On the Existence And Representation of Equilibrium in An Economy With Growth And

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On the Existence And Representation of Equilibrium in An Economy With Growth And
Rajnish Mehra
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This facilitates the development of a framework for testing a class of consumption-based pricing models, with a view to evaluating their predictions against the yardstick of actual ouservation. We pursue the empirical implications of our model in Mehra and Prescott (1985).
APPENDIX We first establish that the expected utility of the element c* e C with the c*ie^) = y^ exists. Let v (y, i) be the expected utility for the first t + 1 periods of the plan if yo = y and xq ^ K. . It satisfies the re
...cursion v^"« - 1 (AD Vl^y'^^ = I'd "■ P ^ ^i V (X y, j) .
J ■' ^ for t = 0, 1, ... . The initializing function is (1-ff), (A2) vo(y, i) = ^ I . 1 By definition, the expected utility of c* is the limit of v (y, i) as t goes to infinity.
It IS easily verified by mathematical induction that (A3) vJy. O = ^^-^-^ y^ - (^, l)\^ . ^) by noting it is true for t = and using (Al) to conclude that if it is true for t then it is true for t + 1. The substitution of (A3) into A(l) yields (A4) Y, i = 1 *P^^j ^f""^ Yj, for I = 1, ....


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