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Econ 4721 HW 1

Econ 4721 HW 1 - Econ 4721 Money and Banking Fall 2009...

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Econ 4721: Money and Banking, Fall 2009 Homework 1 Answer Key Problem 1 (a) A feasible consumption allocation for this economy is two sequences, { c 1 ,t } and { c 2 ,t } for t = 1 , 2 , . . . satisfying: N t c 1 ,t + N t - 1 c 2 ,t N t y 1 + N t - 1 y 2 Other acceptable conditions for feasibility, using the assumptions for this problem, Nc 1 ,t + Nc 2 ,t Ny 1 c 1 ,t + c 2 ,t y 1 Nc 1 ,t + Nc 2 ,t N * 30 c 1 ,t + c 2 ,t 30 (b) A Pareto efficient stationary allocation: 1. Is a stationary feasible allocation - two numbers ( c 1 , c 2 ) satisfying c 1 + c 2 y 1 2. Has the property that no individual can be made better off without harming another individual. Or, solves the problem of maximizing the utility of each member of future generations subject to the feasibility constraint max c 1 ,c 2 ln ( c 1 ) + β ln ( c 2 ) subject to: c 1 + c 2 y 1 1

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(c) The Pareto efficient stationary allocation is found by solving the maximization problem, max c 1 ,c 2 ln ( c 1 ) + β ln ( c 2 ) subject to: c 1 + c 2 y 1 The first order condition for this problem is: 1 c 1 β c 2 = 1 So, c 2 = βc 1 c 2 = y 1 - c 1 βc 1 = y 1 - c 1 c 1 = y 1 1 + β = 30 1 . 5 = 20 c 2 = βy 1 1 + β = 0 . 5 * 30 1 . 5 = 30 3 = 10 (d) A competitive equilibrium without money must involve no trade. Consumers are not willing to exchange because the young cannot trade with the old. There is absence of double coincidence of wants. The old consumers want what the young have (consumption now) but the old don’t have what the young want (consumption tomorrow), because the old will not be alive tomorrow.
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Econ 4721 HW 1 - Econ 4721 Money and Banking Fall 2009...

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