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E312. Lecture 14
13 October 2005
Assignments
Review
pp. 72-75 (Monopolistic Competition)
pp. 76-81 (Next class)
Discussion of term project
III. Imperfect Competition, Virtual Products and Network Industries
A. Motivation
B. Game Theory and Dynamic Incentives.
a. Normal form games
b. Nash equlibria
c. Coordination games and the Prisoners Dilemma
Preview
d. Repeated Games and Trigger Strategies
C. Monopolistic Competition and Price differentiation
E. The Economics of Virtual Products (Information Goods)
1. Cost Characteristics
LECTURE______________________________________________________________
III. Imperfect Competition, Virtual Products and Network Industries
c. Dynamic Games. The primary reason that I introduce the normal form
representation of this game is to provide a simple framework for considering the structure
of a repeated game. Suppose you were one of only two gasoline stations in a small town
(or one of only two sellers of anti-virus software). You could shade on each other’s
prices, but you would both be better off if you did not. Would it be possible to devise a
strategy for a repeated game that might avoid this outcome? Yes!
Notice: What you need in the above game is for something to lower the high pay-off in
the HL payoff box.
In the repeated game, the present value (‘PDV’) of the HH strategy is
500 + 500/i = 500(1+i)/i
Similarly for the LL outcome, the PDV is
200 + 200/i + . = 200(1+i)/i
But consider the off-diagonal elements. It is extremely unlikely that a competitor will see
his or her rival defecting, and continue to post a high price. Rather, it is more likely that
the competitor will respond to a price cut with another price cut.
For simplicity, let us consider a very simple version of such a response:
Strategy: Play H Continue to play H until the rival plays L. Then play L forever after.
This is referred to as a “grim” trigger strategy, “grim” in the sense that one slip prompts
eternal punishment. It is, admittedly, a bit severe, but it is extremely useful for purposes
of illustration.
Consider the earnings in the HL box under a grim trigger strategy. The “defector”
will earn
700 + 200/i
The defected upon will earn
100 + 200/i
To illustrate how this changes incentives for the game, consider i=.10.
Firm 2
H
L
H
5500, 5500
2700, 2100
L
2100, 2700
2000, 2000
Notice that now H, H is the unique Nash equilibrium for the game.
Firm 1
More generally, let us denote D as a “defection” or a play of L when the rival plays H. L
refers to an LL outcome. Then a discount rate will support cooperation as long as
H + H/(i)
Or
(H-D) >
> D + L/(i)
(H-L)/(i)
(H-L)/(H-D)< i
That is, as long as the costs of competition over cooperation are not too small relative to
the short term gain of defection. The point here, is that even if firms do not explicitly
conspire, they may be able to generate high prices as part of a noncooperative strategy in
a repeated game. The success of such strategies depends on the plausibility of the
model’s underlying assumptions. Specifically.
1) The number of players. We have illustrated a 2 firm case. Trigger strategies
are possible with more than firms, however they become more difficult to
implement absent coordination. The primary reason for this is that firms have
difficulty distinguishing punishments from defections.
2) The monitorability of actions. Can a firm even tell when a rival defects? Is
output monitorable? Are the terms of sale monitorable? Is demand stable?
C. Monopolistic Competition and Price Differentiation. In the industry
“Shakeout” from Monopoly to Dominant firm, to Oligopoly, to competition, one
other structure is possible. It is monopolistic competition, which combines the
pricing discretion of Monopoly with the entry exit of competition.
1.Assumptions
a. Differentiated Products, each with a protectable “niche”
b. Free entry and exit into nearby product or geographic space
c. Many buyers (no buyer power)
2. Analysis. Since firms produce distinguishable products,
each firm faces a downsloping demand curve. This
implies, as in the case of monopoly that MR<AR (for
the same reason as in a monopoly). Thus, given any
cost structure a monopolistically competitive firm may
earn profits in the short run.
a. However, profits prompt entry. This
Eq u ilig b r iu m f o r th e M o n o p o lis tic C o m p e tito r
shifts in the residual demand curve. In an
equilibrium, the monopolist competitor
W e lf a r e c o s t o f
earns zero profits.
M o n o p o lis tic
b. Notice that the Monopolistic
C o m p e tito n s .
Competitor is inefficient relative to a
Competitor, even though zero profits are
earned. Some commentators argue that
many ”virtual” products will be
monopolistically competitive. Sellers
offer distinguishable products, with
relatively low entry and exit costs. Does
this imply that these firms are really less
competitive than would be competitors?
No. Some view this welfare cost as the
price of differentiation.
D. The Economics of Virtual Products (Information Goods)
1. Introduction. Many of the goods traded on the internet are virtual goods.
That is, goods that can be reduced to digital format. (CDs, money, information,
books, software, etc.) As we have mentioned previously, these goods are subject
to two critical features that complicate competition: (a) Unusual production costs
and (b) Network Externalities. We now take some time to consider these two
characteristics in more careful detail.
a.
Cost Conditions. Consider production conditions for a
book to be distributed over the internet. The publisher
strikes a contract with a writer (say $45,000 for the
development of the book, which will be given by the
writer to the publisher in digital format. Suppose that the
publisher must also pay $2000 for editing, and suppose
that the publisher gives up some $3000 in opportunity
costs for contracting with THIS author as opposed to
another. Thus the FIXED costs of the e-book are
$50,000. Now the cost to the publisher of distributing
the book is $0.00. However, again in the contract with
the writer, the publisher agrees to pay to the author a
royalty of $0.50 per copy. Thus, the AFC, ATC and
MC=AVC relations are as follows
Quantity
0
1
5000
10,000
20,000
30,000
40,000
50,000
TFC
50,000
50
50
50
50
50
50
50
MC
0.5
0.5
0.5
0.5
0.5
0.5
0.5
ATC
AFC
50,000.5 50,000
10.5
10
5.5
5
3.0
2.5
2.2
1.66667
1.8
1.25
1.5
1
Graphically,
20
15
MC
10
A TC
AFC
5
0
0
20000
40000
60000
This looks a lot like the “Economies of scale” case we observed for long run
competition. However, these cost curves arise in the short run. We will say that the firm
has “short run economies of scale.” Short run economies of scale are a distinguishing
characteristic of virtual products.
b.
Pricing with Virtual Products. Notice that to this point,
we have argued that the optimal price for a firm to
charge is the point where MR = MC. This result will
generate an efficient outcome. However, it is a problem
for the seller of virtual products, since the seller would
go bankrupt.
20
15
10
5
0
0
10000
20000
30000
40000
50000
60000
If, for example, the seller posted a price of $.50 for the
book and sold 20,000 books, the seller would have
revenues of $10,000 – all of which would be distributed to
the writer. The publisher would lose its fixed cost of
$50,000.
A second best option, is one that generates some
deadweight loss, but allows the publisher to break even.
The publisher should price where demand intersects
AVERAGE Costs.
20
15
10
5
0
0
10000
20000
30000
40000
50000
60000
Note: This essentially is an application of Average Cost
pricing. The net result is that competition in virtual
products may have many of the characteristics
of monopolistic competition.
However, unlike other instances of monopolistic
competition, the fixed costs are not always defendable. If
rivals can copy a sellers costs, then a desperate competitive
outcome will result.