Chuong 34

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Chapter Thirty-Four

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Information Technologies

 Computers, answering machines, 
FAXes, pagers, cellular phones, …
 Many provide strong

complementarities.

 E.g. email is useful only if lots of

people use it -- a network externality.
 And computers are more useful if

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Information Technologies

 But then switching technologies

becomes very costly -- lock-in.

 E.g. Microsoft Windows.

 How do markets operate when there

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Competition & Switching Costs

 Producer’s cost per month of

providing a network service is c per 
customer.

 Customer’s switching cost is s.
 Producer offers a one month

discount, d.

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Competition & Switching Costs

 All producers set the same

nondiscounted price of p per month.

 When is switching producers rational

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Competition & Switching Costs

 Cost of not switching is p p

r

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Competition & Switching Costs

 Cost of not switching is

 Cost from switching is

p p
r

 .

p d p

r s

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Competition & Switching Costs

 Cost of not switching is

 Cost from switching is

 Switch if

p p
r

 .

p d p

r s p

p
r

     .

p d p

r s

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Competition & Switching Costs

 Cost of not switching is

 Cost from switching is

 Switch if

 I.e. if

p p
r

 .

p d p

r s p

p
r

     .

p d p

r s

   .

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Competition & Switching Costs

 Switch if

 I.e. if

 Producer competition will ensure at a

market equilibrium that customers 
are indifferent between switching or 
not 

p d p

r s p

p
r

     .

d  s.

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Competition & Switching Costs

 At equilibrium, producer economic

profits are zero.

 I.e. p d c p c

r

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Competition & Switching Costs

 At equilibrium, producer economic

profits are zero.

 I.e.

 Since , at equilibriumd s

p d c p c

r

    0.

p c p c

r s

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Competition & Switching Costs

 At equilibrium, producer economic

profits are zero.

 I.e.

 Since , at equilibrium

 I.e. present-valued producer profit =

consumer switching cost.
d s

p d c p c

r

    0.

p c p c

r s

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Competition & Network

Externalities

 Individuals 1,…,1000.

 Each can buy one unit of a good

providing a network externality.

 Person v values a unit of the good at

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Competition & Network

Externalities

 Individuals 1,…,1000.

 Each can buy one unit of a good

providing a network externality.

 Person v values a unit of the good at

nv, where n is the number of persons 
who buy the good.

 At a price p, what is the quantity

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Competition & Network

Externalities

 If v is the marginal buyer, valuing the

good at nv = p, then all buyers v’ > v 
value the good more, and so buy it.

 Quantity demanded is n = 1000 - v.

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Competition & Network

Externalities

0 1000

n
Willingness-to-pay

p = n(1000-n)

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Competition & Network

Externalities

 Suppose all suppliers have the same

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

c

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Competition & Network

Externalities

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Competition & Network

Externalities

 What are the market equilibria?

 (a) No buyer buys, no seller supplies.

– If n = 0, then value nv = 0 for all 
buyers v, so no buyer buys.

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

(a)
c

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

n’
(a)
c

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Competition & Network

Externalities

 What are the market equilibria?
 (b) A small number, n’, of buyers

buy.

– small n’  small network 
externality value n’v

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Competition & Network

Externalities

 What are the market equilibria?

 (c) A large number, n”, of buyers buy.

– Large n”  large network 
externality value n”v

– good is bought only by buyers with 
n’v  c; i.e. up to small v  v” =

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Competition & Network

Externalities

 Suppose the market expands

whenever willingness-to-pay

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

n’ n”

c

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

n’ n”

c

Which equilibrium is likely to occur?

Willingness-to-pay
 p = n(1000-n)

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

n”
c

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

n”
c

Which equilibrium is likely to occur?

Willingness-to-pay
 p = n(1000-n)

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Competition & Network

Externalities

0 1000

n

Demand Curve

Supply Curve

n”
c

Willingness-to-pay

p = n(1000-n)

Stable

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Rights Management

 Should a good be 
 sold outright,

 licensed for production by

others, or

 rented?

 How is the ownership right of the

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Rights Management

 Suppose production costs are

negligible.

 Market demand is p(y).
 The firm wishes to max

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Rights Management

y
p

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Rights Management

y
p

p y( )

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Rights Management

y * y

p

p y( )

 ( )y  p y y( )

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Rights Management

 The rights owner now allows a free

trial period. This causes

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Rights Management

 The rights owner now allows a free

trial period. This causes

– an increase in consumption

and a decrease in sales per unit of 
consumption

y Y

 .

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Rights Management

 The rights owner now allows a free

trial period. This causes

– increase in value to all users 
increase in willingness-to-pay;

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Rights Management

y Y,

p

p y( )

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Rights Management

 The firm’s problem is now to

max

Y P Y

Y

p Y Y p Y Y

( ) ( ) ( ) .

  




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Rights Management

 The firm’s problem is now to

 This problem must have the same

solution as max

y p y y( ) .
max

Y P Y

Y

p Y Y p Y Y

( ) ( ) ( ) .

  




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Rights Management

 The firm’s problem is now to

 This problem must have the same

solution as

 So

max

y p y y( ) .

y* Y*.
max

Y P Y

Y

p Y Y p Y Y

( ) ( ) ( ) .

  




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Rights Management

y
p

p y( )

 ( )y  p y y( )

y *

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Rights Management

y* Y*

p y( *)
p Y( *)

y
p

p y( )

 ( )y  p y y( )

 ( )Y  p Y Y( )





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Rights Management

y* Y*

p y( *)
p Y( *)

y
p

p y( )

 ( )y  p y y( )

 ( )Y  p Y Y( )





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Sharing Intellectual Property

 Produce a lot for direct sales, or only 
a little for multiple rentals?

 Lending books, software.
 Renting tools, videos etc.

 Sell movies directly, or only sell to 
video rental stores, or pay-per-view? 
 When is selling for rental more

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Sharing Intellectual Property

 F is the fixed cost of designing the

good.

 c is the constant marginal cost of

copying the good.

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Sharing Intellectual Property

 F is the fixed cost of designing the

good.

 c is the constant marginal cost of

copying the good.

 p(y) is the market demand.
 Direct sales problem is to

max

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Sharing Intellectual Property

 Is selling for rental more profitable?
 Each rental unit is used by k > 1

consumers.

 So y units sold  x = ky consumption

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Sharing Intellectual Property

 Is selling for rental more profitable?
 Each rental unit is used by k > 1

consumers.

 So y units sold  x = ky consumption

units.

 Marginal consumer’s

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Sharing Intellectual Property

 Is selling for rental more profitable?

 Each rental unit used by k > 1 consumers.
 So y units sold  x = ky consumption

units.

 Marginal consumer’s willingness-to-pay is 
p(x) = p(ky).

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Sharing Intellectual Property

 Rental transaction cost t reduces

willingness-to-pay to p(ky) - t.

 Rental store’s willingness-to-pay is

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Sharing Intellectual Property

 Rental transaction cost t reduces

willingness-to-pay to p(ky) - t.

 Rental store’s willingness-to-pay is

 Producer’s sale-for-rental problem is

P ys ( ) k p ky[ ( )  t].

P y y cy Fs ( )  

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Sharing Intellectual Property

 Rental transaction cost t reduces

willingness-to-pay to p(ky) - t.

 Rental store’s willingness-to-pay is

 Producer’s sale-for-rental problem is

P ys ( ) k p ky[ ( )  t].

P y y cy Fs ( )   k p ky[ ( )  t y cy F]  

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Sharing Intellectual Property

 Rental transaction cost t reduces

willingness-to-pay to p(ky) - t.

 Rental store’s willingness-to-pay is

 Producer’s sale-for-rental problem is

P ys ( ) k p ky[ ( )  t].

P y y cy F k p ky t y cy F

p ky ky c

k t ky F

s ( ) [ ( ) ]

( ) .

     

 

FH IK

 

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Sharing Intellectual Property

p ky ky c

k t ky F
p x x c

k t x F

( )
( )



FH IK

  


FH IK

 

max
y

is the same problem as the direct sale
problem max

y p y y cy F( )  
max

x

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Sharing Intellectual Property

p ky ky c

k t ky F
p x x c

k t x F

( )
( )



FH IK

  


FH IK

 

max
y

is the same problem as the direct sale
problem max

y p y y cy F( )  

max

x

except for the marginal costs. Direct sale
is better for the producer if c c

k t

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Sharing Intellectual Property

 Direct sale is better for the producer if

 I.e. if

c c

k t

  .

c k

k t



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Sharing Intellectual Property

 Direct sale is better for the producer if

 Direct sale is better if

– replication cost c is low

– rental transaction cost t is high
– rentals per item, k, is small.

c k

k t



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