Theory of Economic Growth

By Michio Morishima | Go to book overview

X Maximization of Bequests: The First Turnpike Theorem

1. Having found the conditions for the Golden Equilibrium we naturally turn to examine the economy for stability. Does a Hicks-Malinvaud competitive equilibrium trajectory starting from the historically given initial point approach nearer and nearer to the state of Golden Equilibrium when the order of the path gets larger? This problem, which amounts to asking whether an economy obeying the principle of competition can attain a Golden Age, will be discussed repeatedly in this chapter and the following. The convergence of this sort will be compared with another kind of convergence recently dealt with by many writers under the common heading of Turnpike Theorems, particular applications of which may occur in more or less planned economies but not in purely competitive economies.

In this chapter, we confine ourselves to the simple case of 'L-shaped' indifference curves. We assume that (i) the Capitalist's propensity to save is unity and the Worker's is zero not only in Golden Equilibrium but also in all other circumstances, and (ii) the Worker has a family of parallel indifference curves to the effect that, unless a commodity is a 'limiting' factor, an increase in the supply of it (the supply of other commodities remaining constant) does not leave the Worker better off than before. It then follows that although the Worker is permitted to choose between alternative bundles of commodities which are equal in value, Engel-coefficients derived from such indifference curves do not respond to price changes at all; they are taken as constant, as in the original von Neumann model which does not allow for consumers' choice. Our model is probably applicable to communist economies in the early stage of their development. It is evident that there is no bourgeoisie in such economies; and when they are put under the dictatorship of Stalinists, all surpluses of production are automatically reinvested, all consumption goods are rationed and workers cannot choose goods according to their own tastes but are only fed at some subsistence level.

Apart from T inequalities stating that in each period t, t = 0, 1, . . . , T − 1, investment must be at least as large as savings, the Hicks-Malinvaud path of order T is characterized (as was shown in Chapter VIII) by the following four sets of inequalities:

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