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CHAPTER 5: Pricing and demand
In 1993, Mars began exporting its popular Snickers chocolate bar to Russia. They had no experience in Russia, so they
based the Russian price on the price in Great Britain. One local distributor began selling the candy to retailers for much
higher prices--and pocketed the difference. Some months after her misdeeds were discovered, Mars did a demand
study that verified what the distributor already knew---that customers were willing to pay six times the amount charged
in Great Britain due to the novelty of the candy and the fact that they were the first western-style candy bar in Russia.
Unfortunately, by the time the mistake was discovered, foreign competitors had already entered the market and the
demand for Snickers dramatically declined.
The purpose of this chapter is to teach you how to price products and to avoid mistakes like this. We introduce demand
curves as a way to describe consumer behavior for the purpose of making profitable pricing decisions.
Aggregate or market demand
There are two distinct types of demand curves: aggregate and individual. Aggregate demand curves are important for
understanding group or aggregate behavior, and individual demand curves are important for understanding individual
behavior.
Aggregate demand can best be described with an example. Suppose that there are nine buyers, each of whom wants to
buy a single unit of a good. To construct a demand curve, simply arrange the buyers by what they are willing to pay,
e.g., ($6, $5, $4, $3, $2, $1). At a price of $6, only one buyer will purchase1; at a price of $5, two buyers will purchase;
at $4, three buyers; and so on. At a price of $1, all six buyers will purchase the good. An aggregate demand curve is
the relationship between the offered price and the number of purchases made by this group of consumers. In the Table
below, we plot this aggregate demand curve.
MR
6
4
2
0
-2
-4
MC
1.5
1.5
1.5
1.5
1.5
1.5
Aggregate Demand
8
Price
Price Quantity Rev.
6
1
6
5
2
10
4
3
12
3
4
12
2
5
10
1
6
6
6
4
2
0
0
2
4
6
8
Quantity
Table 3: Aggregate Demand Curve
Demand curves present sellers with a dilemma. Sellers can raise the price and sell fewer units, but earn more on each
unit sold. Or they can lower price and sell more, but earn less on each unit sold. This fundamental tradeoff is at the
heart of pricing decisions, and is resolved by using marginal analysis because pricing is an extent decision. To sell
more, you have to reduce price.
Definition: The marginal revenue (MR) is the change in total revenue associated with an extra unit sold.
Marginal revenue is the benefit of producing and selling one more unit. As long as marginal revenue is larger than the
marginal cost, profits increases with each extra unit sold. This relationship underscores the usefulness of marginal
1
Do not get distracted by the fact that at a price of $6, the buyer is being charged a price exactly equal to his value, and
is thus earning no surplus. At a price of $6 the buyer is exactly indifferent between buying and not buying. This is an
artifact of the use of whole numbers to describe prices and values. For convenience, imagine value is a fraction above
the price, so that the buyer will purchase
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analysis. You don’t need to know the entire demand curve to know what whether to sell another unit, only the
marginal revenue at the current price.
Proposition: If marginal revenue is greater than the marginal cost then marginal profits are positive, and total
profits increase if you sell one more unit. Sell more (reduce price) if MR>MC and sell less (raise price) if MR<MC.
In the table above, if marginal cost were $1.50, you would want to sell three units; if marginal cost were $2.50, you
would sell two units units. Note that the question “Should I sell less or more?” is equivalent to the question, “Should I
raise or lower price?”
Going back to the problem of selling Snickers in Russia, the company failed to realize that the marginal revenue was
much lower than the marginal cost. If Mars had experimented with different prices, or done marketing studies they
would have discovered that price was too low for Snickers in Russia.
Different prices for different consumers
At the profit-maximizing price of $4, only three of our consumers decide to purchase. Those consumers with values of
$3 and $2 do not purchase the good even though their values exceed the $1.50 marginal cost of producing the goods.
These two consumers represent two unconsummated wealth-creating transactions. The one lesson of business is to
figure out how to profitably consummate them.
The trick is to find a way to sell at a lower price to these low-value consumers without also reducing prices to the highvalue consumers. If you could sell to each of these two low-value consumers at a price of $2, then you would earn $1
more. To do this you have to identify the low-value consumers, figure out a way to lower price to them, and prevent
them from re-selling to high-value consumers. You have to guard against the possibility that offering a unit for sale at
a lower price will “cannibalize” sales to the high value customers. In Chapter 9, we will discuss how to implement
schemes like this.
Discussion Question: Suppose you have nine consumers who make up an aggregate demand curve with values of $4,
$5, $6, $7, $8, $9, $10, $11, and $12. What is the revenue-maximizing price? Now suppose that old people make up
the group of with values of $4, $5, and $6 and young people make up the group with values of $7, $8, $9, $10, $11, and
$12. Design a price discrimination scheme.
Answer: The revenue-maximizing price is $6 for total revenue of $42. But if you can charge different prices to old and
young people, then charge a $4 price to the old people for revenue of $12 and charge a $7 price to the younger group
for revenue of $42. With this pricing scheme total revenue is $54.
Discussion Question: Is this kind of price discrimination wrong, or unethical? (HINT: does it move us towards or
away from efficiency?)
Individual demand
Individual demand curves describe the behavior of a single representative customer who demands more than one unit
of a good. Although individual demand curves look similar to aggregate demand curves, there are several important
differences that affect pricing decisions.
Again, the easiest way to describe individual demand curves is with an example. Consider a single customer who is
willing to pay $6 for the first unit, $5 for the second, $4 for the third, and so on, as above. IF the price is set at $6, our
consumer will purchase one unit; if the price is set at $5, two units; $4, three units; and so on. Each point represents the
value that our single customer places on each unit consumed, e.g. the consumer values the first item at $6; the second at
$5, and so on. This differs from the aggregate demand curve, where each point on the curve represents a different
consumer with a different value for a single unit of the good.
Discussion Question: Why does the individual demand curve slope downward? That is, why does an individual’s value
decline with increased consumption of the good?
Answer: Eventually, after consuming enough of a good, your desire for the good decreases. This means your
marginal value, the value you place on an extra unit of the good---and the amount you are willing to pay for it--declines with each purchase. For example, a retailer who purchases from a manufacturer may find that the first few
items are relatively easy to sell, but to sell more, she may have to lower the price, “hold” the item in inventory for a
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longer period of time, or spend money promoting the item. All of these activities reduce the amount that the retailer is
willing to pay for additional items.
Discussion Question: Why do newspaper vending machines allow buyers to take more than one paper while soft drink
vending machines dispense just one can of soda at a time?
Answer: For most people, the marginal value of a second newspaper is zero. So even when given the chance to take a
second newspaper, most consumers won’t do it. 2 But the marginal value of a second can of soda is positive. Many
consumers would take the extra soda if given the chance.
Different prices for each unit consumed
If a seller is setting a single price, it doesn’t matter whether she faces an aggregate or an individual demand because the
profit calculus is the same. If the marginal cost is $1.50, she will sell all items where MR>MC, in this case three units
at a price of $4. And just as in the aggregate demand curve, at the optimal price, there are unconsummated wealth
creating transactions. At the profit-maximizing price of $6, our representative consumer purchases only three items.
The low-value “extra” goods – those worth $3 and $2 – do not get purchased even though the consumer would pay
more for these “extra goods” than the marginal cost of producing them. These two extra units represent
unconsummated wealth-creating transactions. Again, the one lesson of business is to figure out how to profitably
consummate them.
The trick to profitably selling more units is to find a way to sell these additional units, without dropping the prices of
the earlier units. There are several ways to do this.
i.
You can offer volume discounts, e.g. one good for $12, the second good for $11, and so on….
ii.
You can use two-part pricing. Charge a low enough unit price so that there are no unconsummated
transactions (in this example, $1.50) and then bargain over how to split the resulting consumer surplus.
The consumer’s total value for 5 units is $20 ($6+$5+$4+$3+$2+$1) which costs only $7.50. Bargain
over how to split the $12.50 worth of surplus to split between buyer and seller.
iii.
You can bundle the goods by offering five units at a bundled price of $20. The consumer values the first
good at $6; the first two goods at $11; the first three at $15; the first four at $18, and the first five at $20.
Notice the similarity of bundling to the timber tract pricing discussed in Chapter 4. If you set a bundled price of $20,
then the consumer demands the whole bundle, just as the logger has an incentive to harvest the whole tract under a
fixed payment of $15,000. To see this, construct the logger’s individual demand curve for trees. Recall that the tract
has a mix of fifty fir trees valued at $100, and fifty pine trees valued at $200. If we charge a price of $200, the logger
“consumes” fifty trees and we earn $10,000 but if we reduce the price to $100, the logger consumes one hundred trees
but our earnings don’t change. We can make more money by bundling the 100 trees together and selling them for
$15,000. By
This illustrates a very important lesson for pricing. When bargaining with a customer, do not bargain over unit price;
instead bargain over the price of a bundle. First figure out how much the consumer would demand if price were set at
marginal cost, and then bargain over the bundled price for this amount.
Summary
To summarize, the distinction between aggregate and individual demand is not important if you trying to determine a
single optimal price. The tradeoff—lowering price to sell more units—is the same for both aggregate and individual
demand curves, and leads to the same optimal price, where MR=MC. However, if you want to do better than this, you
need to be able to sell goods at different prices. This allows you to avoid the tradeoff between pricing high but selling
fewer items, and pricing low and selling more.
This practice is called price discrimination. Price discrimination schemes depend on whether you are facing an
aggregate or an individual demand. With aggregate demand, you charge different prices to different consumers; but
with individual demand, you charge different prices for each unit consumed.
2
One student said that he takes several Sunday papers at once because the papers contain valuable discount coupons.
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Summary of main points
Aggregate or market demand is the number of units will be purchased by a group of consumers at a given price.
Individual demand is the number of units an individual will purchase at a given price.
Pricing is an extent decision. Reduce price (increase quantity) if MR>MC. Increase price (reduce quantity) if
MR<MC. The optimal price is where MR=MC.
At the optimal price, there are unconsummated wealth-creating transactions.
For an aggregate demand curve, consummate these transactions by charging different prices to different groups of
individuals.
For an individual demand curve, consummate these transactions by charging different prices for different
quantities consumed.
When bargaining with a customer, do not bargain over a unit price; bargain instead over the cost of a bundle. First
decide how much the consumer would demand if price were set at marginal cost, and then bargain over the price
for this bundle.
Homework problems
Individual problems
Setting a single optimal price: Suppose you have 10 individuals with values {$1, $2, $3, $4, $5, $6, $7, $8, $9, $10}.
Your marginal cost of production is $2.50. What is the profit-maximizing price?
But what about fixed costs?: Using information from question 1, your boss tells you that price cannot drop below $9
because you cannot earn enough profit to cover your fixed cost. What should you tell him?
Different prices to different groups: Using the same demand curve, suppose you find a way to charge one price to the
consumers whose values are {$1, $2, $3, $4, $5}, and a different price to those consumers whose values are {$6, $7,
$8, $9, $10}. If it costs $5 to implement this price-discrimination scheme, should you do it?
Different prices for different quantities: Pretend that the demand curve in question 1 is the demand curve facing a
representative individual, e.g. the individual places a value of $10 on the first item consumed, $9 on the second, and so
on. Suppose that MC=$2.50. If you were going to bundle the goods and set a bundled price, what price would
maximize profits?
Individual Demand: Jennifer loves Czech music. Her favorite composer is Antonin Dvorak who wrote nine
symphonies. Jennifer ranks his 9 symphonies in exactly the order in which they were written. The following data
present the value she places on having these symphonies which she does not currently yet own:
RANK_________Total_Personal_Value
1_______________19
2_______________36
3_______________51
4_______________64
5_______________75
6_______________84
7_______________91
8_______________96
9_______________99
Interpret the above to mean, for example, that Jennifer values her favorite Symphony at $19, and that the total value of
the first Symphony plus Symphony # 2(her second favorite) is $36, etc.
If the symphonies were sold individually on CD's - one symphony per disc - and the price per CD was $10.00, how
many CD?s would she buy?
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Individual demand & bundling: Referring to the question above: If the symphonies were, also offered as a complete set
of 9 CD's and the price of the entire set was $79.00, would she rather buy the individual CD?s or the box set? HINT:
WHICH OPTION GIVES HER MORE CONSUMER SURPLUS?
Group problems
Pricing decision: Describe a pricing decision in your company. Was price set optimally? How would you improve the
price? What information would you want to improve your price? Be careful to make specific references to long-run
and short-run decision-making. Compute the profit consequences of the decision.
Price Discrimination (different prices to different consumers): Describe a price discrimination opportunity facing your
company. How would you implement the discriminatory pricing practice? How would you identify the different
values that consumers have? How would you prevent arbitrage between the consumers? Compute the profit
consequences of such a discriminatory system.
Price Discrimination (different prices for each unit consumed): Describe a price discrimination opportunity facing your
company. How would you implement the discriminatory pricing practice? How would you identify the different
values that consumers have? Compute the profit consequences of such a discriminatory system.
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CHAPTER 6: Pricing and elasticity
Between December 20, 1994 and February 1, 1995, the Mexican peso fell by 40 percent against the dollar. Interest
rates in rose sharply, business activity slowed, and unemployment increased dramatically, particularly among those
industries that had paid in dollars for raw materials and debt capital. All of these changes resulted in a dramatic decline
in consumer income and Firm X saw consumption of its processed meats, including hot dogs, decline by 35%. This
was surprising to the company's management because they had thought of their products as staples whose consumption
would hold steady, or perhaps even rise as income fell.
They did a survey and found that many of their customers had turned to a cheaper source of protein---cat food mixed
with eggs and rolled up in a tortilla. Further analysis showed that the decline was limited to Firm X’s premium brands.
The lower-priced brands took off with double-digit volume increases. Unfortunately for Firm X, the lower-end brands
were priced below marginal cost and so lost money.
Firm X would have undoubtedly benefited from a better understanding of demand for its products, and how to set
profitable prices. In this chapter we continue with our analysis of pricing decisions and demand by considering
elasticity, a useful summary statistic of demand.
Defining elasticity
Elasticity describes the sensitivity of demand to changes in various factors. Elasticity is typically the only quantitative
information you will have about demand. Fortunately, it is often enough to make good pricing decisions.
Definition: price elasticity=(% change in quantity demanded)  (% change in price)
If |e| is less than one, demand is inelastic.
If |e| is greater than one, demand is elastic.
Price elasticity is negative (because price and quantity move in opposite directions).
Definition: income elasticity=(% change in quantity demanded)  (% change in income)
Negative income elasticity means the good is inferior, i.e. as income increases demand declines.
Positive income elasticity means the good is normal, i.e. as income increases demand increases.
Definition: cross-price elasticity=(% change in quantity of good one)  (% change in price of good two)
Positive cross price elasticity means the good two is a substitute for good one, i.e. as the price of a substitute increases,
demand increases.
Negative cross price elasticity means the good two is a complement to good one, i.e. as the price of a complement
increases, demand decreases.
Definition: advertising elasticity=(% change in quantity)  (% change in advertising)
Advertising elasticity is positive.
Describing demand using price elasticity
Proposition: Price elasticity is negative because price and quantity move in opposite directions, i.e., demand curves
slope downward.
This law reminds us of the fundamental tradeoff: you can raise price and sell less, but earn more on each unit sold; or
you can reduce price and sell more, but earn less on each unit sold. Consumers respond to a price increase by
switching to their next-best alternative. If their next-best alternative is a very close substitute, then demand is very
elastic. A next-best alternative can be a substitute product, or the “no purchase” option.
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Discussion Question: Do all demand curves slope downward?
Answer: No. Some demand curves may not react at all to price. This is true especially in the short run.
Proposition: In the long-run, demand curves become more price elastic -- |e| increases. If given more time, people
react more to price changes. They are able to find better substitutes when price goes up, and to find more uses for the
good when price goes down.
The second law of demand also could be explained by the speed at which pricing information is disseminated. As time
passes, information about a price change becomes more widely known. A greater number of consumers will have the
information necessary to react to the price change.
Discussion Question: Give an example of the second law of demand.
Answer: In the short-run, the cross-price elasticity of demand for electric water heaters with respect to the price of
electricity is very low. But given enough time, consumers will react to an increase in the price of electricity by
switching to from electric to gas water heaters. The long-run cross-price elasticity of demand for gas water heaters
with respect to the price of electricity is relatively large.
Answer: Another example is ATM fees. Firm X is a bank in a medium-sized mid-western city. In 1997, the bank ran
an experiment to determine elasticity of demand with respect to ATM fees. At a selected number of ATM machines,
user fees were raised from $1.50 to $2.00. When informed of the fee, users typically completed the current transaction,
but avoided the higher-priced ATM machines in the future. In the short-run, elasticity was low. In the long-run, it was
much higher.
Proposition: As price increases, demand curves become more price elastic -- |e| increases. As price goes up,
consumers find previously unattractive substitutes more attractive. As price increases, more and more alternatives
compete with the original good.
Discussion Question: Give an example of the third law of demand.
Answer: High fructose corn syrup (HFCS) is a caloric sweetener used in soft drinks that is a perfect substitute for
sugar. Due to U.S. sugar import quotas and price supports, the price of sugar is about twice that of HFCS. Since there
are no close substitutes for the low-priced HFCS, its demand is relatively inelastic. But if the price of HFCS were to
rise to that of sugar, sugar would become a good substitute and the demand for HFCS would become very elastic. In
the figure below, HFCS demand becomes very elastic as the price approaches the price of sugar.
HFCS
Price
Sugar Price
HFCS Demand
HFCS Quantity
Figure 1: HFCS demand
Estimating Elasticity
Note there are several ways to compute percentage changes, depending on whether you use the beginning numbers or
the ending numbers in the denominator. I like to use the midpoint of the prices and quantities in computing percentage
changes, which leads to the following formula.
Definition: Arc price elasticity=[(q1-q2)/(q1+q2)]  [(p1-p2)/(p1+p2)]
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In computing the midpoints, one would use the formulas (q1+q2)/2 and (p1+p2)/2. Since two divides both
denominator and numerator, the formula simplifies, as above.
Discussion Question: Firm X is a small retail supermarket chain with stores located in rural areas of Tennessee,
Kentucky, and Mississippi. In 1999, in one of the stores, the price of all three-liter coke (diet, caffeine-free, and
regular) was decreased from $1.79 to $1.50 in order to match a similar price being offered at Wal-Mart. Quantity of
three-liter coke increased from 210 to 420 units/day, but quantity of two-liter coke declined from 120 to 48 units/day
because the price of two-liter coke stayed constant at $1.19
i.
ii.
iii.
What is the price elasticity of daily demand for three-liter coke at this store?
What is the cross-price elasticity of demand for two-liter coke with respect to the price of three-liter
coke?
What is the price elasticity of daily aggregate demand for coke (two-liter and three-liter)?
Answer:
i.
ii.
iii.
3 Litre
2 Litre
The price elasticity of demand for three-liter coke is [(210-420)/(210+420)]  [(1.791.50)/(1.79+1.50)]=-3.87.
Cross price elasticity is [(120-48)/(120+48)]  [(1.79-1.50)/(1.79+1.50)]=4.86.
Aggregate demand increases from 870 to 1356 liters of coke. The difficult part about computing
aggregate elasticity is computing the changes in aggregate price. Here we use a price index based on
the initial quantities of two- and three-liter coke.3 The price index drops from $0.52/liter to
$0.46/liter. The aggregate demand elasticity is [(870-1356)/(870+1356)]  [(.52-.46)/(.52+.46)]=1.92.
Product
Q 3-liter
P of 3-liter
Initial
210
$1.79
Final % change
420
66.67%
$1.50 -17.63%
Q 2-liter
P of 3-liter
120
$1.79
48
$1.50
-85.71%
-17.63%
4.86
870
$0.52
1356
$0.46
10.92%
-3.12%
-3.50
Total Litres Q liters
P liters
elas.
-3.78
Figure 2: Spreadsheet for computing elasticities
Three-liter coke has a very elastic demand (i), due to the presence of a very close substitute (two-liter coke), as
indicated by its large and positive cross-price elasticity (ii). As the price of three-liter coke falls, consumers substitute
three-liter coke for two-liter coke. The aggregate elasticity is lower (iii), as we would expect because brand loyalty is
much stronger than package loyalty. However, it is not much lower, probably due to the presence of a close substitute,
canned Coke.
Discussion Question: As a grocery store manager, you alternate weekly pickle promotions between Heinz and Vlasic.
On a promotion week for Vlasic, the price of the Vlasic pickles drops by 25 percent and quantity demanded increases
by 300 percent. Compute the price elasticity of demand from this natural experiment.
Answer: Although many students are tempted to mechanically apply the formula to compute 300 percent  25
percent=-12, that would be wrong. Elasticity measures the price sensitivity of demand, holding other factors constant.
Here, the price of Vlasic decreases by 25 percent, but the price of Heinz also increases by 25 percent as it goes “off
promotion.” The change in the Heinz price “pollutes” the natural experiment of reducing the Vlasic price. Also,
consumers could be “stockpiling” their favorite brands, essentially “stealing” consumption from next week when they
do not buy any pickles. Both of these factors will make the weekly price elasticity of demand for Vlasic pickles appear
more elastic than it really is. Failure to recognize this could lead to mistaken pricing decisions.
3
It is important to use a fixed weight price index, one whose weights do not change. Otherwise, you will
overerestimate the degree to which price decreases. This will lead to computed elasticities that are too low.
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Quick and Dirty Estimators of Price Elasticity
Elasticity of demand can be estimated from survey data, or from naturally occurring experiments like the decline in the
price of 3-litre Coke. However, these data can be costly to collect and may not be precise enough to offer much
practical information. As an alternative to formal estimation, we propose two “quick and dirty” formulas for
computing elasticities.
Linear demand curve elasticity: If you assume that demand can be approximated by a linear function, you can use the
formula, e=p/(p-pmax) to elicit individual price elasticities from consumers. Simply ask what they currently pay for the
product (p) and how high price would have to be for them to stop consuming the product (p max).
Discussion Question: Who recently bought a pair of branded running shoes? What price did you pay? How high
would the price of the brand have to go before you would switch to another brand of running shoes?
Answer: I paid $80 for a pair of Saucony running shoes. At a price of $100, I would switch to another brand such as
Nike. My price elasticity of demand for Saucony brand running shoes is 80/(80-100)=-4. Typically demand for
individual brands is demand is very elastic or sensitive to price, ranging from –1.5 to –4.
Let’s try the same exercise, but at a higher level of aggregation. For example, consider running shoes in general.
Discussion Question: Who recently bought a pair of running shoes? What price did you pay? How high would the
price of all running shoes have to go before you should switch to a different type of shoe?
Answer: I paid $80 for a pair of running shoes. At a price of $280, I would switch to a different type of shoe such as
tennis shoes. My price elasticity of demand for all running shoes is 80/(80-280)=-0.4.
Proposition: Demand for aggregate categories of products is less elastic than demand for the individual brands
comprising the aggregate.
Your elasticity of demand is determined by the attractiveness of your next-best alternative – the opportunity cost of the
purchase. If you next-best alternative is comparable to the one you are making – meaning all you have to do is switch
brands – then your demand is very elastic. But if your next best choice is much less attractive – meaning you have to
switch to a different product altogether – then your demand is relatively inelastic.
Elasticity and market share: The individual brand demand elasticity is approximately equal to the industry elasticity
divided by the brand share.4
Discussion Question: Suppose that the elasticity of demand for all running shoes is –0.4 and the market share of a Nike
running shoe is 20 percent. What is the price elasticity of demand for Nike running shoes?
Answer: The brand elasticity is (–0.4/.20)=-2.0
Using elasticities for prediction
Prediction Formula: (% change in factor)*factor elasticity=(% change in quantity demanded)
Discussion Question: You have an estimate of income elasticity of demand for the Wall St. Journal of 0.50. Between
1997 and 1998, real income grew by 3.5% in the United States. Estimate how this affected demand for the Wall St.
Journal.
Answer: Since the income elasticity of demand is positive, the Wall St. Journal is a “normal” good, i.e. its demand
increases with income. The change in income times the elasticity gives you an estimate of the change in demand,
.5*3.5%=1.75%. Demand for the Wall St. Journal is estimated to increased by 1.75%.
Discussion Question: The 1995 real per-capita median income in Arizona is $30,863; and in Colorado, $40,706. 5
Estimate the difference between per capita consumption of the Wall St. Journal in Colorado and in Arizona?
Answer: The difference in income between Arizona and Colorado is (40,706-30,863)/( 40,706+30,863)/2=27.50%.
The difference in demand is equal to the income elasticity times the difference in income, .5*27.50%=13.75%.
4
The intuition behind this approximation is that an individual brand price change does not have much effect on
industry price.
5
http://www.census.gov/.
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Demand is estimated to be 13.75% higher in Colorado than in Arizona. Note that these are differences in real, not
nominal, income. Real income is nominal income divided by the price level so that it represents purchasing power.
Using price elasticity to make pricing decisions
Price elasticity and revenue
The reason that price elasticity is such a useful measure of demand is that it is related to the marginal revenue, which
is the marginal benefit of selling another unit. To understand the relationship between marginal revenue and elasticity,
note that %Revenue  %Price+ %Quantity.6 When price goes up, quantity goes down, and vice-versa. If the
percentage increase in price is larger than the percentage decrease in quantity, then revenue goes up. This occurs when
demand is relatively inelastic, or relatively unresponsive to price.
We can express the implied relationship between the marginal revenue and elasticity as follows:
Proposition:7 MR=P(1-1/|e|)
It follows that if demand is elastic (|e|>1), then marginal revenue is positive, i.e. you can increase revenue by increasing
quantity. If demand is inelastic (|e|<1), then marginal revenue is negative, i.e. you can increase revenue by decreasing
quantity.
Discussion Question: In 1980, Marion Barry, mayor of the District of Columbia, raised the sales tax on gasoline sold in
the District by 6 percent. What happened to gas tax revenue?
Answer: The increase in the gasoline tax amounts to an increase in price. Quantity declines, but to determine what
happens to revenue, we have to know whether the percentage decline in quantity is larger or smaller than the
percentage increase in price. And this depends on the elasticity of demand for gasoline in the District of Columbia.
Since DC has a lot of commuters who from Virginia and Maryland, it’s gasoline in Maryland and Virginia is a close
substitute for gasoline in the District. In other words, demand for gasoline sold in the District is very elastic. Before the
tax was put into law, gasoline station owners in the District argued against the tax, predicting that it would reduce
quantity by 40 percent. Bill Cook, associate director of the city’s department of finance and revenue predicted that the
tax would raise revenue. He was horribly wrong. The reduction in quantity was 38 percent, very close to what the gas
station owners had predicted. The DC Council repealed the tax within three months. To raise tax revenue, Barry
should have lowered the sales tax instead of raising it.
Note the similarity of the effect of the gas tax to the effect of the turnover tax on the Swedish stock exchange. Demand
for trading on the Swedish stock exchange was very elastic because traders had close substitutes, i.e., trades on the New
York and London exchanges.
Discussion Question: If demand for Nike sneakers is inelastic, should Nike raise or lower price? 8
Answer: If demand is inelastic, you can raise revenue by raising price. You also lower total costs because as you raise
price, you can sell fewer units (fewer units means lower total costs). If total revenue goes up and total costs go down,
then profits increase. It follows that an individual firm should never price on the inelastic portion of its demand curve--always raise price to the point where demand becomes elastic.
Discussion Question: If demand for Nike sneakers is elastic, should Nike raise or lower price? 9
Answer: If demand is elastic, revenue goes up, but so do costs because quantity increases. To determine what to do,
use marginal analysis.
6
This is a first-order approximation and will work well for small changes. The approximation does not work well for
large changes.
7
MR=Revenue/Q=(PQ)/Q=(PQ+QP)/Q=P(1-1/|e|); The symbol “” means "change in."
8
Discussion Question: If demand for Nike sneakers is elastic, should Nike raise or lower price? Answer: It depends
on marginal costs.
9
Discussion Question: If demand for Nike sneakers is elastic, should Nike raise or lower price? Answer: It depends
on marginal costs.
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Price elasticity and profits
The profit-maximizing or optimal price depends on marginal costs as well as on marginal revenue. From our
discussion of marginal analysis, we know that if MR>MC, then we should lower price and sell more, and if MR<MC,
then we should raise price and sell less. Price is set optimally when MR=MC. We exploit our knowledge of the
relationship between marginal revenue and elasticity to compute a formula for the profit-maximizing price.
Proposition: The profit-maximizing price, i.e. that price where MR=MC, is:
P(1-1/|e|)=MC; or
P=MC/(1-1/|e|); or
(P-MC)/P=1/|e|
Discussion Question: In the Coke example above, the mark-up of 3-liter Coke is 2.7% at a price of $1.50. Should you
raise or lower price?
Answer: In this case the current markup 2.7% is less than the desired markup 1/|3.78|=26% so the current markup is
too low. However, 3-liter Coke is being used as a “loss leader,” and is deliberately priced low as an advertisement to
attract customers in the hope that they will spend money on other items once they come to the store. In this case, you
forego profits by pricing Coke too low in exchange for higher profits on other items.
Discussion Question: Sales people have incentive-compensation schemes based on revenue. Consequently they are
willing to make a sale as long as it increases revenue, i.e., as long as MR>0. The company, for whom the sales people
work, would like to maximize profits, that is make sales as long as MR>MC. This often leads to conflict between the
sales people and their supervisors because the sales people prefer lower prices, those where MR>0, whereas the
company prefers higher prices, those where MR>MC. How should you solve this incentive conflict?
Answer: Sales people make all sales where MR>0 because they are compensated on the basis of revenue. A simple
solution would be to base the incentive-compensation scheme on profitability, rather than on revenue.
Discussion Question: There are five horseracing tracks in Kentucky. The Kentucky legislature allows only one track to
be open at a time. How does this affect the price the track can charge for its product?
Answer: By making sure that there are no close substitutes for the open track, the Kentucky legislature lowers the
elasticity of demand for the track that is open and indirectly permits each track to charge higher prices. Remember (PMC)/P=1/|e|. If the track owners had agreed to this on their own, without the help of the legislation, they would be
violation of the U.S. antitrust laws. This would be a form of collusion to eliminate competition between them. When
they get the Kentucky legislature to do it for them, it is OK because everyone is allowed to petition the government—
even colluders.
Discussion Question: What happened to demand for racetrack betting when a riverboat gambling casino opened up in
the state of Indiana?
Answer: Although the casino’s entrance into the market caused horseracing attendance to fall, the horse-track
gambling profits did not change very much. High-income customers for whom riverboat gambling is a poor substitute
drive horse track profitability. It was the lower-income, lower-profit customers who tended to abandon the racetrack for
riverboat gambling.
Summary of main points
factor elasticity=(% change in quantity demanded)  (% change in factor)
Price elasticity, income elasticity, cross-price elasticity, and advertising elasticity measure how sensitive quantity
demanded is to changes in these factors.
Three characteristics of demand can be expressed in terms of price elasticity:
Demand curves are negatively sloped --- e<0.
In the long-run, demand curves become more sensitive to price changes --- |e| increases.
As price increases, demand curves become more sensitive to price changes --- |e| increases.
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Demand for individual brands is more elastic than demand for aggregate categories of goods.
You can predict changes in demand, (% change in factor)*factor elasticity=(% change in quantity demanded)
Marginal revenue is related to the elasticity of demand, MR=P(1-1/|e|), i.e. if demand is elastic (|e|>1) and you
raise price, revenue decreases. If demand is inelastic (|e|<1) and you raise price up, revenue increases.
You can do marginal analysis with an estimate of elasticity. The following conditions are all equivalent and tell
you when to produce more, or equivalently, reduce price:
MR>MC
P(1-1/|e|)>MC; or
P>MC/(1-1/|e|); or
(P-MC)/P>1/|e|
Homework problems
Individual problems
Marginal Analysis: If elasticity is –2, price is $10 and marginal cost is $8, should you raise or lower price?
Luxury Boxes at Adelphia Coliseum: Among the many design problems that face designers of Adelphia Coliseum is
the number of luxury boxes to include. (Luxury boxes are enclosed suites that look out onto the playing field,
containing plush furniture, bar facilities, and the like) For simplicity, suppose that luxury boxes are sold outright to
local businesses, and that a particular stadium can be built with up to 100 luxury boxes at a cost of construction of
$300K apiece. The designer of this stadium is planning to build 25 boxes, and expects (if he builds 25) to be able to
sell each for $1,000K, for a net profit of 700K X 25= 17,500K. An associate opines that this is crazy—since boxes can
be built at $300K and sold for $1000K apiece, building only 25 leaves money on the table. Is the associate correct?
Why or why not?
Domestic Steel Monopolist: In a small country, a domestic steel monopolist produces and sells steel at $680 per ton,
well above the world price of $375 per ton. This firm is protected against foreign competition by high tariffs that
eliminate competition from foreign firms. The firm maintains the tariffs by contributing heavily to the ruling party. On
the decision of the CEO, the firm has never exported steel. Why export at $375 per ton, when you can sell steel for
$680 per ton domestically? In addition, the average cost of producing steel is never below $400 per ton. Is the CEO
necessarily correct? Can this company make money by exporting steel? Why or why not?
Vandy vs. Tennessee at Adelphia: The Vanderbilt football team is playing Tennessee at Adelphia Coliseum and the
Vanderbilt athletic director is trying to decide how many tickets to sell to both Vanderbilt and Tennessee fans. He can
institute a system of direct price discrimination (different prices to different fans) by selling the tickets through their
different alumni associations. He does not have to worry about arbitrage. Tennessee Fans will purchase as many
tickets as Vanderbilt wants to sell at $10/ticket. For Vanderbilt fans, the athletic director estimates the demand curve in
Table 1. The athletic director decides to sell 50K tickets to Vanderbilt fans because that would imply that the price for
Vanderbilt fans was just equal to the opportunity cost (the foregone opportunity to sell to a Tennessee fan). Is this the
right decision?
Table 1: Vanderbilt Fan Demand for Tickets
Tickets
Price
10K
$18
20K
$16
30K
$14
40K
$12
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50K
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$10
Pricing ATM machines.: Firm X is a bank in a medium-sized mid-western city that currently charges $1/transaction at
its ATM machines. To determine whether to raise price, the bank experimented with two higher prices at selected
ATM machines. The following numbers reflect long-run behavior and are adjusted for seasonality. The marginal cost
of an ATM transaction is $0.50. What price should they charge?
ATM Fee
Usage
$2.00
1000
$1.50
1700
$1.00
2000
Pricing hospital services: Firm X is a private, for-profit hospital in a large southern city. It currently performs about
30 deliveries/month in its obstetrics unit. The price of a delivery is about $5,000 and the marginal cost of a delivery is
about $4,000. The obstetrics unit has the capacity to handle about 50 deliveries/month. The hospital is contemplating
lowering price to attract more patients to run the unit at capacity. What should it do?
Group problems
Elasticity of Demand: Describe the elasticity of demand for one or more of your products and describe how you could
profitably use the information about elasticity. Compute the profit consequences of the advice.
Forecasting Demand: Forecast demand for one of your products. If you used elasticity, how did you estimate it? How
would you profitably use the information contained in the forecast. Compute the profit consequences of the advice.
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