In the above equation it is parameter 7that denotes the nature of infrastructure. If 7 = 0, v and F are
pure public goods. If 7 = 1, v and F are pure private goods.
The supply price of the finished manufactured goods must be equal to Pm (prices are measured
in terms of wheat)11. The profits in the sector of the economy where the intermediate goods are
assembled into final manufactured goods will be zero. This means that:
PM = PcX 0 n (14)
The above relationship can be transformed, with the use of equation 4, to become:
P = n 1~ aP (15)
mc
It is apparent from the last equation that an increase in n will have, as a result, an increase in
productivity, and subsequently a decrease in the supply price of finished manufactured goods. An
increase of Pc, will have the opposite effect - that is it will increase Pm.
Holtz-Eakin and Lovely asked the question, what would be the effects of an increase of public
capital12 in the context of this particular model. The system of basic equations of the model (equations
9, 12, 13, and 15) can be used for the purpose of answering this question.
An increase in public capital would have, as a result, a change in the cost structure of
intermediate goods (by changing the preferred levels of output). Equation 16 can be derived from
equation 12 by total differentiation:
A _ F A v A A A
x 0 =-----F H--v ≡~δp F +δv v (16)
bFv
- F a - v
where the symbol {^} denotes proportional changes.
Equation 16 shows that increases in F will reduce x0, and increases of v will raise x0. Similarly, total
differentiation of the other basic equations (equation 9, 13, and 15) provides that:
AAA
Pc = ξ m -δ vv (17)
and
m = φ nn+φ Xx-φ vv-φ FFA (18)
11 As is usually the norm in economic modelling, a good (in this case wheat) ‘plays’ the role of money, and the prices
for the other goods are calculated on the basis of how many units of wheat can be bartered for one unit of the particular
good in question.
12 It has to be noted that Holtz-Eakin and Lovely, in order to clarify the effects of an infrastructure increase, abstracted
“from issues of distortionary-tax financing and assumed that government spending is funded by lump-sum taxation of
households” (Holtz-Eakin and Lovely 1996, p.111).