Knowledge that Transforms

In this paper we provide a statement of the relationship between the weak axiom of revealed preference (WA) and the negative semidefiniteness of the matrix of substitution terms (NSD). As a corollary we determine the relation between WA and the strong axiom of revealed preference (SA). The latter is equivalent to NSD and the symmetry of the matrix of substitution terms. The former, WA, implies NSD but is not implied by NSD. Also, WA is implied by the condition that the matrix of substitution terms is negative definite (ND), but it does not imply ND. Application of these results yield an infinity of demand functions which satisfy WA but not SA.

WE CONSIDER A MICROECONOMIC growth model in which a certain product or service, supplied and consumed period by period, becomes more valuable to a consumer-objectively or subjectively-as its use becomes widespread, up to some level of saturation. A reasonable example might be the rental of communication facilities. Taking the standpoint of the producer, we ask for that schedule which maximizes the present value of the profit stream. We show that the solution to this problem differs considerably from that given by profit maximization in each individual period (sometimes termed myopic): it calls for lower prices to the consumer. As such, it provides some quantitative justification for practical policies of pricing for development. Its intuitive explanation is that lower prices (i.e., larger outputs) in the initial stages speed the buildup of demand to its saturation value; the larger profits realizable on larger volume are thereby brought foward in time and increase their contribution to the discounted stream. This effect, being independent of the shape of demand or cost curves, may be attributed to growth alone. It suggests that growth potential, when properly perceived and utilized, can yield a mutual gain to the producer and consumers, since the latter benefit not only from lower prices, but also from the fact that the value of the product to them, which is assumed to increase with higher use, likewise rises more rapidly.

[This paper presents a Bayesian analysis of a single equation from a simultaneous equations system. The analysis is carried out under "limited information" because no prior information (other than a list of endogenous and exogenous variables) is introduced on the parameters of the remaining equations in the in the system. These parameters are integrated out analytically. The equation of interest may or may not be identified by means of exact a priori information; probabilistic prior information is equally acceptable. The prior density is either of the non-informative or the natural conjugate type. The kernel of the posterior density for the regression coefficients is a ratio of t kernels. The existence of posterior moments is ascertained. This approach is applied for illustrative purposes to Tintner's model of the meat market.]