Price Uncertainty and the Cooperative Firm
研究竞争性合作企业在最终产品价格不确定时的行为，发现风险规避的合作企业会在不确定性下增加产出和劳动投入，这与资本家企业相反，从而缩小了两类企业在产出和就业上的差距。
The behavior of a cooperative firm which is interested in the well-being of its members has attracted economists' attention in quite a few studies. The pioneer work of Benjamin Ward compares the policy of such a firm with that of a profit maximizer under perfect competition. The analysis is further carried out by Evsey Domar (1966) and Jaroslav Vanek (1969). The comprehensive study of Vanek (1970) establishes a general theory of labor-managed market economies. The theory of cooperatives and participatory structures of enterprises has recently been further extended in several directions by S. Charles Maurice and Charles E. Ferguson, J. E. Meade, Eirik Furubotn, among others. However, the basic assumption in all these studies is that the cooperative operates with complete information about the prices of the final demand markets. This paper is concerned with the behavior of a competitive cooperative firm under price uncertainty. That is, the price of the final product is not perfectly anticipated, for instance, as a result of inflation, but is rather uncertain and takes the form of a stochastic variable with a known distribution. A recent paper of Allan Taub deals with the very same subject. However, the treatment here is more comprehensive and the results are entirely different.' Compare the output policy of two types of firms: The profit maximizer whose labor input consists of workers with no share in the firm's profits and a second firm which seeks the optimum number of members to maximize profits or net income per member. We shall call the first type a capitalist and the second type a cooperative. As noted by Vanek (1970) and others, there are several aspects which distinguish the cooperative firm from the capitalist firm. However, we disregard all the other characteristics and concentrate in this paper on the difference of the objective functions of the two types of firms. Ward has already shown that under perfect competition and with complete price anticipation, a cooperative produces less than a capitalist who has the same production technology. On the other hand, Agnar Sandmo and Hayne Leland have found that under price uncertainty a risk-averse capitalist firm produces less than under complete certainty. The main finding of this paper is that Sandmo's result does not apply to cooperatives. That is, a cooperative even if risk averse produces more under uncertainty and therefore increases its demand for labor input. As a consequence of this result, Ward's conclusion is weakened and becomes less significant. That is, in the case of price uncertainty the discrepancy between cooperative and capitalist with respect to production and occupation is smaller than under price stability. Section I states the assumptions of the model and compares the optimum solution of a capitalist with that of a cooperative firm under certainty as well as under risk conditions. Section II presents comparative statics first with respect to the basic parameters of the price distribution (the average price and the variance), and second, with respect to the basic parameters of the profit function (the wage rate and the fixed cost).