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Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 8

Chapter 8 Equilibrium with Complete Markets 8.1. Time- 0 versus sequential trading This chapter describes competitive equilibria for a pure exchange infinite horizon economy with stochastic endowments. This economy is useful for studying risk sharing, asset pricing, and consumption. | Chapter 8 Equilibrium with Complete Markets 8.1. Time-0 versus sequential trading This chapter describes competitive equilibria for a pure exchange infinite horizon economy with stochastic endowments. This economy is useful for studying risk sharing asset pricing and consumption. We describe two market structures an Arrow-Debreu structure with complete markets in dated contingent claims all traded at time 0 and a sequential-trading structure with complete one-period Arrow securities. These two entail different assets and timings of trades but have identical consumption allocations. Both are referred to as complete market economies. They allow more comprehensive sharing of risks than do the incomplete markets economies to be studied in chapters 16 and 17 or the economies with imperfect enforcement or imperfect information in chapters 19 and 20. 8.2. The physical setting preferences and endowments In each period t 0 there is a realization of a stochastic event st G S. Let the history of events up and until time t be denoted s s0 s _ . s . The unconditional probability of observing a particular sequence of events s is given by a probability measure nt s . We write conditional probabilities as n s sT which is the probability of observing s conditional upon the realization of sT . In this chapter we shall assume that trading occurs after observing s0 which is here captured by setting n0 s0 1 for the initially given value of s0.1 In section 8.9 we shall follow much of the literatures in macroeconomics and econometrics and assume that n s is induced by a Markov process. We 1 Most of our formulas carry over to the case where trading occurs before s0 has been realized just postulate a nondegenerate probability distribution n0 s0 over the initial state. - 203 - 204 Equilibrium with Complete Markets wait to impose that special assumption because some important findings do not require making that assumption. There are I agents named i 1 . I. Agent i owns a stochastic endowment