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CHAPTER THREE
DEMAND ANALYSIS AND
OPTIMAL PRICING
OBJECTIVES
1. To take a closer quantitative look at demand starting with a multi-variable
demand equation and continuing with a verbal description.
(Determinants of Demand)
2. To present the price elasticity of demand, other elasticities, and show how
elasticities can be used to predict sales (Elasticity of Demand)
3. To show the relationship between price elasticity and revenue changes i.e.
marginal revenue. Maximum revenue occurs at EP = -1 or MR = 0.
(Demand analysis and Optimal Pricing)
4. To demonstrate how the firm can maximize its profit by using optimal
markup pricing and price discrimination. (Demand analysis and Optimal
Pricing)
5. To examine the demand and pricing of information goods. (Information
Goods).
TEACHING SUGGESTIONS
I. Introduction and Motivation
A good teaching strategy is to introduce demand analysis by means of a
real-world business application. Here is one example:
A. Pricing Software. Consider a firm that produces a best-selling software
program. The firm continues to spend a great deal of money revising and
improving its software in an effort to maintain its market share lead over
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its next two or three strongest competitors. In fact, its last revision and
update cost much more than the company expected. In light of these
added development costs and any other relevant factors, how should top
management determine its pricing policy for the updated program?
B. Pricing Software, Discussion. Based on intuition, many students offer
pricing recommendations based on shaky logic. This deliberately
“leading” question prompts the following student reasoning “Since
development costs were higher than expected, the firm should increase
the unit price of its software to help cover these costs.” Besides being
incorrect, this reasoning misses the main point. The firm’s optimal
pricing policy depends on how sensitive demand is to price changes -- in
other words on the elasticity of demand. Because development costs are
fixed (indeed largely sunk), they do not affect the pricing decision. Since
the marginal cost of producing an extra copy of the software is trivial, the
firm’s problem is essentially pricing to maximize revenue. Thus, the
price and performance characteristics of competing spreadsheet software
are extremely important factors affecting demand elasticity.
II. Teaching the “Nuts and Bolts”
A. Teaching Approaches. According to design, the chapter combines two
important topics: demand analysis and pricing decisions. This suggests
two teaching approaches: 1. Teaching them together, or 2. Teaching
demand analysis alone and postponing the discussion of pricing until
after a discussion of monopoly. Though the second option is the
traditional approach, we obviously favor the first method. In either case,
the following “tried and true” points merit emphasis:
1. The difference between a movement along a demand curve and a shift
in the curve. Many instructors even make a distinction in terminology
between “increased demand” and “an increase in demand.”
2. The definition and computation of price elasticity. The text’s
presentation focuses on point elasticities (either discrete or
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continuous). The instructor may choose to extend the discussion to
arc elasticities. Another option we recommend is to present actual
elasticity estimates.
3. How elasticity varies along a linear demand curve and the relationship
between elasticity and marginal revenue. If only demand analysis is
covered, these points make a natural bridge into the empirical analysis
of demand covered in Chapter 4. (The instructor may also wish to
assign the appendix to Chapter 3.)
In turn, the discussion of pricing decisions emphasizes the following
points:
1. Maximizing revenue in pure selling problems. (The instructor should
continually emphasize that this is a special case of the general rule:
MR = MC. Otherwise, the occasional student may mistakenly start to
take MR = 0 as the monopolist’s optimal rule even when marginal
costs are significant.)
2. The logic and application of the optimal markup rule. (Reemphasize
that the firm’s current price cannot be optimal if demand is inelastic.
Thus, the markup rule does not apply for inelastic demand. Rather it
tells the manager how high to push the price into the region of elastic
demand.)
3. The logic and application of price discrimination.
B. Suggested Examples: Problems 5, 6, 7, 8, 9, 10, and 13.
C. Additional Problems
1. A golf-course operator must decide what greens fees (prices) to set on
rounds of golf. Daily demand during the week is: PD = 36 - QD/10 where
QD is the number of 18-hole rounds and PD is the price per round. Daily
demand on the weekend is: PW = 50 - QW/12. As a practical matter, the
capacity of the course is 240 rounds per day. Wear and tear on the golf
course is negligible.
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a. Can the operator profit by charging different prices during the week and
on the weekend? Explain briefly. What greens fees should the operator
set on weekdays, and how many rounds will be played? On the
weekend?
b. When weekend prices skyrocket, some weekend golfers choose to
play during the week instead. The greater the difference between
weekday and weekend prices, the greater are the number of these
“defectors.” How might this factor affect the operator’s pricing
policy? (A qualitative answer will suffice.)
Answer
a. Because demand conditions differ, the operator can profit from a policy
of price discrimination. She faces a pure selling problem. In order to
maximize weekday revenue (and profit), management sets
MRd = 36 - .2Qd = 0 implying Qd = 180 rounds and Pd = $18 per
round. On weekends, we have MRw = 50 - Qw/6 = 0 implies Qw =300
rounds. However, maximum capacity of the golf course is 240 rounds,
so the operator must set Qw = 240. The optimal weekend price is PW =
$30.
b. To deter defections (and preserve revenue), the operator should narrow
the price gap: raise weekday prices and lower weekend prices slightly.
2. A hardback book publisher has just released an exciting political thriller that
is likely to be a best-seller. The book’s marginal cost (including printing,
shipping, author royalty, and so on) is $8 per book, and its projected
demand curve is: P = 28 - .4Q, where Q denotes monthly sales (in
thousands) of books. (In short, Q = 20 means 20 thousand books.)
a. Determine the publisher’s profit-maximizing output and price for the
best-seller.
b. At this chosen price, suppose that the price elasticity of demand turns out
to be EP = -2. Would this lead the publisher to change its price? If so, to
what?
c. The publisher plans to sell foreign editions of the best seller for $20 in
Western Europe, $14 in Taiwan, and $11 in India. How might the
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publisher profit from this pricing strategy? (A qualitative answer is
sufficient.)
d. The publisher expected Amazon to sell the corresponding e-book at a $14
price; instead Amazon has chosen to release the e-book at $10. In light of
this development, how should the publisher adjust its pricing strategy for
the hardback best seller (relative to part a)? (A qualitative answer is
sufficient.)
Answer
a. With P = 28 – .4Q, the publisher maximizes profit by setting MR = MC,
so MR = 28 – .8Q = 8, implying Q* = 25 thousand and P* = $18.
b. Applying the markup rule, we find: P = (-2/-1)($8) = $16. The publisher
should cut its price in part (a) by $2.
c. These prices constitute profitable price discrimination by geographic
location. With very different incomes per capita, the best-seller is offered
at different prices. The more price elastic markets (due to their low
incomes) receive the lower prices.
d. Because the e-book format is a substitute for the hardback book, the
reduced e-book price causes reduced demand for the hardback, i.e. a
shift inward in that demand curve. As a result, the publisher’s optimal
response is to (partially) cut the hardback price and plan for smaller
hardback sales.
ADDITIONAL MATERIALS
I. Short Readings
D. Fennjan, “Some Businesses go Creative on Pricing, Applying
Technology,” The New York Times, January 23, 2014, p. B9.
S. Kapner, “The Dirty Secret of ‘Black Friday’ Discounts,” The Wall Street
Journal, November 26, 2013, p. B1.
A. Davidson, “How much is Michael Bolton Worth to you?” The New York
Times Magazine, June 4, 2013, p. 16.
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R Frank, “How can they Charge that? (and other Questions),” The New York
Times, May 12, 2013, p. BU8.
“Groupon Anxiety,” The Economist, March 19, 2011, pp. 70-71.
E. Maltby, “Raising Prices Pays off for Some,” The Wall Street Journal, May
24, 2010, p. R8.
J. Raju and J. Zhang, “How much should you Charge? Why Smart Pricing
Pays Off,” Knowledge@Wharton, April 14, 2010.
(Online at: knowledge.wharton.upenn.edu/article.cfm?articleid=2471.)
K. Auletta, “Publish or Perish,” The New Yorker, April 26, 2010, pp. 24-31.
(This article discusses the economics of e-book and print publishing.)
D. Ariely, “The Irrationality of Product Pricing,” The Wall Street Journal,
September 22, 2008, p. R2.
T. Aeppel, “Seeking Perfect Prices, CEO Tears up the Rules,” The Wall
Street Journal, March 27, 2007, pp. A1, A16
G. Anders, “In a Tech Backwater, A Profit Fortress Rises,” The Wall Street
Journal, July 10, 2007, pp. A1, A19
The following articles provide examples of market segmentation and price
discrimination.
P. Healy, “Ticket Pricing puts ‘Lion King’ Atop Broadway’s Circle of Life,”
The New York Times, March 17, 2014, p. A1.
A. Lowry, “Is Uber’s Surge-Pricing an Example of High-Tech Gouging?”
The New York Times Magazine, January 12, 2014, pp. 18-20.
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B. Fritz, “Sales of Digital Movies Surge?” The Wall Street Journal, January
8, 2014, p. B3.
J. Valentino-Devries, J. Singer-Vine, and A. Soltani, “Websites vary Prices,
Deals based on Users’ Information,” The Wall Street Journal, December 24,
2012, p. A1.
S. McCartney, “You Paid What for that Flight?” The Wall Street Journal,
August 26, 2010, pp. D1, D2.
“Uniform Prices for Online Music is no way to Maximize Profit, The
Economist, October 24, 2009, p. 88.
T. Lewin, “Students Find $100 Textbooks Cost $50, Purchased Overseas,”
The New York Times, October 21, 2003, pp. A1, A16.
J. Kronholz, “On Sale Now: College Tuition,” The Wall Street Journal, May
16, 2002, pp. D1, D6.
D. Leonhardt, “Tiptoeing Toward Variable Pricing,” The New York Times,
May 12, 2002, p. BU4.
H. R. Varian, “A Big Factor in Prescription Drug Pricing: Location,
Location, Location,” The New York Times, September 21, 2000, p. C2.
“Apple Computer’s Choice: Preserve Profits or Cut Prices,” The Wall Street
Journal, February 22, 1995, p. B1.
“Pennies that Add up to $16.98: Why CD’s Cost so Much,” The New York
Times, July 5, 1995, p. C11.
(This article illustrates: 1) demand-based pricing when MC is close to zero
and 2) how stores set retail prices by marking up wholesale prices.)
II. Longer Readings
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L. Barrage, E.T. Chyn, and J. S. Hasting, “Advertising, Reputation, and
Environmental Stewardship: Evidence from the BP Oil Spill,” NBER
Working Paper W19838, February 2014.
M. Gladwell, “Priced to Sell,” The New Yorker, July 6, 2009, pp. 80-84.
R. Metters et al, “The ‘Killer Application’ of Revenue Management:
Harrah’s Cherokee Casino and Hotel, Interfaces, Vol. 38, May-June 2008,
pp. 161-175.
C. Meyerhoefer and S. Zuvekas, “The Shape of Demand: What does it Tell
Us about Direct-to-Consumer Marketing of Antidepressants?” The B.E.
Journal of Economic Analysis and Policy, Vol 8, Issue 2 (Advances), 2008.
M. Connolly and A. Krueger, “Rockonomics: The Economics of Popular
Music, in V.A. Ginsburgh & D. Throsby (ed.), Handbook of the Economics
of Art and Culture, Elsevier Publishing, 2006.
R. Oberwetter, “Building Blockbuster Business,” OR/MS Today, June, 2001,
pp. 40-44. (This article discusses revenue management by movie theaters.)
T. Jacobs, R. M. Ratliff, and B. C. Smith, “Soaring with Synchronized
Systems,” OR/MS Today, August 2000, pp. 36-44. (This article discusses
airline yield management.)
R. Dorfman and P. O. Steiner, “Optimal Advertising and Optimal Quality,”
American Economic Review, 1954, pp. 826-836.
III. Cases
Virgin Mobile USA: Pricing for the very First Time (9-504-028), Harvard
Business School, 2004.
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Coca-Cola’s New Vending Machine (A) (9-500-068), Harvard Business
School, 2000. Teaching Note (5-501-086).
Biopure Corporation (9-598-150), Harvard Business School, 1999, Teaching
Note (5-599-094)
Precision Pricing for Profit in the New World Order (9-999-003), Harvard
Business School, 1998.
DHL Worldwide Express (9-593-011), Harvard Business School, 1997.
Teaching Note (5-594-094). (This is an excellent “pricing” case.)
American Airlines: Revenue Management (9-190-029), Harvard Business
School, 1993, Teaching Note (5-190-192)
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