Market Equilibrium in a Model of a Planned Economy of the Soviet Type: A Proof of Existence and Results of Numerical Simulations

Abstract

One of the major problems in neo-classical economics has been how to identify the conditions that ensure the existence of equilibrium in an economy. A great deal of work has concerned itself with weakening the conditions required for equilibrium in a competitive economy; relatively little research has, however, examined the possibilities for its existence in economies with fundamentally different rules of behaviour. A number of articles have examined what are essentially competitive models with non-competitive elements in them, in particular with the presence of a governmental agency that collects and redistributes taxes and, in some cases, produces public goods. Shoven (1976) and Shoven and Whalley (1972, 1973) assume private production under competitive conditions and a government that acts purely as a tax collector. Diamond and Mirrlees (1971) consider only public production and introduce a special tax on labour income and a tax on the aggregate value of transactions in certain selected commodities. Fourgeaud (1969) has a more complicated model in which, with the usual assumptions about motivations of the firm and the consumer, there are ad-valorem taxes on the sales and purchases of commodities, the tax rate being the same in both cases, a proportional profit tax, and a tax on fixed income. He also assumes that labour is inelastically supplied and that government administrators have preferences on the production of public goods. In Mantel (1975) the government has preferences on public goods and private consumption, and consumer preferences are interdependent, and Foley (1970) assumes that consumers decide upon a tax scheme to produce the public goods that they desire, and that the level of production of public goods affects the levels of production and consumption of private goods. In this paper we construct a one period model of a very non-competitive economy, one that is based upon a traditional Soviet-type system, and examine a modified notion of equilibrium in it. The model differs from those analysed in the papers we have just mentioned in several aspects, the most important of which we may briefly discuss before we begin the consideration of the model itself. Producers in our system are not profit maximizers, but rather have quantity oriented incentive functions. The concept of profits only enters as a constraint imposed by the central planners upon producers in order to restrain them from producing outputs that would require excessive subsidies. The system of turnover, profit, and income taxes that we shall describe has a role in this Soviet model unlike those taxes in the various competitive models, since in each of those models the competitive solution without taxes is always a feasible solution, and, indeed, guarantees the nonemptiness of the solution set. In our case, however, the tax scheme is an essential part of the planning procedure, since without it, as we shall see, there would not be an equilibrium