Public infrastructure capital, scale economies and returns to variety

In the Holtz-Eakin and Lovely model consumption goods (wheat) are used as numeraire (p.
108). As consumption goods and factor bundles are produced and sold under conditions of perfect
competition, their relative price will be:

Pm =-f ^,(m)                                                               (2)

This comprises the opportunity cost for the production of factor bundles.

As was mentioned earlier, factor bundles are used for the production of intermediate goods.
Intermediate goods, in turn, are used for the production of the final goods of the manufacturing
sector, in a manner described by the following production function:

n γβ
xç ^xi
£ n
wherexi is the input of intermediate good i into the production of final goods of the manufacturing
sector, M. It is supposed that there are n varieties of intermediate goods in the model economy.
Parameter a is a measure of economies of scale with respect to the range of intermediate goods (a >
1 denotes increasing returns to variety). Parameter J is a measure of the degree of differentiation
between any pair of intermediate goods, as it has been assumed that they are imperfect substitutes⁵.
Higher (lower) values of J denote less (more) differentiation among the intermediate goods. Holtz-
Eakin and Lovely pointed out that ‘intermediate goods’ (components in their terminology) have been
interpreted in different ways in the existing examples of similar economic modelling⁶. In any case, the
crucial point is that the final goods production process is dependent on a wide variety of specialised
services and goods (see for this point Holtz-Eakin and Lovely 1996, p.109). They assumed that all
varieties of intermediate goods have identical production technologies, and argue that “since each
variety enters symmetrically into the production of finished manufactures, in equilibrium an
identical quantity,x0, will be supplied of each variety” (ibid.). Under this assumption, equation 3 will
become:

M = n^a x 0                                                               (4)

It is obvious from this last equation that the final goods of the manufacturing sector are
linearly homogeneous in input x0, and homogeneous to degree a in n. It is assumed that there are
many competitive firms which produce final goods using the intermediate factor bundles. For this
reason Holtz-Eakin and Lovely (1996, p. 109) argue that “each of [these firms] takes n as given”
and, more crucially, that the n varieties of intermediate goods can be viewed as an index of the range

⁵ The elasticity of substitution between any pair of intermediate goods is 1/(1-3).

⁶ See, for instance, Holtz-Eakin and Lovely’s own interpretation (1996), Ethier’s (1982) as specialised intermediate
inputs, or Markusen’s (1989) as producer services.

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