Public infrastructure capital, scale economies and returns to variety

of economic activity in an economy. Higher values for n, in this context, indicate a more dynamic
economy.

An increase of the public infrastructure can raise x0⁷. But even in cases where there is no such
increase, there is the possibility of an indirect increase of productivity, as there is the possibility that a
change of infrastructure capacity can increase the number of n (therefore, the range of economic
activity).

There are several other assumptions for the model used here. It is assumed that unlimited
quantities of consumption and finished manufactured goods can be traded at Pm price. In the Holtz-
Eakin and Lovely model it is assumed that intermediate goods are not tradeable⁸. It is also assumed
that the producers of intermediate goods behave as monopolistic competitors (n is adequately large
and there is free entry into this sector of the economy).

Each variety of intermediate goods (x) is produced by factor bundles, under the relationship
ax+b, where a, b > 0. A certain part of the necessary factor bundles in the economy, such as road
networks, sewage systems, etc, can be provided by the public sector. This will save private resources
that would, otherwise, have been directed to the production of this infrastructure.

As Holtz-Eakin and Lovely point out, public infrastructure can decrease either fixed or
variable costs, or both. If F is the reduction in fixed costs, and v the reduction in variable costs, then
the production of x units of any variety of intermediate goods would require the use of a quantity of
factor bundles given by:

Q(x) = (a - v)x + b - F                                                     (5)

The private cost of these factor bundles will be:

Cfb = Pm ((a - v)x + b - F )                                                    (6)

The marginal private cost for the intermediate goods producers will be:

MPC = Pm (a - v)                                                      (7)

and the marginal revenue will be⁹:

MR = β Pc                                                          (8)

where,

⁷ This case corresponds to the increases in productivity usually considered with production and cost function analyses.
⁸ This assumption is important for spatial analysis. Ethier (1979, 1982) assumed that intermediate goods can be traded.
However, Markusen (1991) and Holtz-Eakin and Lovely (1996) presumed that intermediate goods (and services) that
contribute to the manufacturing sector are unique to the local economy.

Thus, finished manufactured goods are “assembled from intermediate goods and services produced exclusively in the
home jurisdiction” (Holtz-Eakin and Lovely 1996, p.110).

⁹ For the derivation of this marginal revenue, see Holtz-Eakin and Lovely (1996), footnote 9.

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