Public infrastructure capital, scale economies and returns to variety



prefectures, though, at this level there is no sectoral breakdown. The second is that of a sectoral
breakdown for Greece as a whole. Third, is the sectoral breakdown for the metropolitan area of
Athens. The findings for Athens are then compared to those obtained in the fourth and last level that
represents the sectoral breakdown for manufacturing in the Rest of Greece.

The final part of this paper draws some basic conclusions from the empirical analysis based on
the modelling. These results are then compared to those of the Holtz-Eakin and Lovely paper for the
US economy, and have been also used to put this analysis in perspective. More particularly, the results
for the infrastructure’s impact on a number of establishments are compared to recent findings and
research.

2 Scale economies, returns to variety, and public capital

One of the most important recent models used in public capital research was that constructed
by Holtz-Eakin and Lovely (1996). There follows a concise presentation of this model, which has
been the basis for the empirical analysis for the Greek case. It has to be noted that the origin of the
model can be attributed to the research by Ethier (1979, 1982). The economy of the model is sketched
as a small, open one, with two sectors, one producing consumption goods (‘wheat’ in the Holtz-Eakin
and Lovely terminology2) and the other finished manufactured goods (‘manufactures’ as they call
them). In this economy there are two production inputs (factors of production), labour and capital3.

In the model, consumption goods are produced by firms that operate under perfect
competition. The perfect competition framework implies constant returns to scale (in the use of the
two production inputs). The model ascribes a sector for the production of intermediate goods
(‘components’ as they are termed. These intermediates are necessary for the production of the final
goods of the manufacturing sector. It is hypothesised again that the intermediate goods sector is
operating under perfect competition.

The two production factors, labour and private capital, can be used either for the production
of consumption goods (
W), or for the production of ‘factor bundles’ (m). The latter are used as inputs
for the production of the intermediate goods. It is assumed that there is the following transformation
function4 for the economy (as the quantities of the production factors are given):

W = f ( m )                                                            (1)

2 Here, some of the terminology is different to that of Holtz-Eakin and Lovely.

3 This model can easily extended for the case of three production inputs, private capital, labour, and land (see Holtz-
Eakin and Lovely (1996), footnote 6).

4 The ‘transformation function’ is a description of the technologically efficient plans (of the particular economy), or,
equivalently, this function picks out the maximal vectors of net outputs (Varian 1992). Equation 6.1 may be represented
by a production possibilities frontier, which is convex to the origin. This implies that the first derivative of equation 6.1
is
f '(m) 0, and the second derivative is f ff(m) 0 (see, for this point, Holtz-Eakin and Lovely (1996), p. 108, and
for the convexity of transformation functions in a multioutput context refer to Chambers (1988), pp. 260-261).



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