Union Rivalry and Economic Growth: A Differential Game Approach

Abstract

Two decades ago Sen (1961, 1967) demonstrated how private saving versus consumption decisions are fundamentally different from collective decisions and how individual decisions may result in an insufficient amount of investments for the future. His analyses were essentially applications of the prisoner's dilemma. Assuming that, given the decisions of others, each individual would be better off by not saving an additional unit whereas all would be better off by saving collectively, it follows that no one will save although everyone would have preferred one more unit of saving by each individual. Because of the external effects between individuals' decisions and the lack of influence on others' actions, nobody wants to invest himself, although each individual would like to see others invest, i.e., all try to shift the burden of saving onto others. A very similar result was obtained a decade ago by Lancaster (1973) in a fully dynamic context by applying nonzero-sum differential game theory to the modelling of growth and distribution in a two-class economy. He demonstrated that the separation of saving and investment decisions leads to a Pareto-inferior outcome in a model where workers can control their share of consumption in total output, but have no influence on the investment decision, which is in the hands of capitalists and where both classes devise their strategies so as to maximize their own consumption over a fixed horizon. The fundamental fact here is that workers and capitalists have to act under a dynamic externality. One group's decision to save or invest for the future is affected by the fact that the accumulated amount may be consumed by the other group. This paper was written to illustrate how dynamic inefficiency may also result from the feature of present-day societies whereby the working class is not a single decision-making unit but has organized itself in a number of trade unions which have to operate under the above-mentioned dynamic externality. It is shown that the welfare loss which results from the isolation