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.
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
p
 Cost of not switching is p  .
r
Competition & Switching Costs
p
 Cost of not switching is p  .
r
p
 Cost from switching is p  d   s .
r
Competition & Switching Costs
p
 Cost of not switching is p  .
r
p
 Cost from switching is p  d   s .
r
p
p
 Switch if p  d   s  p  .
r
r
Competition & Switching Costs
p
 Cost of not switching is p  .
r
p
 Cost from switching is p  d   s .
r
p
p
 Switch if p  d   s  p  .
r
r
 I.e.
if d  s.
Competition & Switching Costs
p
p
 Switch if p  d   s  p  .
r
r
if d  s.
 Producer competition will ensure at a
market equilibrium that customers
are indifferent between switching or
not  d  s.
 I.e.
Competition & Switching Costs
 At
equilibrium, producer economic
profits are zero.
pc
 I.e.
pd c
 0.
r
Competition & Switching Costs
 At
equilibrium, producer economic
profits are zero.
pc
 I.e.
pd c
 0.
r
pc
 Since d  s, at equilibrium p  c 
 s.
r
Competition & Switching Costs
 At
equilibrium, producer economic
profits are zero.
pc
 I.e.
pd c
 0.
r
pc
 Since d  s, at equilibrium p  c 
 s.
r
 I.e.
present-valued producer profit =
consumer switching cost.
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
(a)
Supply Curve
c
0
n
1000
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
(a)
Supply Curve
c
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
(a)
c
(b)
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
(a)
c
(b)
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
Supply Curve
c
0
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
0
n
n” 1000
Which equilibrium is likely to occur?
Competition & Network
Willingness-to-pay Externalities
p = n(1000-n)
Demand Curve
Stable
Stable
Supply Curve
c
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
– an increase in consumption
Y   y,   1
Rights Management
 The
rights owner now allows a free
trial period. This causes
– an increase in consumption
Y   y,   1
and a decrease in sales per unit of
consumption
Y
y .

Rights Management
 The
rights owner now allows a free
trial period. This causes
– 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?
 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
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 I
F
 p( ky ) ky 
 t ky  F .
Hk K
Sharing Intellectual Property
c I
F
max p( ky ) ky 
 t ky  F 
Hk K
y
c I
F
max p( x ) x 
t xF
Hk K
x
is the same problem as the direct sale
problem max p( y ) y  cy  F
y
except for the marginal costs.
Sharing Intellectual Property
c I
F
max p( ky ) ky 
 t ky  F 
Hk K
y
c I
F
max p( x ) x 
t xF
Hk K
x
is the same problem as the direct sale
problem max p( y ) y  cy  F
y
except for the marginal costs. Direct sale
is better for the producer if c  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.