Public infrastructure capital, scale economies and returns to variety

(a - 1)(φ_x δ F +φ F ) > 0
D

nl ^ξ<^φx^δF ^+φF ) > 0

Γ ^D

where D ≡ ξφ _n - (a -1) > 0.¹3

The provision of public capital attracts production factors into the production process of
intermediate goods. This has, as a consequence, an increase in the marginal cost of factor bundles (in
terms of consumption goods). The producers of intermediate goods would pass on this cost, ceteris
paribus, but only to the extent of their market power and in terms of a mark-up percentage). Holtz-
Eakin and Lovely observed that “an increase in component prices must be accompanied by an
expansion in varieties if the economy is to retain a competitor in finished manufactures” (Holtz-
Eakin and Lovely 1996, p.113). Due to the mark-up, the intermediate goods industry will have profits
at the initial phase of the economy (the phase with n varieties). These profits will generate entry of
new firms into the sector producing intermediate goods. As Holtz-Eakin and Lovely argue “an
increase in public infrastructure increases the number of component producers and enhances any
external economies of the finished manufactures industry” (ibid.).

From equation 4 the proportionate change in finished manufactured goods is:

M_ an+ x 0                                                        (27)

An increase in the number of the firms producing intermediate goods does not ensure an
expansion of the sector producing manufactured goods. It can also be seen in equation 16 that a
public capital increase which reduces the fixed costs (F) will decrease the level of output of the

manufacturing sector that is maximising profits. If the solutions for n and x0 are substituted in the
above equation, the effect of F on the manufacturing sector can be derived as:

A

M _ ξδ G (aφ x

A

F

The sign of the numerator of the right-hand side of equation 28 depends on the sign of quantity

A

aΦ_x -φ_n (as all the other terms are positive). If this quantity is positive then M will be positive. This
will be the case if:

¹³ This condition is necessary in order to have a positive price-output relation for the manufacturing sector. This
assumption restricts the analysis to the concave part of the production frontier for the consumption and manufactured
goods (for further analysis, see Holtz-Eakin and Lovely 1996, footnote 11).

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