Theory of Economic Growth

By Michio Morishima | Go to book overview

IX Equilibrium Growth. (III) Normative Properties

1. We have so far discussed three kinds of equilibrium growth paths, the Cassel-von Neumann path of balanced growth, the Lindahl-Hicks sequence of temporary equilibria and the Hicks-Malinvaud perfect equilibrium over time, which we will now examine for efficiency and optimality. Each of them will in succession be compared with any other feasible path to see in what sense the former is superior. The subject is important for its own sake; from the results obtained we may decide our attitude towards the conventional but yet unsolved choice between competition or planning. It is also important as a prelude to the Turnpike problem, one of central and most attractive up-to-date topics of growth economics, which we shall discuss in a number of the following chapters.

Let us begin by giving the necessary definitions. First, the efficiency of a growth path is defined in terms of 'net' or 'consumable' outputs. Following our previous notation, we write qi(t − 1) for the intensity of process i operating in period t − 1. The total output of good j available at the beginning of period t is then written as

, and the total amount of the same good used by various manufacturing processes for further production as . It is evident that the remainder of the total output, after subtracting the total input, might be devoted to consumption by workers and capitalists; we call the 'net' or 'consumable' output of good j in period t. For the last period T, hj(T) is defined as

which is the amount of good j bequeathed to the future generations after T.

In the following we say that a path of order T with a net output stream, H* = {h1*(t), . . . , hn*(t); t = 0, 1, . . . , T}, is weakly efficient (of order T) if there is no other feasible path yielding a different sequence of net outputs H = {h1(1), . . . , hn(t); t = 0, 1, . . . , T}, such that there is more of some commodity and no less of any other commodity to consume in H than

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