By Kenneth J. Arrow
Booklet through Kenneth J. Arrow, Frank H. Hahn
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Additional resources for General Competitive Analysis
In any case, in this volume the distinction between stock and flow equilibrium will become relevant only in the analysis of what, in our d~finition, are disequilibrium situations. " This can be helpful in overcoming some of the conceptual problems raised by continuous time, but it can also be misleading. For instance, Swedish authors at one time found it helpful to define the length of the period by the time interval over which prices could be taken as fixed. Starting with g~ven prices at the beginning of the period, a flow equilibrium over the period, then, would involve stock disequilibrium at the end of the period unless the economy was in full equilibrium.
Let us expand & to include all allocations for 'which the inputs satisfy (3); that is, define so that g = g+ - g- g- ;:::: (4) o. L: x/ ¿x L(x) = j 67 q¡j*, is bounded. 1-. j Obviously, a set of vectors, S, is bounded if and only if U(x) and L(x) are both bounded from above as x varies over S. is closed since it is defined by the continuous function THEOREM 2. 4 hold, then the set of feasible production allocations, &, is compact and convex. Proof. Por any lf E qy = X Y1, let y = f L; (y¡t¡ -y¡¡)= f 2: y1 .
To a very considerable extent, the manufacturing of commodities in continuous-process industries, such as chemicals, is the handling of materials in a sequence of containers. ) Even if the divisibility of commodities is accepted, at least as an approximation, that of divisibility of production activities does not follow as a logical truth. Rather ít is an empirical generalization that, for the great majority of ordinary production processes, a uniform reduction in scale preserves feasibility. The assumption of additivity, on the other hand, can always be defended and indeed made essentially tautologous.