Yes, we agree

[Peter Skott <ecoskott@xxxxxxxxxxxxxx>]

Dear Paul,

Yes, I think there is basis for agreement. In fact, I thought we
agreed on substance all along. Having pursued the matter so
far, however, it may be worthwhile to try to pin down the
agreement a bit more precisely.

Consider a firm facing an (expected, inverse) demand curve
pd=f(q;x) where x=(x1,x2,...,xn) is a vector of parameters describing
the position and shape of the function. If the cost function is given
then profit maximization gives an optimal solution q*=q*(x) and
p*=p*(x). One may represent the SUPPLY SET of optimal solutions in
a q-p diagram, each point in the set being the optimal choice for
some value of the parameter vector x.

The supply set may be very large. For instance, let the marginal
cost function be linear - MC(q)=cq - and assume that the expected
demand curves are linear pd=a-bq. Then ANY point above the MC-curve
will be an optimal choice for some value of the parameters a and b:
(q0,p0) is optimal for a=2p0-cq0 and b=-c+p0/q0  (I hope I got the
algebra right).

Restrictions on the permissible parameter values will
reduce the supply set and in some special cases the supply set takes
the form of a simple supply curve. Each point on this supply curve
still describes a choice of output and price that is optimal for some value
of the parameters. Because the price is chosen endogenously I'm
slightly reluctant to talk of "the minimum market price ... that firms
will require in order for them to undertake the effort necessary
for different output and hiring decisions". But, yes, the supply
set can in some cases be described by a functional relation between
q and p.

Finally, you suggest that I "take the plunge" and use the
"well-established market period vs short period toolkit".  I cannot
resist the temptation to point out that in fact I have done that
already. My book on "Conflict and Effective Demand in Economic Growth"
(CUP 1989) develops a dynamic theory along these lines. It analyses
ultra-short run equilibria and firms' supply (and investment) response
to unfulfilled expectations. The analysis even includes money (and
different monetary regimes and their implications).

Cheers,
Peter Skott
University of Aarhus
ecoskott@xxxxxxxxxxxxxx