On Asset Prices in Exchange And Production Economies
On Asset Prices in Exchange And Production Economies
Rajnish Mehra
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Intuitively, the equilibrium stochastic process generated by any production economy can also be generated by an exchange economy that is endowed with the same stochastic process. A direct empirical implication is that if a model is rejected in an exchange paradigm, introducing production and the concomitant restrictions will not change the result. We formalize this below. Let 6 denote preferences, r technologies, E the set of exogenous processes on the aggregate consumption good, P the set of t...echnologies with production opportunities, and m(C, r) the set of equilibria for economy (e. R) . Theorem U„m(^, f) 3 Um(e, r) ret -^ r I? Proof. For 6^ t 6 and r^ « P let (8^, 0^) be a Joint equilibrium process on asset prices and consumption. A necessary condition for equilibrium is that the asset prices a^, be consistent with Cq, the optimal consumption for the household with preferences Sq. Thus, if (aQ, CQ) is an equilibrium then where g is defined by the first-order necessary conditions for household maximization.
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