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By Adler R.

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Extra info for An Intro to Continuity, Extrema & Related Topics for general gaussian process

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N , without observations of initial endowments we can without loss of generality assume that each observation of the income distribution {Itr }Tt=1 is derived from collinear individual endowments. More precisely, for each r and t define Ir αrt = r t r p ·ω and αr = (αr1 , . . , αrT ). Given utility functions {Ut }Tt=1 , the distribution economy Eαr is the economy in which consumer t has preferences represented by the utility function Ut and endowment αrt ω r . Using this observation we can now restate Lemma 2 as follows: given a finite set of observations pr , ω r , {Itr }Tt=1 , r = 1, .

N be a finite set of observations. There exist smooth, strictly quasiconcave, monotone utility functions rationalizing this data and initial endowments {ωtr }Tt=1 such that pr is an equilibrium price vector for the economy E r if and only if there exist numbers Vtr , λrt and vectors qtr for t = 1, . . , T and r = 1, . . , N such that: (a) the dual strict Afriat inequalities hold for each consumer t = 1, . . , T , (b) pr · qtr = −λrt (Itr )2 for t = 1, . . , T and r = 1, . . , N (c) “markets clear”: T xrt = ω r ∀r t=1 where xrt = −(1/λrt )(qtr /Itr ) for each r and t.

To our knowledge, there is no comparable result in the literature for quasilinear rationalizations of consumer demand data. 3 We then extend our analysis to aggregate demand data. That is, given aggregate demands, the distribution of expenditures of consumers and market prices we give necessary and sufficient conditions for the data to be rationalized as the sum of individual demands derived from maximizing quasilinear utility functions subject to a budget constraint. Our analysis differs from Varian’s in that it is the form of the Afriat inequalities for the homothetic and quasilinear case that constitute the core of our analysis.

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An Intro to Continuity, Extrema & Related Topics for general gaussian process by Adler R.

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