Knowledge that Transforms

La distinction classique entre biens individualisables et biens collectifs ne tient pas compte des biens et services, tels que la circulation automobile, dont la quantite est individualisable mais dont la qualit& a un caractere collectif et d&pend du niveau de la demande en raison d'effets externes. On etudie dans ce papier comment les conditions classiques de l1'quilibre &conomique sont a modifier pour introduire cette categorie de biens et quelles doivent etre leurs regles de tarification. Les resultats theoriques obtenus sont ensuite appliques au cas de la circulation automobile.

In this paper an attempt is made to give precise expression to the conditions under which a profit maximizing firm with fixed research budget will choose each type of technical change (i.e., neutral and nonneutral). It was found that the optimal choice depends on the initial technology, relative factor prices, and relative costs of acquiring different types of technical change. The preferred technical change need not be exclusively of one sort (e.g., neutral chanige). Once neutral technical change becomes optimal, however, it remains so until there is a change in relative factor prices. On the other hand, adoption of a biased technical change may eventually cause neutral advance to become desired even in the absence of relative factor price changes. Examination of the firm's decision criterion under the assumption that it is a monopsonistic buyer of factors of production, discloses that under identical initial conditions (i.e., relative factor prices and relative costs of alternative forms of technical change) the firm will prefer more biased technical change relative to the situation in which it purchases factors competitively. In particular, the firm will, under these conditions, seek those biased technical changes which economize on the factor whose elasticity of supply is relatively smaller. Finally, it was also discovered that, contrary to previous suppositions, changes in the elasticity of substitution do affect the optimal capital-labor ratio for each factor price combination in all cases but one.

ONE OF THE common problems facing an economist dealing with production functions is the problem of aggregation of factors. In a rather neglected paper, Houthakker advances an ingenious approach for explaining the possibility of finding a neoclassical production function for an industry even when production within each of the firms (or cells)3 is done according to a fixed coefficients production function. These fixed proportions vary in a regular way from one cell to another so that the overall input-output relationship takes the form of a regular neoclassical production function. As Solow notices in a survey article on production functions4 this paper has been forgotten and not followed in any direction. In this note we try to reverse Houthakker's procedure and to show how each neoclassical production function implies some density function or distribution function over the cells. We here do it for CES production functions, but it will be obvious that the same method applies to any production function. Following Houthakker we normalize the cells so that each of them is capable of producing one unit of output. Each cell has a requirement, say t, of the variable factor and this requirement varies from one cell to another. If the wage rate in terms of output produced is p then all the cells with tp < 1 will produce a unit of output, all others will be idle. Assume that we are given a density function of the various cells by g(t). Output produced will then be Q = f Pg(t)dt and the input used A f f'IP tg(t)dt. By eliminating i/p one gets a relationship between Q and A. In this way Houthakker has shown that a Pareto distribution implies a CobbDouglas production function. Notice that the relationship between Q and A the cumulated product and factor used-is the familiar Lorenz curve. Assume that the overall relationship between output and the variable factor follows a CES production function with elasticity of substitution (a) smaller than 1;