SØK/ECON 535: Imperfect Competition and Strategic Interaction
TERM PAPER
Please note: papers must be handed in no later than October 31.
Firms’ incentives to introduce cost saving technologies (and hence to undertake research to
develop such technologies) depend not only on direct cost savings but also on how the
change in cost structure affects competition on the market.
I. Consider the following Cournot model. There are n firms on the market, all producing the
same product. Market demand is given by the inverse demand function p = 1 − Q , where p is
market price and Q aggregate output. All firms produce with constant unit costs. One firm
(called Firm 1) has unit costs c − ∆ (where ∆ ≥ 0, ∆ ≤ 1 − c and ∆ ≤ c ), while all other firms
have unit costs equal to c. Firms choose outputs simultaneously.
Derive firms’ equilibrium strategies and show that equilibrium profits are
2
2
1 − c − ∆ 
 1 − c + n∆ 
=
=
=
π 1 ( n) = 
π
π
,
(
)
...
(
)
n
n
2
n
 n + 1  .
 n + 1 
Explain how a reduction in Firm 1’s costs (i.e. an increase in ∆) affect outputs, profits and the
market price. How do these variables depend on the number of firms on the market?
II. Assume that initially all firms produce with the same technology (i.e. ∆ = 0 ) each earning
a profit of π 0 ( n ) = {[1 − c ] [ n + 1]} . One firm may obtain a patent on a new technology that
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reduces unit costs by ∆ (the rest of the firms continue producing with the old technology).
Explain why a firm’s maximum willingness to pay for the new technology is V m in the
monopoly case (i.e. n = 1 ) and V o in the oligopoly case, where
2[1 − c]∆ + ∆2
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2[1 − c]∆ + [n − 1]∆2
V o = π 1 ( n) − π 2 ( n) =
n +1
V m = π 1 (1) − π 0 (1) =
How does willingness to pay depend on the number of firms and the size of the cost
reduction?
III. Assume next that also a firm who is not initially on the market may obtain a patent on the
new technology and that, if so, such a firm would enter (we assume that all incumbent firms
stay on and produce with the old technology). Suppose that initially the market is a monopoly
and explain why the willingness to pay for the patent is W e for the firm that is initially alone
on the market (i.e. the monopolist), and W i for a firm that is initially outside the market,
where
1
5[1 − c] + 26[1 − c] ∆ + 5∆2
W = π 1 (1) − π 2 ( 2) =
36
2
4[1 − c] + 16[1 − c] ∆ + 16∆2
i
W = π 1 ( 2) =
36
2
e
Explain why W e ≥ W i . Discuss also how the analysis could be undertaken if the market was
initially an oligopoly.
IV. In light of the above analysis, discuss how incentives for R&D depend on market
structure and competition. Discuss also other features that may affect strategic interaction
between firms that do R&D, including the extent of patent protection and transfer of
knowledge between firms (spillovers).
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