[where, φ n
φ x
φ v
φ F
n((a - v)x0 + b - F) + γnγ (vx0 + F)
(19)
(20)
(21)
(22)]
(23)
m
n((a - v) x0 + nγ vx0 )
m
( n - nγ ) vx 0
m
( nγ - n ) F
m
PM = (1 - a) n+ P c = 0
Equation 17 shows the changes in the price of intermediate goods as a result of a change of
public capital provision (the subsidy to variable costs, v). This equation also shows that Pc is affected
by changes in m (factor bundles). Holtz-Eakin and Lovely argued that if resources are withdrawn
from the production of consumption goods (the case where m> 0), then the price of factor bundles
will rise. The magnitude of this increase depends on the curvature of the production possibility
frontier, ξ (see Holtz-Eakin and Lovely, p. 112).
The changes in the demand for factor bundles are given by equation 18. It is clear from this
equation that there are three sources of such changes. One results from changes in the number of
intermediate goods producers (shown by the first term of the right-hand side of equation 18). Another
source is changes of the production level of these producers (shown by the second term). Finally,
government purchases can affect the demand for factor bundles (shown by the third and fourth terms).
Equation 23, which closes the system, shows the external price constraint on the supply price
of finished manufactured goods. As this equation demonstrates, an increase (decrease) in the number
[varieties] of intermediate goods will decrease (increase) the supply price (if a > 1). This change must
be offset by the positive (negative) effect in the price of the intermediate goods.
Holtz-Eakin and Lovely, using this theoretical model, studied the effects of changes in public
capital on the level of output and productivity in equilibrium. They first examined changes in that part
of infrastructure that decreases fixed costs (that is, F). If the system of equations 16, 17, 18, and 23 is
solved, it is possible to derive the proportionate changes in the price of intermediate goods, the
demand for factor bundles, and the number of intermediate goods. These changes are given in
equations 24, 25, and 26 respectively:
A
Pc
(a - 1)ξ(φ x δ F +φ F )
D
(24)