[A decision scheme makes the probabilities of alternatives depend on individual strong orderings of them. It is strategy-proof if it logically precludes anyone's advantageously misrepresenting his preferences. It is unilateral if only one individual can affect the outcome, and duple if it restricts the final outcome to a fixed pair of alternatives. Any strategy-proof decision scheme, it is shown, is a probability mixture of schemes each of which is unilateral or duple. If it guarantees Pareto optimal outcomes, it is a probability mixture of dictatorial schemes. If it guarantees ex ante Pareto optimal lotteries, it is dictatorial.]
[A limiting feature of several theoretically superior "shrinkage" estimators for the linear regression model lies in the fact that there must be a certain degree of orthogonality in regressors in order for them to dominate the ordinary least squares estimator. In this paper we apply variants of pre-test and Stein estimators to data on international trade, and discuss their merits in light of the limitations imposed by the non-orthogonality of these and other sets of economic data.]
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.