Discussion: Price Competition and Convex Costs

1
Discussion Price Competition and Convex Costs
Bertrand model with convex costs and the
restriction that firms are committed to serve the
demand they face. Restriction gt It can be
costly to undercut competitors price, because
demand increases and so will the (convex) costs.
gt Pure strategy equilibria sometimes exist,
where they would not exist without the
restriction.
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Ex. Bertrand-Edgeworth model Two firms have
constant marginal cost c up to capacity K. Firms
face perfectly inelastic demand D up to a
reservation price . Assume that KltD2K.
Any price between c and is a NE in a
one-shot game. Because slightly undercutting
implies a very high cost. Would it be possible to
refine the equilibrium to make a more precise
prediction?
Industry marginal cost
c
D
2K
Is it realistic to assume that firms have to
serve demand at any cost? Even if serving is
mandatory one would expect some opt-outs in the
laws. Perhaps there is an optional fine if
demand is not fully served.
Summary Model is not realistic and it gives
imprecise predictions for very convex costs. It
seems to be more realistic and useful for
moderately convex costs.
3
Relevance for electricity markets
Some retailers also distribute electricity (but
not necessarily to the same customers) gt Perhaps
they will approximately behave like price-setting
oligopolists with convex costs.