SSE/EFI Working Paper Series in Economics and Finance
Price competition and convex costs
Abstract: In the original model of pure price competition, due to
Joseph Bertrand (1883), firms have linear cost functions. For any number of
identical such price-setting firms, this results in the perfectly
competitive outcome; the equilibrium price equal the firms’ (constant)
marginal cost. This paper provides a generalization of Bertrand’s model
from linear to convex cost functions. I analyze pure price competition both
in a static setting - where the firms interact once and for all - and in
dynamic setting - where they interact repeatedly over an indefinite future.
Sufficient conditions are given for the existence of Nash equilibrium in
the static setting and for subgame perfect equilibrium in the dynamic
setting. These equilibrium sets are characterized, and it is shown that
there typically exists a whole interval of Nash equilibrium prices in the
static setting and subgame perfect equilibria in the dynamic setting. It is
shown that firms may earn sizable profits and that their equilibrium
profits may increase if their production costs go up.
Keywords: Bertrand competition; (follow links to similar papers)
JEL-Codes: D43; (follow links to similar papers)
16 pages, February 14, 2006, Revised February 23, 2006
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