Pc is the price of each intermediate good.
This price can be expressed in the terms of the Pm numeraire. As the producers of intermediate goods
will equate their marginal cost to their marginal revenue, Pc will be:
Pc = Pm (β v) [as Pm (a - v) = βPc ] (9)
The equation for the profit of each intermediate goods producer will be:
π = Pcx0 - Pm ((a - v)x0 + b - F) (10)
In equilibrium there will be free entry and exit of producers, and the profit π will be equal to zero.
Equating equation 10 to zero and replacing Pc with the right hand side of equation 9, equation 10 will
be:
Pm (aβ v) x0 - Pm ((a - v) x0 + b - F) = 0
(11)
(12)
Rearranging equation 11 means that:
x = β(b - F)
0 (1 -β)(a - v)
Equation 12 can be interpreted as follows. As x0 is increasing in β, the more a variety of
intermediate goods can be substituted from other varieties, the more each firm will produce that
particular variety.
In this model the demand for factor bundles comes from the producers of intermediate goods
and the public sector (for the creation of the infrastructure stock). There are two extreme possibilities
regarding the nature of the public capital. One possibility is for it to be a pure public good. Such
goods are not excludable and non-rival, i.e. “people cannot excluded from consuming them...and one
person’s consumption does not reduce the amount available to other consumers” (Varian 1992, p.
414). Another possibility is for it to be a public sector good that is little different from those produced
in the private sector (in this case the goods are ordinary, that is both excludable and rival)10.
Holtz-Eakin and Lovely, in order to capture the whole range of possibilities (including the two
extremes), sketched the total demand for factor bundles as:
m = n((a - v)x0 + b - F) + nγ (vx0 + F) (13)
10 There can be many in between cases. On such intermediate type are the ‘club’ goods (nonrival, but excludable [see
Varian 1992, p. 415]).