Knowledge that Transforms

[Suppose that social choice is based on interpersonal comparisons of welfare levels. Suppose too that, whenever all but two persons are indifferent between two options, a choice is made between these options which is equitable, in some sense. Then provided that individual welfare functions are unrestricted, and social choice is independent of irrelevant alternatives, it follows that social choice is always equitable, in the same sense. This applies when equity means satisfying Suppes' indifference rule, or Suppes' original justice criterion, or the lexicographic extension of Rawls' difference principle.]

Ann D. Witte, Howard J. Sumka, Homer Erekson, An Estimate of a Structural Hedonic Price Model of the Housing Market: An Application of Rosen's Theory of Implicit Markets, Econometrica, Vol. 47, No. 5 (Sep., 1979), pp. 1151-1173

This paper examines various theorems of trade and general equilibrium in a generalized framework involving arbitrary numbers of goods and factors. It develops structural relations among the changes in outputs, commodity prices, factor rewards, and factor endowments. By finding a way of inverting a bordered matrix with a singular Hessian, the paper derives explicit expressions for the following matrices: the Stolper-Samuelson matrix; the Rybczynski matrix; the matrix which measures the effect of a change in factor endowments upon factor rewards at constant commodity prices; and the matrix which measures the effect of a change in commodity prices upon outputs at constant factor endowments. Various properties of these matrices are used to obtain, among other results, the reciprocity relations and general results on factor-price equalization. The paper also ey.amines the problem of indeterminacy in production when the number of commodities exceeds the rank of the input-coefficient matrix and presents the correct specifications of the supply functions of outputs. Finally a new theorem on the degree of flatness of the production transformation surface is derived.

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In an economy with complete markets, the owners of a firm will unanimously desire the firm to maximize profits if it is a perfect competitor. We generalize this result to an economy with incomplete markets. We show that if competitive conditions prevail-that is, if each firm is negligible relative to the aggregate economy-a firm's shareholders will want the firm to maximize the (net) market value of its shares. This result holds whether or not the so-called spanning condition is satisfied. However, while there may be agreement about what goal the firm should pursue, there may be disagreement among shareholders about how best to pursue this goal.

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[Consider a society with n individuals who must choose an alternative from a given non-empty set X. For an integer d ≤ n, a d-majority equilibrium is an alternative x* ∈ X such that no alternative in X is preferred to x* by at least d individuals. It is proved that when X is a compact and convex set of dimension m, a necessary and sufficient condition that, for every profile of individuals' convex and continuous preferences, there exists a d-majority equilibrium, is that d be greater than (m/(m + 1))n. Using this result for the case when X consists of a finite number, T, of alternatives, it is shown that a necessary and sufficient condition that for every individuals' preference orderings there exists a d-majority equilibrium is that d exceeds ((T - 1)/T)n.]

[This paper proves that for majority voting over multidimensional alternative spaces, the majority rule intransitivities can generally be expected to extend to the whole alternative space in such a way that virtually all points are in the same cycle set. In other words, given almost any two points in the alternative space, it is possible to construct a majority path which starts at the first, and ends at the second. It is shown that for the intransitivities not to extend to the whole space in this manner, extremely restrictive conditions must be met on the frontier (or boundary) of the cycle set. Similar results are shown to hold for any social choice rule derived from a strong simple game. These results hold under fairly weak assumptions on individual preferences: individuals need only have continuous utility representations of their preferences such that no two individuals' preferences coincide locally. The results seem to rule out the possibility, at least in models of interest to economists, of using the transitive closure of the majority relation as a useful social choice function. They also imply that under any social choice rule meeting the conditions assumed here, it is generally possible to design agendas based on binary procedures which will arrive at virtually any point in the alternative space, even Pareto dominated points.]

[This paper investigates the behavior of the winning bid in a sealed bid tender auction where each bidder has private information. With an appropriate concept of value, the winning bid will converge in probability to the value of the object auction (as the number of bidders grow large) if and only if a certain information condition is satisfied. In particular, it is not necessary for any bidder to know the value at the time the bids are submitted. These results bear on the relationship between price and value and on the aggregation of private information by the auction mechanism.]