[The Arrow-Debreu model is extended to include a sequential market model with financial markets. This is done by dropping the contingent contracts from the Arrow-Debreu model, leaving only a sequence of spot markets for commodities. The resulting market structure is inefficient. Efficiency is restored with a sequence of stock markets and option markets. In addition, consumers are shown to be unanimous in wanting each firm to maximize the price of its common stock.]

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].

[This paper studies the effects of irreversibility of capital investment upon optimal exploitation policies for renewable resource stocks. It is demonstrated that although the long-term optimal sustained yield is not affected by the assumption of irreversibility (except in extreme cases), the short-term dynamic behavior of an optimal policy may depend significantly upon the assumption. It is suggested that the results may have profound implications for problems of rehabilitation of overexploited fisheries and other renewable resource stocks.]