View
213
Download
1
Category
Preview:
Citation preview
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
Cost of not switching is ppr
.
Competition & Switching Costs
Cost of not switching is
Cost from switching is
ppr
.
p dprs .
Competition & Switching Costs
Cost of not switching is
Cost from switching is
Switch if
ppr
.
p dprs p
pr
.
p dprs .
Competition & Switching Costs
Cost of not switching is
Cost from switching is
Switch if
I.e. if
ppr
.
p dprs p
pr
.
p dprs .
d s .
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 dprs p
pr
.
d s .
d s .
Competition & Switching Costs
At equilibrium, producer economic profits are zero.
I.e. p d cp cr
0.
Competition & Switching Costs
At equilibrium, producer economic profits are zero.
I.e.
Since , at equilibriumd s
p d cp cr
0.
p cp cr
s
.
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 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.
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 Externalities
0 1000n
Willingness-to-pay p = n(1000-n)
Demand Curve
Competition & Network Externalities
Suppose all suppliers have the same marginal production cost, c.
Competition & Network Externalities
0 1000n
Demand Curve
Supply Curvec
Willingness-to-pay p = n(1000-n)
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 Externalities
0 1000n
Demand Curve
Supply Curve(a)
c
Willingness-to-pay p = n(1000-n)
Competition & Network Externalities
0 1000n
Demand Curve
Supply Curve
n’
(a)c
Willingness-to-pay p = n(1000-n)
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 Externalities
0 1000n
Demand Curve
Supply Curve
n’
(b)
n”
(c)
(a)c
Willingness-to-pay p = n(1000-n)
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 Externalities
0 1000n
Demand Curve
Supply Curve
n’
(b)
n”
(c)
(a)c
Which equilibrium is likely to occur?
Willingness-to-pay p = n(1000-n)
Competition & Network Externalities
Suppose the market expands whenever willingness-to-pay exceeds marginal production cost, c.
Competition & Network Externalities
0 1000n
Demand Curve
Supply Curve
n’ n”
c
Which equilibrium is likely to occur?
Willingness-to-pay p = n(1000-n)
Competition & Network Externalities
0 1000n
Demand Curve
Supply Curve
n’ n”
c
Which equilibrium is likely to occur?
Willingness-to-pay p = n(1000-n)
Unstable
Competition & Network Externalities
0 1000n
Demand Curve
Supply Curve
n”
c
Which equilibrium is likely to occur?
Willingness-to-pay p = n(1000-n)
Competition & Network Externalities
0 1000n
Demand Curve
Supply Curve
n”
c
Which equilibrium is likely to occur?
Willingness-to-pay p = n(1000-n)
Stable
Competition & Network Externalities
0 1000n
Demand Curve
Supply Curve
n”
c
Which equilibrium is likely to occur?
Willingness-to-pay p = n(1000-n)
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
The rights owner now allows a free trial period. This causes
– an increase in consumption
and a decrease in sales per unit of consumption
yY
.
Y y , 1
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
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
The firm’s problem is now to
This problem must have the same solution as max
yp y y( ) .
maxY
P YY
p YY
p Y Y( ) ( ) ( ) .
Rights Management
The firm’s problem is now to
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
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
maxy
p y y cy F( ) .
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-to-
pay 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-to-pay 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 isP y k p ky ts ( ) [ ( ) ].
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 isP y k p ky ts ( ) [ ( ) ].
P y y cy Fs ( ) maxy
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 isP y k p ky ts ( ) [ ( ) ].
P y y cy F k p ky t y cy Fs ( ) [ ( ) ] maxy
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 isP y k p ky ts ( ) [ ( ) ].
P y y cy F k p ky t y cy F
p ky kyck
t ky F
s ( ) [ ( ) ]
( ) .
FH IK
maxy
Sharing Intellectual Property
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.
Sharing Intellectual Property
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 .
Sharing Intellectual Property
Direct sale is better for the producer if
I.e. if
cck
t .
ckk
t 1
.
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.
ckk
t 1
.
Recommended