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