Theory of Economic Growth

By Michio Morishima | Go to book overview

XIII Consumption En Route: The Second Turnpike Theorem

1. In Chapter X , we were concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to maximize the stocks of goods which they can bestow, at the horizon, upon the future citizens. Such a partial optimization for the sake of the future should more properly be superseded by a general mutual optimization, so that the benefits from the properties initially available are shared between the people living in the planning period and those after that. This would inevitably confront us with one of the hardest problems of economics, the interpersonal and intertemporal comparisons of utilities.

Attempts to solve the crux of the problem have to be abandoned. We content ourselves by running to the other extreme. In this chapter, we derive the conditions for Ramsey optimality as distinct from DOSSO-efficiency, that is to say, we optimize in favour of the people in the planning period; the satisfaction of the future residents is pegged at a certain level that the present residents approve of. Among all feasible programmes that leave, at the end of the planning period, necessary amounts of goods for the future residents, will the people living choose a single one which is most preferable from their own point of view. There is a switch-over of ideology from abstinence for the future to satisfaction in the transient life.

People of the coming generation yet to be born have no chance to reveal to their seniors their own preferences; they can only give the planning authorities a carte blanche. Let kj be the stock of good j per man which is available when the planning period closes at the end of period T − 1. It may directly be consumed by the future residents of the society or may be combined with the stock of other goods for further production of goods. As attorney for the future generation, the planning authorities partition all possible combinations of goods (k1, k2, . . . , kn) into classes such that any two belonging to the same class are equally useful. To each class is attached a number in such a way that a class consisting of combinations of goods that are more useful than a combination of goods of another class has a number that is greater than the number of the second class. Such a function is referred to as the posterity utility function which describes the preference preordering of the stocks of goods that the planning authorities set on behalf of the coming generation. It is denoted by

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