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By Kenneth J. Arrow

Publication through Kenneth J. Arrow, Frank H. Hahn

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Connexity (b), In view of xJi >-h x~ if and only if not x~ >n xk. 4 are fairly stanuard. Parts (a) and (b) state simply that the individual is capable of ranking alternative commodity vectors in order of preference. Part (e) and the term "continuity". attached to it, may be slightly less familiar. 4(c). Suppose, for example, there was no such neighborhood, N 1 • Then in every neighborhood of xli there would exist Xn such that x~ :P:h x", that is, a member of the set {xa 1 x~ :P:" x,¡}. Since (e) asserts that this set is closed, it 1 Analogous to the choice of production vectors in the profitmaximizing firm, there is a choice of preferred consumption vectors by the household.

1 lil . il 111 11 46 47 GENERAL COMPETITIVE ANALYSIS MARKET EQUILIBRIUM : A FIRST A;PPROACH Since p* is determined without reference to demand conditions, it follows also that we now do not need any elaborate assumptions to ensure that all demand functions are continuous over SN. Indeed, the theory of household behavior can be left in a most rudimentary state. All we need is H and W, the most innocuous of the assumptions. Por all these reasons, the L-economy has proved attractive to many economists.

The individuals are assumed to make their labor and consumption choices simültaneously for the future as well as for the present. Then there is a time constraint for each period. For subsequent purposes this' detailed description of the consumption possibility set will be used only as informal justification for certain axioms. The set has been characterized as the set of nonnegative vectors that, in addition, satisfy certain inequalities. , which satisfy these inequalities, 1s convex. 77 where dlt 1 :::: O, 2 dltf = l.

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