ps8macro2sp06 - Econ 387L: Macro II Spring 2006, University...

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Econ 387L: Macro II Spring 2006, University of Texas Instructor: Dean Corbae Problem Set #8- Due 3/28/06 I. This question explores the equivalence between time 0 Arrow-Debreu forward markets and Arrow’s sequential representation in a nonstochastic exchange economy. There are I households and the horizon is in f nite. Goods are nonstorable and household i has an endowment of goods y i > 0 each period. Household i ’s utility function is given by X t =0 ¡ β i ¢ t u i ( c i t ) where u i is strictly increasing and concave, continuously differentiable. 1. Write household i ’s budget constraint in a forward markets economy where p t is the forward price of the consumption good delivered at time t set at time 0 . 2. Write household i ’s budget constraint in a sequential markets economy where q t is the spot price of the consumption good in period t, a i t +1 are loans (if positive) or borrowings (if negative) by household i between time t and t +1 , and r t is the interest paid at t on assets chosen at t 1 . Assume that a 0 =0 . 3. Show under what conditions the two constraints equivalent. Would a borrowing constraint be suf f cient to generate the equivalence? 4. De f ne a competitive forward market equilibrium. 5. Can the value of a household’s income be in f nite in a competitive forward market equilibrium? What implications does this have for the value of the aggregate endowment? How is this used in the proof of the f rst welfare theorem for this economy (i.e., that a competitive forward market equilibrium is Pareto optimal)? 6. What are the conditions which characterize a forward market equilibrium? Count
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ps8macro2sp06 - Econ 387L: Macro II Spring 2006, University...

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