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8105-11Midterm

8105-11Midterm - MACROECONOMIC THEORY ECON 8105 MIDTERM...

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1 MACROECONOMIC THEORY T. J. KEHOE ECON 8105 FALL 2011 MIDTERM EXAMINATION Answer two of the following three questions. 1. Consider an economy with two infinitely lived consumers. There is one good in each period. Consumer i , 1, 2 i , has the utility function 0 log ti t t c . Here , 01  , is the common discount factor. Each of the consumers is endowed with a sequence of goods: 1111 0123 ( , , , ,...) (2,1,2,1,. ..) wwww 2222 01 23 (,,,, ...) (1,4,1,4,. ..) . There is no production or storage. (a) Describe an Arrow-Debreu market structure for this economy, explaining when markets are open, who trades with whom, and so on. Define an Arrow-Debreu equilibrium for this economy. (b) Describe a sequential market structures for this economy, explaining when markets are open, who trades with whom, and so on. Define a sequential markets equilibrium for this economy. (c) Carefully state a proposition or propositions that establish the essential equivalence of the equilibrium concept in part a with that in part b. Be sure to specify the relationships between the objects in the Arrow-Debreu equilibrium and those in the sequential markets equilibrium. (d) Calculate the Arrow-Debreu equilibrium for this economy. (This equilibrium is unique, but you do not have to prove this fact.)

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