( a -1) >
1 -β
β
(29)14
As Holtz-Eakin and Lovely helpfully point out “the left-hand side of this equation is the rate at
which the economy realizes returns to variety (see Ethier, 1982) while the right-hand side is a
measure of the firms’ market power: the percentage mark-up over marginal cost. If the return to
variety dominates the ability of firms to capture the returns to restricting output M will rise.
Alternatively, if firms have sufficient market power to enforce greater mark-ups, the contraction of x0
will dominate and M will fall” (Holtz-Eakin and Lovely 1996, p.114).
In summary, it can be argued that changes in the provision of public capital can affect the
economy in different ways depending, on the one hand, upon market structure, and, on the other, on
technological factors.
Holtz-Eakin and Lovely argue that infrastructure changes do not affect the economy only by
reducing the fixed costs (F), but also by reducing the variable costs (v). For the study of the effects of
the latter they reproduced the aforementioned analysis for v. These effects are given by the following
set of equations:
P_ _- (a -1)⅛ (φχ»S, - φ, ) - S, )
v D
(30)
(31)
(32)
m _ φn8, - (φ»8, -φ,)(a -1)
λ D
,
Λ
n
Λ
,
- (ξ(φ x 8,-Φ, )-8, )
D
Equation 30, 31, and 32 give the effects of the price of intermediate goods, factor bundles used in the
production process of manufactured goods, and the variety of intermediate goods, respectively. It has
to be emphasised that all these expressions can be either > 0, or = 0, or < 0.
Generally speaking, as these equations show, the net effects of the reduction of variable costs,
due to an increase of public capital, are not too clear15. This can be seen in the following equation,
which is the counterpart for variable costs of equation 28:
Λ
M _ aεφ, +8 , -ε8 , (aφ, -φ n )
(33)
λ D
,
14 For the derivation of this equation, see Holtz-Eakin and Lovely (1996), p.114.
15 See Holtz-Eakin and Lovely (1996), p 114-115, for an analysis of these ambiguities.
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