Full text: Study week on the econometric approach to development planning

530 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
are identical in the sense that each of them can only offer one 
unit of labour and their utility functions are identical. Fur- 
thermore, we assume that the utility function is log-linear in 
the quantities of the commodities consumed by the worker. 
We obtain a set of output-determining equations and a set 
of price-determining equations. In the former, we explicitly 
take into account not only the current inter-industrial demand 
but also the investment demand due to the multi-sectoral accel- 
eration principle; and the latter states that prices are determin- 
ed so as to cover capital losses as well as the unit cost of pro- 
duction. 
As the input coefficients (as well as the consumption of 
various goods per worker) depend on prices, the mechanism of 
determination of outputs is influenced by the price-valuation 
mechanism, though the latter is independent of the former by 
virtue of the prevalence of the constant returns to scale. We 
can show that the characteristic roots of the whole system 
appear in pairs with their reciprocals. This leads to a Turn- 
pike Theorem which asserts that there is a long-run tendency 
for the optimal path of economic growth to approximate to 
the path of steady balanced growth at the maximal rate. 
In the second section of this paper, we examine various 
effects of technological changes, neutral and biased, on the long- 
run equilibrium prices and on the long-run output configuration 
to which efficient paths converge. We shall also deal with 
effects of technological changes on the allocation of labour 
among various industries. 
.. A TURNPIKE THEOREM 
1. Let us consider an economy consisting of n industries, 
whose products may serve capital requirements as well as cur- 
rent production requirements of various industries. Let 
(o] Morishima - pag. z
	        
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