Entrepreneurial and Consumer Demand Theories for Commodity Spectra: Part I

Deference to the reader calls for a blueprint of the article's contents. Its contributions are of two distinct varieties. The first and prime contribution consists in the extension of existing analyses for finite numbers of commodities to the case of infinitely many. Hotelling and others have emphasized the desirability of stating the results of entrepreneurial and consumer demand theories for infinite numbers of goods. Apart from its utility in treating commodity groups embracing large, though not necessarily infinite, numbers of items, the economic properties of which shade from one member to the next, the extension is stamped with true intellectual concinnity. The finite theories are contained, as very special cases, in the infinite analyses. A more distinctly economic flavor breathes from the second species of offering. It includes propositions and economic tools novel even to the finite analyses. The theorem that an entrepreneur's derived demand functions for factors of production are stable in the sense of Hicks' extension of the classical definition is an example.' Evolution of the inverse utility function (more properly functional), described in ?2, is another. Unlike its counterpart, the inverse utility function is a function of prices. Economically, it is the negative of the maximum utility attainable by the consumer, income specified, when a stated price regime prevails in the competitive market. Noteworthy operational properties characterize the inverse utility function. Designate the consumer's budgetary limitation, prices constant and quantities varying, direct. Term it inverse when quantities remain constant and prices vary. Maximization of the utility function subject to the direct budgetary limitation results in individual consumer demand functions. Maxi-