3 Microeconomics Questions

  Please read the lecture notes and do the questions with detailed procedures.  

PROBLEM SET 4

1. Suppose a firm offers two products, a word processor and a spreadsheet, and produces

each at a marginal cost of zero. There are two consumers: Justin values a word processor at

$120 and a spreadsheet at $100, while Ubaldo values a word processor at $100 and a

spreadsheet at $120. It is easy to show that the optimal pricing strategy is to offer both

products as a bundle at a price of $220.

But in the real world, we often see “mixed bundling” of products – that is, the individual

products are offered at separate prices and they are also offered as a bundle (usually at a

discount from the sum of the two separate prices). The example above does not give us

mixed bundling because only the bundle is offered, and not the separate components. Let’s

look at an example where the firm might like to offer mixed bundling.

(a) Draw a graph, similar to the one in class, with valuations of the word processor and the

spreadsheet on the horizontal and vertical axes. Put a J and U on the graph to represent

the preferences of Justin and Ubaldo, respectively.

(b) Suppose we add a third customer, Michael, who values a word processor at $150 and a

spreadsheet at $10 (perhaps Michael is a professional writer, or perhaps he is the best

defensive center fielder in baseball). Add an M to your graph. What are the profits if we

only offer a bundle, at $220, as before?

(c) If we still use only pure bundling, what is the optimal bundle price and what are profits?

(d) If we now use mixed bundling, what are the optimal bundle and component prices?

What are profits?

(e) Suppose now we add a fourth customer, Chris, who values a word processor at $20 and

a spreadsheet at $160 (perhaps Chris is an accountant, or perhaps he’s a late-inning

reliever with emotional problems). Add a C to your graph. Now what are the optimal

mixed bundling prices and profits?

(f) Graph the prices from mixed bundling. Break this graph up into four regions: those that

consume only word processors, those consuming only spreadsheets, those consuming

both, and those consuming nothing.

2. Suppose the demand for a new pharmaceutical drug, on which the manufacturer has a

patent monopoly, is given by:

Q(P,A) = (100 – P) ∙ A0.5

where Q is output per period, P is the price, and A is the current period promotional

expenditure.

Total production costs are given by C(Q) = 60Q.

(a) Calculate the profit-maximizing price, advertising expenditure, and profits for the firm.

(b) At the firm’s optimal choices, what are the: (i) price elasticity of demand; (ii) elasticity

of demand with respect to advertising expenditure; and (iii) advertising / sales ratio for

this product? What does all this have to do with the Dorfman-Steiner condition?

3. PRN Problem 2, p. 634 (f denotes the fraction of consumers who purchase the service).

Assume that consumers contemplating buying a network service have reservation prices

uniformly distributed on the interval [0, 50] (measured in dollars). Demand by a consumer

with reservation price wi for this service is

𝑞𝑖
𝐷 = {

0 𝑖𝑓 𝑓𝑤𝑖 < 𝑝 1 𝑖𝑓 𝑓𝑤𝑖 ≥ 𝑝

(a) Calculate the demand function for this service.

(b) What is the critical mass if the price is set at $5?

(c) What is the profit maximizing price for the service?

Slides 1

5

(Chapter 22)

What do we mean by

network effects?

 Willingness to pay increases with the number of

people that acquire the good

 Example: cell-phone, fax machine, Facebook…

 People choices depend on the expected network size!

 Often, there is a coordination problem!

3

How can we model demand with

network effects?

 Setup for demand model:

 Very large number of consumers. Thus, each

consumer doesn’t think he/she affects the overall

fraction that buys the good

 Consumers have unit demand (e.g. they only want

one Facebook account)

 Reservation values for the good are between 0 and

100, and uniformly distributed

 Call these values v

i

 Price of good is p

4

How can we model demand with
network effects?
 Setup for demand model:

 Call the fraction of consumers buying the good f

 Then individual demand is

 Implication, even if a consumer has vi>>p, the

consumer won’t buy if nobody else is buying!

 We are interested in aggregate demand f(p)

0 if
( )

1 if

i
i

i

fv p

q p

fv p


 



5

Let us start without network effects…

 Then individual demand is

qi (p) = 0 if vi < p and qi (p) = 1 if vi ≥ p

 If vi is uniformly distributed [0, 100] then

f(p) = (100 – p)/100

6

What happens with network effects?

 The indifferent consumer satisfies vi = p/f

 All consumers with vi > p/f buy the good!

 His decision depends on i’s believes about what

everyone else is doing!

7

What happens with network effects?

 We can think about aggregate demand in terms of

Nash equilibrium among consumers

 Each consumer takes as given others’ choices while

deciding whether to buy the good or not

 In equilibrium, each consumer selects the optimal

choice and correctly predicts the choices of others

8

How do we get aggregate demand?

 Let all consumers believe f will get the good

 Is f(p) = 0 a NE? Yes!

 If f = 0, then vi f = 0 < p

 This means that no consumer wants to get the good!

 Is there another NE with f(p) > 0 ? Yes!

9

How do we get aggregate demand?

 Is there another NE with f(p) > 0 ? Yes!

 Let all consumers believe f > 0 will get the good

 Recall indifferent consumer satisfies vi = p/f

 Since vi is uniformly distributed [0, 100] then

f(p) = (100 – p/f)/100

 The NE solve

100 f(p)2 – 100 f(p) + p = 0

 Smallest of the two solutions f* is called critical mass

10

What are the profits of the firm?

 For each p, profits depend on the selected NE!

 It makes more profits in the largest NE

 How can the firm affect equilibrium selection?

Slides

13

(Chapter 8)

2

Bundling

 Firms sell goods as bundles

 Selling two or more goods in a single package

 Goods are close in nature, but slightly different

 Goods are not necessarily complements

 Complementary goods: buying one good
increases your utility from buying the other good

3

Bundling example: Microsoft

 Consider MS Office

 Can buy Office package for $350. This contains
Word, Excel, Outlook, and Powerpoint

 Each component costs $140

 So purchasing the bundle via individual
purchases costs $560.

 The bundle offers a $210 discount!

 Why might Microsoft do this?

4

Bundling: an example

 Two movies are available from the same producer

 Star Wars and

Superbad

 Selling to two theatres: A and B. 1st degree price

discrimination is illegal

 Willingness to pay is:

Theater A

Theater B

Willingness to

pay for

Star Wars

Willingness to

pay for

Superbad

$8,000

$7,000

$2,500

$3,000

5
Bundling: an example

 Suppose component pricing (no bundling)

 What price should producer set for Star Wars?

 For Superbad?

 Profits?

Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$2,500

$3,000

6
Bundling: an example
 Suppose component pricing (no bundling)
 What price should producer set for Star Wars?
 For Superbad?

 Profits?

Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$2,500
$3,000

$7000

7
Bundling: an example
Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$2,500
$3,000

$7000

$2500

 Suppose component pricing (no bundling)
 What price should producer set for Star Wars?
 For Superbad?
 Profits?

8
Bundling: an example
 Suppose component pricing (no bundling)
 What price should producer set for Star Wars?
 For Superbad?
 Profits?
Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$2,500
$3,000
$7000
$2500

$19000

9
Bundling: an example

 Now suppose the producer tries pure bundling

 This means the producer charges a single price at

which a theatre can buy both movies, or neither

 No option to buy only one movie

 What price to set for the bundle?

Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$2,500
$3,000

10
Bundling: an example
Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$2,500
$3,000

Total

Willingness

to pay

$10,500

$10,000

 The producer can charge $10,000 and both theatres
will buy the bundle

 Profits are $20,000

 This is greater than profits with component pricing!
($19,000)

11

Why did bundling work?

 With component pricing, had to set low price for
each component

 Only way to have both consumers buy each
product

 With bundling, producer can exploit the
aggregate willingness to pay

 The theatre that dislikes Star Wars likes
Superbad, and vice-versa

 This is a form of price discrimination!

 Will this always work?

12

Bundling: alternative example

 Will stick with the same movie problem, but now

change one payoff.

 Theatre A now will pay $7000 for Superbad, not just

$2500

 Now what are component prices? Bundle price?

Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$7,000
$3,000

13
Bundling: alternative example

 Component prices are $7000 for Star Wars and

$7000 for Superbad. Profits with component pricing

are $21000 (sell only one Superbad)

 Bundle price is $10000. Bundling profits are only

$20000

Theater A
Theater B
Willingness to
pay for
Star Wars
Willingness to
pay for
Superbad
$8,000
$7,000
$7,000
$3,000

14

Why didn’t bundling work in the

changed example?
 I only changed a number, and now producer is

better off with component pricing than pure
bundling

 What happened?

 Producer was better off selling Superbad only to
theater A

 Theatre A also had a relatively high value for Star
Wars

 Bundling doesn’t allow the producer to capture
A’s high valuation

15

When doesn’t pure bundling

increase profits?
 Original paper on this is by Jim Adams and Janet

Yellen, 1976

 One punchline: component pricing may work
better if buyers’ valuations are positively
correlated

 That is, if a buyer has a high valuation for one
product, he/she will probably have a high valuation
for the other product too

 Can also use mixed bundling: offer both the
bundle and separate components

 Monopolist can extract even more value

16

Adams and Yellen paper shows

intuition through graphs
 Suppose monopolist has two goods: good 1 and

good 2

 Total production cost is c(q1,q2) = c1q1 + c2q2
 No economies of scale or scope

 Each consumer i has a reservation price for each
good: R1i and R2i
 Value of buying both is simply R1i + R2i
 Goods are not complements!

 Valuations vary across consumers

 Do graphs on board (also see section 8.1 of
PRN)

17

Introducing tying

 Tying (tie-in) sales occur when, if consumers

want to buy one product from you, you require

them to buy a particular complementary product

 Notice the similarity with bundling

 Main difference is that with tying, the two goods

are complements

 Microsoft case example: consumers who wanted

to buy Windows were required to buy Internet

Explorer rather than Netscape

18

Introducing tying

 In some ways, the difference is semantics…

 Tying: “To buy A, you must also buy B”

 Pure Bundling: “You can only buy A and B

together”

19

Two motives for tying

 Motive one: Price discrimination

 We’ve already talked a lot about this

 Example: low price for inkjet printers but high price

for ink cartridges

 Cartridges incompatible across brands

 Tying for this reason is not illegal (firms do this all

the time, after all)

 May be efficiency enhancing relative to single

product linear pricing

20

Two motives for tying

 Motive two: Use your market power in one

product to gain market power in the other

 Tying to enhance or maintain a monopoly is

illegal under the Sherman Act

 This sort of tying was one of the issues in the

Microsoft case

 And other cases as well (e.g., Kodak in the 1980s)

Slides 14

(Chapter 19)

2

Advertising: what do we want to know?

 How do firms choose how much to spend on

advertising?

 Do firms advertise too much or too little relative

to what is socially optimal?

 Does advertising lead to market

power?

 How does advertising affect demand?

3

Much controversy on nature of

advertising: informational or persuasive?

 Economists have typically tried to categorize

advertising as being of one of two types:

1. Informational advertising: conveys information about

a product’s quality and / or price

2. Persuasive advertising: Attempts to “change

preferences” to create product differentiation

(without actually providing info)

4
Much controversy on nature of
advertising: informational or persuasive?

 What are the competitive effects of these
two types of advertising?
 i.e. Do we expect each type of advertising to

raise or lower prices?

 If informational advertising is making people
aware of price differences, that means search
costs are lower

 Should see lower prices. That’s good.

 Persuasive advertising artificially increases
product differentiation.

 Should see higher prices. That’s bad.

5

Historically, lots of concern in industrial

organization regarding persuasive ads

 During 1960s and 1970s, lots of economists

looked at profits and price – cost margins

across many industries

 Generally find that industries in which firms

spend lots of money on advertising are also

more profitable and have bigger margins

 Conclusion: Does advertising increase market

power?

6

Explaining correlation between

advertising and price – cost margins

 Two potential stories:

 Could interpret regression results as advertising

increases market power and margins

 Or could interpret regression as: in industries

where market power can be exerted, there are

also incentives to advertise

 There exist theoretical models consistent with

both stories!

7

The Dorfman-Steiner advertising model

 Second story basically says: If you have market

power, you have incentives to increase

demand

 Otherwise, no point in advertising!

 Dorfman and Steiner (1954) have simple

model showing this intuition

 Result: The amount of advertising you should

do (as a proportion of sales revenue) increases

with the

elasticity of demand

with respect to

advertising and decreases with the price

elasticity of demand

8

A different story: Sutton (1991)

 Sutton wanted to explain why some large

markets have lots of small firms, while other

large markets

have a few big firms

 Example: large cities have lots of small

restaurants, but few newspapers

 Sutton’s view: markets characterized by

endogenous sunk costs have high

concentration even when market size is large

9

What are endogenous sunk costs?

 Endogenous sunk costs are initial investments

that increase the size of the market

 Example: sunk cost of building the factory is

not endogenous: this doesn’t grow demand

 Advertising is an endogenous sunk cost. The

more you advertise, the more you increase

demand

 If you want to enter an industry where the

incumbents advertise a lot, you will need to sink

up-front $ into advertising

10

Advertising means that sunk costs

increase with

market size

 Sutton’s idea: in markets where demand is

responsive to investment…

 There is an incentive to advertise

 This incentive is bigger in larger markets

 Thus firms advertise more in larger markets

 This means that sunk entry costs increase with

market size

 So barriers to entry increase with market size

 So high concentration (and market power) even in

large markets

11

Which story is right?

 Still an open question!

 Maybe both are right?

12

Another question: is there too much

advertising?

 It certainly seems as though there are a lot of ads

out there

 What are the social benefits and costs of

advertising?

 Do ads increase or decrease profits?

 What about consumer welfare?

 If informative ad: benefits come from lower prices,

consumers making better decisions

 If persuasive ad: less clear

 Ads potentially lead to higher prices

 “Artificial” or “real” altering of preferences?

13

Advertising’s impact on profits: a

prisoners’ dilemma?

 Maybe ads just lead firms to try to steal each

other’s business, without even increasing profits

 Simple two firm example:

 Coke and Pepsi set advertising expenditures AC
and AP

 Simplified profit functions are:

 Coke: πC = (60 – AP)AC –

 Pepsi: πP = (60 – AC)AP –

 We work out Nash Equilibrium on the board

2

C
A

2

P
A

14
Advertising’s impact on profits: a
prisoners’ dilemma?

 So both Coke and Pepsi spend $20 on advertising

 Profits are $400

 Could the firms have done better by cooperating?

 Total industry profits are:

 (60 – AP)AC + (60 – AC)AP – –

 This is maximized when the firms spend $15 each.

Profits are $450 each.

2
C
A
2
P
A

15
Advertising’s impact on profits: a
prisoners’ dilemma?

 If the firms cooperate (or merge), they internalize

the business stealing effects of advertising

 No point stealing business from yourself

 Like differentiated Bertrand vs collusion

 Collusive prices are higher because you’re no

longer trying to steal business from other firms

 But at least with price competition, consumers got

lower prices!

 Here, they get more ads. Prices may increase!

16

Do consumers get anything out of

persuasive advertising?

 Are some ads purely manipulative or do they

actually provide real value to consumers?

17
Do consumers get anything out of
persuasive advertising?

 Maybe a brand is something that has value

 When you buy a Nike shoe, you’re not just getting

a shoe, you’re getting value from the Nike brand

 You get to “be seen” in cool shoes

 Brand is a complement to the product

 So maybe advertising really does make some

products better?

 So in some cases, maybe there aren’t enough

ads?

 All of this is an open issue