chapter thirty-four

Chapter Thirty-Four

Information Technology

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 many people use the same software.

Information Technologies

But then switching technologies becomes very costly -- lock-in.

E.g. Microsoft Windows. How do markets operate when there

are switching costs or network externalities?

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. Rate of interest is r.


All producers set the same nondiscounted price of p per month.

When is switching producers rational for a customer?


Cost of not switching is ppr

.


Cost of not switching is

Cost from switching is

ppr

.

p dprs .




Switch if

ppr

.

p dprs p

pr

.

p dprs .




Switch if

I.e. if

ppr

.

p dprs p

pr

.

p dprs .

d s .


Switch if

I.e. if Producer competition will ensure at a

market equilibrium that customers are indifferent between switching or not

p dprs p

pr

.

d s .

d s .


At equilibrium, producer economic profits are zero.

I.e. p d cp cr

0.



I.e.

Since , at equilibriumd s

p d cp cr

0.

p cp cr

s

.



I.e.

Since , at equilibrium

I.e. present-valued producer profit = consumer switching cost.

d s

p d cp cr

0.

p cp cr

s

.

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.


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 demanded of the good?


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. So inverse demand is p = n(1000-

n).


0 1000n

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

Demand Curve


Suppose all suppliers have the same marginal production cost, c.


0 1000n

Demand Curve

Supply Curvec



What are the market equilibria?


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.

– If no buyer buys, then no seller supplies.


0 1000n

Demand Curve

Supply Curve(a)

c



0 1000n

Demand Curve

Supply Curve

n’

(a)c



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

buy.

– small n’ small network externality value n’v

– good is bought only by buyers with n’v c; i.e. only large v v’ = c/n’.


0 1000n

Demand Curve

Supply Curve

n’

(b)

n”

(c)

(a)c



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” = c/n”.


0 1000n

Demand Curve

Supply Curve

n’

(b)

n”

(c)

(a)c

Which equilibrium is likely to occur?



Suppose the market expands whenever willingness-to-pay exceeds marginal production cost, c.


0 1000n

Demand Curve

Supply Curve

n’ n”

c




0 1000n

Demand Curve

Supply Curve

n’ n”

c



Unstable


0 1000n

Demand Curve

Supply Curve

n”

c




0 1000n

Demand Curve

Supply Curve

n”

c



Stable


0 1000n

Demand Curve

Supply Curve

n”

c



StableStable

Rights Management

Should a good be sold outright, licensed for production by

others, or rented?

How is the ownership right of the good to be managed?

Rights Management

Suppose production costs are negligible.

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

yp y y( ) .

Rights Management

y

p

p y( )

Rights Management

y

p

p y( )

( ) ( )y p y y

Rights Management

y* y

p

p y( )

( ) ( )y p y y

p y( *)

Rights Management

The rights owner now allows a free trial period. This causes

– an increase in consumptionY y , 1

Rights Management


– an increase in consumption

and a decrease in sales per unit of consumption

yY

.

Y y , 1

Rights Management


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

P Y p Y( ) ( ), . 1

Rights Management

y Y,

p

p y( )P Y p Y( ) ( )

Rights Management

The firm’s problem is now to

maxY

P YY

p YY

p Y Y( ) ( ) ( ) .

Rights Management


This problem must have the same solution as max

yp y y( ) .

maxY

P YY

p YY

p Y Y( ) ( ) ( ) .

Rights Management


This problem must have the same solution as

So

maxy

p y y( ) .

y Y* *.

maxY

P YY

p YY

p Y Y( ) ( ) ( ) .

Rights Management

y

p

p y( )

( ) ( )y p y y

y*

p y( *) P Y p Y( ) ( )

Rights Management

y Y* *

p y( *)p Y( *)

y

p

p y( )

( ) ( )y p y y

( ) ( )Y p Y Y

1 higher profit

P Y p Y( ) ( )

Rights Management

y Y* *

p y( *)p Y( *)

y

p

p y( )

( ) ( )y p y y

( ) ( )Y p Y Y

1 lower profit

P Y p Y( ) ( )

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

profitable than selling for personal use only?

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


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

maxy

p y y cy F( ) .


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

consumers. So y units sold x = ky consumption

units.


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 willingness-to-

pay is p(x) = p(ky).


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). Rental transaction cost t reduces

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


Rental transaction cost t reduces willingness-to-pay to p(ky) - t.

Rental store’s willingness-to-pay isP y k p ky ts ( ) [ ( ) ].



Rental store’s willingness-to-pay is

Producer’s sale-for-rental problem isP y k p ky ts ( ) [ ( ) ].

P y y cy Fs ( ) maxy





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





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

p ky kyck

t ky F

s ( ) [ ( ) ]

( ) .

FH IK

maxy


p ky kyck

t ky F

p x xck

t x F

( )

( )

FH IK

FH IK

maxy

is the same problem as the direct saleproblem max

yp y y cy F( )

maxx

except for the marginal costs.


p ky kyck

t ky F

p x xck

t x F

( )

( )

FH IK

FH IK

maxy

is the same problem as the direct saleproblem max

yp y y cy F( )

maxx

except for the marginal costs. Direct saleis better for the producer if c

ck

t .


Direct sale is better for the producer if

I.e. if

cck

t .

ckk

t 1

.


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.

ckk

t 1

.

chapter thirty-four

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