five cities
for which all the data were available, fifty
had a substantially smaller (usually rang-
ing from 5-15$) full-serve premium for
super unleaded than for either leaded or
regular unleaded. In the remaining fifteen
cities,
the premium was within It of the
lowest of the other two. Interestingly, the
regular unleaded premium for full-serve
was very close to that of leaded.
A two-part tariff—a fixed price for the
service (or for using the pump in the case
of self-service) and a per gallon price for
the gasoline—also covers costs. A problem
with this scheme is monitoring the atten-
dant who can pocket the fixed part of a
cash payment unless the pump cheaply
and accurately registers the number of
transactions. As noted above, current
pumps do not. The failure to observe a
two-part tariff is also inconsistent with an
explanation based on monopoly power—
if stations have monopoly power then a
two-part tariff that can be cheaply admin-
istered is also likely to improve profits if
the customers of different grades impose
different costs on the firm.
Whether transaction size can explain
the variation in gasoline pricing is an em-
pirical question. Our goal in this section
has been to show that plausible variations
in purchase size can lead to the observed
variation in prices. Even under perfect
18
ECONOMIC INQUIRY
competition, real world pricing is not sim-
ply a matter of wholesale cost plus a con-
stant markup. Not only will prices vary
with purchase size, but variations in
prices across grades may arise from many
other sources. For example, the inventory
costs of each grade of gasoline may differ
if there are differences in the predictability
of demand across grades. Even prices for
a single grade will vary across stations
due to quality differences; stations com-
pete on many dimensions including qual-
ity of service and expected queuing time
during times of peak demand. The failure
to explain retail price variations with
wholesale price variations is simply not
evidence of monopoly power.
III.
THE "HIGH" PRICE OF COFFEE, TEA,
AND DINNER IN RESTAURANTS
Several authors (e.g., Heyne, [1987,
191-2]) attribute the higher prices for the
same,
meal at dinner relative to lunch to
price'discrimination. While the size of din-
ners are assumed to be larger, this is not
thought to be sufficient to explain the
price differential. According to Heyne,
lunch-time diners have searched more and
thus have more elastic demand curves for
lunches. We have seen no evidence that
the typical restaurant has monopoly
power. Whether lunch patrons have more
information than dinner patrons is an-
other empirical question.
A different explanation for the price
differential, consistent with competition,
is that there is quicker turnover at lunch
because diners face more severe time con-
straints. Analogous to our discussion of
gasoline pricing, the cost of producing a
meal is not just the cost of the food but
also the rental cost of the space used dur-
ing the meal. The more leisurely dinners
that people enjoy result in a higher im-
plicit rent at dinner time embodied in the
prices. Dinner meals are larger for the
same reason—the patrons have more time
to enjoy them. While two-part tariffs are
also theoretically possible to separate the
cost of the food from that of the rent, we
assume that explicitly charging for the
time at the table, say in the form of a tick-
ing meter, would affect the quality of the
meal.
This opportunity cost of using a table
explains why the retail over wholesale
mark-up in a restaurant varies across the
types of food. For instance, coffee, tea, and
wine are priced seemingly so far above
their "marginal costs" because people ei-
ther linger over these items, or linger
longer over meals that include them. The
prices of these items must include the cost
of renting the table. This implies that for
items with little or no labor preparation
costs,
such as beverages, the mark-up is
largest for those beverages that people lin-
ger over longest. So wine should have a
larger absolute difference between its re-
tail and wholesale price compared to beer,
and both are going to be larger than for a
soda.
5
Alcohol and coffee also have large
inventory costs. Restaurants typically
stock all types of liquor and will throw out
many cups of coffee over the course of a
day to insure its freshness.
If this explanation is correct, why
doesn't McDonald's charge a lower price
for take-out items? If McDonald's charged
a lower price for take-out, they would
incur monitoring costs making sure take-
out customers did not stay inside and use
a table anyway. Many restaurants do,
however, charge a lower price for take-
out.
A related puzzle is why restaurants
offer free refills of coffee and iced tea. One
answer is that most people wish to drink
more than one cup or glass, and that
rather than have the waitress keep track
of all the refills (which she could chisel on
in search of larger tips), the restaurant sets
5.
There is the additional cost of the liquor license
in the case of alcohol.