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Scale and Productivity Measurement under Risk

American Economic Review 1983
The literature on risk and uncertainty gives an important place to studies comparing behavioral and comparative static results obtained under certainty and uncertainty. The standard neoclassical theory of the firm, however, has much more to offer than behavioral results. For example, the optimizing behavior of the profit-seeking firm insures that the degree of the firm's returns to scale can be measured by the ratio of cost to revenue. Furthermore, it is also possible to isolate measures of the rate of technical change for a profit-maximizing firm which depend solely upon observed prices and quantities. This note demonstrates some of the implications of uncertainty for measuring scale economies and the rate of technical change. Specifically, using a model developed by Agnar Sandmo (1971), it is demonstrated that under conditions of risk and uncertainty, there are generally no measures of the scale elasticity or the rate of technical change which can be derived from observations on prices and quantity without information on either the structure of production or the utility function which underlies Sandmo's analy-

Price Aggregation When Price-Taking Firms' Prices Vary

Review of Economic Studies 1989 56(2), 297
In many cases, heterogeneous prices occur in price-taking environments. In empirical work, an aggregate price index is often created from such prices and used to explain aggregate supply and derived demands. We show that consistent aggregation places strong restrictions on functional forms which may be used to describe behaviour. Unlike the case of aggregation of consumer income (but similar to the case of aggregation of wages), these functional forms are inconsistent with standard microtheory.