Download Chapter Thirty-Four

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.
 Choose pOS to maximize
pOS(a – b(pC + pOS)) – FOS
 pOS = (a – bpC)/2b.
(C)
(OS)
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)
 A NE is a pair (p*C,p*OS) solving (C)
and (OS).
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)
 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/3b
and 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/3b
and 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/3b
and 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.
Competition & Switching Costs
 All
producers set the same
nondiscounted price of p per month.
 When is switching producers rational
for a customer?
Competition & Switching Costs
 Consumer’s
cost of not switching is
p
p
p
p

  p  .
2
1  r (1  r )
r
Competition & Switching Costs
 Consumer’s
cost of not switching is
p
p
p
p

  p  .
2
1  r (1  r )
r

Consumer’s cost from switching is
p
p
p
pd s

  p  d  s  .
2
1  r (1  r )
r
Competition & Switching Costs
 Consumer’s
cost of not switching is
p
p
p
p

  p  .
2
1  r (1  r )
r

Consumer’s cost from switching is
p
p
p
pd s

  p  d  s  .
2
1  r (1  r )
r

Consumer should switch if
p
p
pd  s  p .
r
r
Competition & Switching Costs
 Consumer’s
cost of not switching is
p
p
p
p

  p  .
2
1  r (1  r )
r

Consumer’s cost from switching is
p
p
p
pd s

  p  d  s  .
2
1  r (1  r )
r

Consumer should switch if
p
p
pd  s  p .
r
r
 i.e. if d  s.
Competition & Switching Costs
should switch if d  s.
 Producer competition will ensure at a
market equilibrium that customers
are indifferent between switching or
not  d  s.
I.e., the equilibrium value of the
discount only just makes it
worthwhile for the customer to
switch.
 Consumer
Competition & Switching Costs
 With
d = s, the present-value of the
producer’s profits is
pc pc
pc
π  pd

  p  d 
2
1  r (1  r )
r
pc
ps
.
r
Competition & Switching Costs
 At
equilibrium the present-value of the
producer’s profit is zero.
pc
r
π ps
0  pc
s.
r
1 r

The producer’s price is its marginal cost
plus a markup that is a fraction of the
consumer’s switching cost.
Competition & Switching Costs
 At
equilibrium the present-value of the
producer’s profit is zero.
pc
r
π ps
0  pc
s.
r
1 r

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
Competition & Switching Costs
 At
equilibrium the present-value of the
producer’s profit is zero.
pc
r
π ps
0  pc
s.
r
1 r

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
r
consumer by a then
p  c a
1 r
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.
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
demanded of the good?
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.
 So inverse demand is p = n(1000-n).
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
0
n
1000
Competition & Network
Externalities
 Suppose
all suppliers have the same
marginal production cost, c.
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
Supply Curve
c
0
n
1000
Competition & Network
Externalities
 What
are the market equilibria?
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.
– If no buyer buys, then no seller
supplies.
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
Supply Curve
c
(a)
0
n
1000
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
Supply Curve
c
(a)
0
n’
n
1000
Competition & Network
Externalities
 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’.
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
c
(b)
(a)
0
n’
(c)
n
n” 1000
Supply Curve
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” =
c/n”.
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
c
(b)
(a)
0
n’
(c)
n
Supply Curve
n” 1000
Which equilibrium is likely to occur?
Competition & Network
Externalities
 Suppose
the market expands
whenever willingness-to-pay exceeds
marginal production cost, c.
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
Supply Curve
c
0
n’
n
n” 1000
Which equilibrium is likely to occur?
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
Unstable
Supply Curve
c
0
n’
n
n” 1000
Which equilibrium is likely to occur?
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
Stable
Supply Curve
c
Stable
0
n
n” 1000
Which equilibrium is likely to occur?
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 p( y ) y .
y
Rights Management
p
p( y )
y
Rights Management
p
 ( y )  p( y ) y
p( y )
y
Rights Management
p
 ( y )  p( y ) y
p( y )
p( y*)
y*
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; Y   y ,   1
– lower sales per consumption unit
y
Y

.
Rights Management
 The
rights owner now allows a free trial
period. This causes
– a consumption increase; Y   y ,   1
– lower sales per consumption unit
y
Y

.
– increase in value to all users  increase
in willingness-to-pay;
P (Y )   p(Y ),   1.
Rights Management
p
p( y )
P (Y )   p(Y )
y,Y
Rights Management
 The
firm’s problem is now to
Y
Y 
max P (Y )   p(Y )  p(Y )Y .
Y



Rights Management
 The
firm’s problem is now to
Y
Y 
max P (Y )   p(Y )  p(Y )Y .
Y


 This

problem must have the same
solution as max p( y ) y .
y
Rights Management
 The
firm’s problem is now to
Y
Y 
max P (Y )   p(Y )  p(Y )Y .
Y
 This



problem must have the same
solution as max p( y ) y .
y
 So y*  Y*.
Rights Management
p
 ( y )  p( y ) y
p( y )
P (Y )   p(Y )
p( y*)
y*
y
Rights Management

 (Y )  p(Y )Y

 ( y )  p( y ) y
p
p(Y *)
p( y )
P (Y )   p(Y )
p( y*)
y*  Y*
y

1

 higher profit
Rights Management

 (Y )  p(Y )Y

 ( y )  p( y ) y
p
p(Y *)
p( y )
P (Y )   p(Y )
p( y*)
y*  Y*
y

1

 lower profit
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
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 p( y ) y  cy  F .
y
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.
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 willingness-topay is p(x) = p(ky).
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-topay is p(x) = p(ky).
 Rental transaction cost t reduces
willingness-to-pay to p(ky) - t.
Sharing Intellectual Property
 Rental
transaction cost t reduces
willingness-to-pay to p(ky) - t.
 Rental store’s willingness-to-pay is
Ps (y)  k[p(ky)  t].
Sharing Intellectual Property
 Rental
transaction cost t reduces
willingness-to-pay to p(ky) - t.
 Rental store’s willingness-to-pay is
Ps (y)  k[p(ky)  t].

Producer’s sale-for-rental problem is
max Ps (y)y  cy  F
y
Sharing Intellectual Property
 Rental
transaction cost t reduces
willingness-to-pay to p(ky) - t.
 Rental store’s willingness-to-pay is
Ps (y)  k[p(ky)  t].

Producer’s sale-for-rental problem is
max Ps (y)y  cy  F  k[p(ky)  t]y  cy  F
y
Sharing Intellectual Property
 Rental
transaction cost t reduces
willingness-to-pay to p(ky) - t.
 Rental store’s willingness-to-pay is
Ps (y)  k[p(ky)  t].

Producer’s sale-for-rental problem is
max Ps ( y) y  cy  F  k[p(ky )  t ]y  cy  F
y
c 
 p(ky )ky    t ky  F.
k 
Sharing Intellectual Property
c 
max p(ky )ky    t ky  F 
y
k 
c 
max p( x) x    t  x  F
x
k 
This is the same as the direct sale problem
max p( y) y  cy  F
y
except for the marginal cost.
Sharing Intellectual Property
c 
max p(ky )ky    t ky  F 
y
k 
c 
max p( x) x    t  x  F
x
k 
This is the same as the direct sale problem
max p( y) y  cy  F
y
except for the marginal cost. Direct sale
c
is better for the producer if c   t.
k
Sharing Intellectual Property
 Direct
sale is better for the producer if
c
c   t.
k
k
 i.e. if c 
t.
k 1
Sharing Intellectual Property
 Direct
sale is better for the producer if
k
c
t.
k 1
 Direct sale is better if
– replication cost c is low
– rental transaction cost t is high
– rentals per item, k, is small.