A PITFALL IN THE COMPARATIVE STATICS OF OLIGOPOLY
| DOI | http://doi.org/10.1111/j.1467-9485.1992.tb00607.x |
| Date | 01 February 1992 |
| Published date | 01 February 1992 |
| Author | F. W. McElroy |
.Scoiioh
Journal
of
Poliiicul
Eronoiny.
Vol.
39.
No.
I.
February
1992
I992
Scottish
Economic
Society
A
PITFALL IN THE COMPARATIVE STATICS OF
OLIGOPOLY
F.
W.
MCELROY*
Georgetown University
I
INTRODUCTION
This note shows that a comparative-static technique that works well for
monopoly is not reliable for oligopoly, even though second-order conditions
(socs) that are often assumed to rule out paradoxical results hold everywhere.
Specifically, in the monopoly model with decreasing marginal revenue (MR)
and marginal cost (MC) such that MC'
>
MR' everywhere, one can deduce
comparative static effects by comparing the shifted MR and MC
at
the old
equilibrium. This is because, eg., an output level where MR
<
MC must be
above the new unique equilibrium. How does this technique generalize
to
a
quantity-setting homogeneous oligopoly model with a unique equilibrium?
For
example,
if
each firm's downward-sloping perceived MR falls short
of
its
marginal cost and the corresponding second-order condition holds Gverywhere,
must
it
be that aggregate output is above its equilibrium?' That this is not
necessarily the case, even in Cournot models giving rise to downward-sloping
linear reaction functions meeting at a unique globally stable equilibrium is
demonstrated in Section 11. The intuition behind these counterexmples is that
the second-order conditions on each firm do not directly impinge on
total
output as in monopoly. It turns out that, even
if
we insist that each duopolist's
MC cuts its perceived MR curve from below, this only implies that reaction
curves are negatively sloped. It does not rule out the situation depicted in
Figure
1
in which their intersection is globally stable (under the usual textbook
adjustment process) and yet counterinituitive comparative static results are
produced. Clearly, if the latter are to be ruled out, stronger assumptions than
the global socs are needed. Sufficient stronger assumptions are that the reaction
curve
of
each firm be less steeply sloped than the
45"
line when viewed from
the axis representing its rival's output. In Section I11 this result is generalized
*
1
am grateful
to
my colleague
John
T.
Cuddington and to an anonymous referee for
helpful suggestions.
'
An example of reliance on this type of comparative static technique in analysis
of
oligopoly is in Farrell and Shapiro (1990, Propositions
1,2).
Levin (1985) examines the effects
of
pollution tax changes in a Cournot model with a linear marginal cost, and discusses
conditions
for
avoiding 'perverse' output effects
of
such tax changes.
Date
of
receipt
of
final manuscript: 18th December 1990.
95
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