This paper provides a complete set of local duality results for a utility maximizing consumer (or single output cost minimizing firm). Given a continuous local expenditure function defined on a compact, convex set of positive prices we establish the existence of continuous local direct, indirect utility and distance functions. This procedure avoids troublesome continuity problems at the boundary of IR N. In addition it is shown that if two utility functions are second order approximations at some point, then their respective expenditure, distance, and indirect utility functions are also second-order approximations to each other at some point. This latter result provides additional impetus for using duality theory and substantial justification for the use of flexible functional forms which can provide second-order differential approximations to any twice continuously differentiable function at a point

[Defining a choice as a function which picks a subset of every set of alternatives, we consider a list of over thirty conditions (expressed as functional inequalities) which a choice may satisfy, demonstrating &-semilattices formed by certain sublists, thus summarily presenting as "synopses" all the implications obtaining between logical conjunctions formed within these sublists. The list studied includes many well known conditions, such as Plott's [13] path independence, for which we offer over a dozen new characterizations of various types.]

[In an economy with incomplete markets, firms' profits at different dates and contingencies cannot be aggregated into a single index and so profit maximization is not well-defined. In this paper we propose an objective for firms to pursue which is a generalization of the idea of profit maximization. We show that, if firms' managers can transfer current income between shareholders at the first date, and if shareholders have what we call competitive perceptions concerning the effect of a change in production plan on share prices, then each firm will maximize a weighted sum of shareholders' private valuations of the firm's production plan, where the weights are the initial shareholdings. We then define, and prove the existence of, a competitive equilibrium in which firms pursue this proposed objective. Finally, we analyze the optimality properties of the competitive equilibrium

The notion of stability in the sense of Lyapunov is applied to economic dynamic processes of the Champsaur-Dreze-Henry type. Our purpose in this note is to fill a small gap in the literature concerning dynamic processes in economic theory, of the type presented by Champsaur, Dreze, and Henry [3]. Indeed, these authors do not discuss stability in the sense of Lyapunov [7]. However, a recent result of Maschler and Peleg [9] on this kind of stability (presented in a discrete model) can easily be applied to both continuous and discrete processes used in economics. We shall present this result for a very general class of such processes and conclude with references to a few economic applications. For our purpose a (set valued) dynamic system is simply a pair 〈X,φ〉, where X is a compact subset of R and φ a correspondence from X to its nonempty subsets. Let T be a subset of [0,∞) containing 0 and x0 an element of X. Then a φ-process starting at x0 is a pair of functions: x(·) : T → X, ẋ(·) : T → R, such that: x(0) = x0 and, ∀ t ∈ T , ẋ(t) ∈ φ(x(t)). If T = {0, 1, 2, · · · , } and ẋ(t) = x(t + 1) then the process 〈x(·), ẋ)(·)〉 is called discrete. If T = [0,∞), if x(·) is absolutely continuous on any interval [0, τ ] in T , and ẋ(t) = dx(t)/dt for almost every t in T , then the process 〈x(·), ẋ(·)〉 is called continuous. In the first case the Econometrica, 47(3), 733-737, 1979. As pointed out by Negishi [10], this is the same as Samuelson’s stability of the second kind [11]. The term “stability in the sense of Lyapunov” is used by Arrow and Hahn [1]. Heal [5] and Hori [6] also use this concept of stability. See Champsaur, Dreze, and Henry [3, Section 5].