chapter thirty-five information technology. information technologies u the crucial ideas are:...

Chapter Thirty-Five

Information Technology

Information Technologies

The crucial ideas are:

– Complementarity

– Network externality

Information Technologies;Complementarity

Definition: Commodity A complements commodity B if more of commodity A increases the value of an extra unit of commodity B.

– More software increases the value of a computer.

– More roads increase the value of a car.

Information Technologies;Network Externality

Definition: A commodity has a positive (negative) network externality if the utility to a consumer of that commodity increases (decreases) as more people also consume the commodity.– Email gives more utility to any one user

if more other people use email.– A highway gives less utility to any one

user as more people use it (congestion).

Complementarity

Information technologies have increased greatly the complementarities between commodities.– Computers and operating systems

(OS).– DVD players and DVD disks.– WiFi sites and laptop computers.– Cell phones and cell phone towers.

Complementarity

How should a firm behave when it produces a commodity that complements another commodity?

The problem is: When you make more of your product (commodity A) you increase the value of firm B’s product (commodity B). Can you get for yourself some of gain you create for firm B?

Complementarity

An obvious strategy is for firms A and B to cooperate somewhat with each other.

– Microsoft releases part of its OS to firms making software that runs under its OS.

– DVD manufacturers agree upon a standard format for their disks.

Complementarity

The price of a computer is pC.

The price of the OS is pOS. The quantities demanded of computers

and the OS depends upon pC + pOS, not just pC or just pOS.

Complementarity

The price of a computer is pC. The price of the OS is pOS. The quantities demanded of computers

and the OS depends upon pC + pOS, not just pC or just pOS.

Suppose the computer and software firms’ marginal production costs are zero. Fixed costs are FC and FOS.

Complementarity

Suppose the firms do not collude. The computer firm’s problem is:

choose pC to maximize pCD(pC + pOS) – FC.

The OS firm’s problem is:choose pOS to maximize pOSD(pC + pOS) – FOS.

Complementarity

Suppose the firms do not collude. The computer firm’s problem is:

choose pC to maximize pCD(pC + pOS) – FC.

The OS firm’s problem is:choose pOS to maximize pOSD(pC + pOS) – FOS.

Assume D(pC + pOS) = a – b(pC + pOS).

Complementarity

The computer firm’s problem is: choose pC to maximize pC(a – b(pC + pOS)) – FC.

The OS firm’s problem is:choose pOS to maximize pOS(a – b(pC + pOS)) – FOS.

Complementarity

Choose pC to maximize pC(a – b(pC + pOS)) – FC

pC = (a – bpOS)/2b. (C)

Choose pOS to maximize pOS(a – b(pC + pOS)) – FOS

pOS = (a – bpC)/2b. (OS)

Complementarity


pC = (a – bpOS)/2b. (C)



A NE is a pair (p*C,p*OS) solving (C) and (OS).

Complementarity


pC = (a – bpOS)/2b. (C)



A NE is a pair (p*C,p*OS) solving (C) and (OS). p*C = p*OS = a/3b.

Complementarity

p*C = p*OS = a/3b. When the firms do not cooperate the

price of a computer with an OS is p*C + p*OS = 2a/3band the quantities demanded of computers and OS are q*C + q*OS = a - b×2a/3b = a/3.

Complementarity

What if the firms merge? Then the new firm bundles a computer and an operating system and sells the bundle at a price pB.

The firm’s problem is to choose pB to maximize pBD(pB) – FB = pB(a – bpB) – FB.

Complementarity

What if the firms merge? Then the new firm bundles a computer and an operating system and sells the bundle at a price pB.

The firm’s problem is to choose pB to maximize pBD(pB) – FB = pB(a – bpB) – FB.

Solution is p*B = a/2b < 2a/3b.

Complementarity

When the firms merge (or fully cooperate) the price of a computer and an OS is p*B = a/2b < 2a/3band the quantity demanded of bundled computers and OS is q*B = a - b×a/2b = a/2 > a/3.

Complementarity

When the firms merge (or fully cooperate) the price of a computer and an OS is p*B = a/2b < 2a/3band the quantity demanded of bundled computers and OS is q*B = a - b×a/2b = a/2 > a/3.

The merged firm supplies more computers and OS at a lower price than do the competing firms. Why?

Complementarity

The noncooperative firms ignore the external benefit (complementarity) each creates for the other. So each undersupplies the market, causing a higher market price.

These externalities are fully internalized in the merged firm, inducing it to supply more computers and OS and thereby cause a lower market price.

Complementarity

More typical cooperation consists of contracts between component manufacturers and an assembler of a final product. Examples are:

– Car components and a car assembler.

– A computer assembler and manufacturers of CPUs, hard drives, memory chips, etc.

Complementarity Alternatives include:

– Revenue-sharing. Two firms share the revenue from the final product made up from the two firms’ components.

– Licensing. Let firms making complements to your product use your technology for a low fee so they make large quantities of complements, thereby increasing the value of your product to consumers.

Information Technologies;Lock-In

Strong complementarities or network externalities make switching from one technology to another very costly. This is called lock-in.

E.g., In the USA, it is costly to switch from speaking English to speaking French.

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?


Consumer’s cost of not switching is.

)1(1 2 r

pp

r

p

r

pp


Consumer’s cost of not switching is

Consumer’s cost from switching is

.)1(1 2 r

psdp

r

p

r

psdp

.)1(1 2 r

pp

r

p

r

pp




Consumer should switch if

.r

pps

r

pdp

.)1(1 2 r

psdp

r

p

r

psdp

.)1(1 2 r

pp

r

p

r

pp




Consumer should switch if

i.e. if

.r

pps

r

pdp

.sd

.)1(1 2 r

psdp

r

p

r

psdp

.)1(1 2 r

pp

r

p

r

pp


Consumer should switch if Producer competition will ensure at a

market equilibrium that customers are indifferent between switching or not I.e., the equilibrium value of the discount only just makes it worthwhile for the customer to switch.

.sd

.sd


With d = s, the present-value of the

producer’s profits is

.

)1(1 2

r

cpsp

r

cpdp

r

cp

r

cpdpπ


At equilibrium the present-value of the producer’s profit is zero.

The producer’s price is its marginal cost plus a markup that is a fraction of the consumer’s switching cost.

.1

0 sr

rcp

r

cpspπ



The producer’s price is its marginal cost plus a markup that is a fraction of the consumer’s switching cost. If advertising reduces the marginal cost of servicing a consumer by a then

.1

0 sr

rcp

r

cpspπ



The producer’s price is its marginal cost plus a markup that is a fraction of the consumer’s switching cost. If advertising reduces the marginal cost of servicing a consumer by a then

.1

0 sr

rcp

r

cpspπ

.1

sr

racp

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 Curvec


(a)


0 1000n

Demand Curve

Supply Curve

n’

c


(a)


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)c

Which equilibrium is likely to occur?


(a)


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



Stable

Stable

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– a consumption increase; Y y , 1

Rights Management

The rights owner now allows a free trial period. This causes– a consumption increase;– lower sales per consumption unit

yY

.

Y y , 1

Rights Management

The rights owner now allows a free trial period. This causes– a consumption increase;– lower sales per consumption unit

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

yY

.

Y y , 1

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? Sell a tool, or rent it? Allow a movie to be shown only at a

theatre, or sell only to video rental stores, or sell only by pay-per-view, or sell DVDs in retail stores?

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 is].)([)( tkypkyPs



Rental store’s willingness-to-pay is

Producer’s sale-for-rental problem is].)([)( tkypkyPs

FcyyyPsy

)(max





FcyytkypkFcyyyPsy

])([)(max





.)(

])([)(max

Fkytk

ckykyp

FcyytkypkFcyyyPsy


Fxtk

cxxp

Fkytk

ckykyp

x

y

)(max

)(max

This is the same as the direct sale problem

Fcyyypy

)(max

except for the marginal cost.


Fxtk

cxxp

Fkytk

ckykyp

x

y

)(max

)(max

This is the same as the direct sale problem

Fcyyypy

)(max

except for the marginal cost. Direct sale

is better for the producer if .tk

cc


Direct sale is better for the producer if

i.e. if

.tk

cc

.1

tk

kc


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.

.1

tk

kc

chapter thirty-five information technology. information technologies u the crucial ideas are:...

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