ECON 4820 Strategic Competition
TERM PAPER 1
Note: Paper should be handed in by March 5, 2004.
Introduction
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.
Question 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
⎡ 1 − c + n∆ ⎤
⎡1 − c − ∆ ⎤
.
, π 2 (n) = ... = π n (n) = ⎢
π 1 (n) = ⎢
⎥
⎣ n +1 ⎦
⎣ n + 1 ⎥⎦
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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?
Question 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
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on a new technology that 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
V m = π 1 (1) − π 0 (1) =
V o = π 1 ( n) − π 2 ( n ) =
2 [1 − c ] ∆ + ∆ 2
4
2 [1 − c ] ∆ + [ n − 1] ∆ 2
n +1
How does willingness to pay depend on the number of firms and the size of
the cost reduction?
Question III
Assume next that also a firm which is initially not 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 i for the firm that is initially alone on the
market (i.e. the monopolist), and W e for a firm that is initially outside the
market, where
5 [1 − c ] + 26 [1 − c ] ∆ + 5∆ 2
W = π 1 (1) − π 2 (2) =
36
2
i
4 [1 − c ] + 16 [1 − c ] ∆ + 16∆ 2
W = π 1 (2) =
36
2
e
Explain why W i ≥ W e . Discuss also how the analysis could be undertaken if
the market was initially an oligopoly.
Question 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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