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hw03 - Homework 3 Econ 4721-002 Money and Banking Fall 2011...

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Homework 3 Econ 4721-002: Money and Banking, Fall 2011 Due Tuesday, November 22, beginning of class Problem 1: Risks Consider an individual consumer who lives for two periods, endowed with y = 40 goods when young and nothing when old. The consumer wants to save half of the endowment (thus, 20 goods). Saving can be done in either a safe asset (asset a ) or a risky asset (asset b ). The real rate of return on asset b is uncertain, and depends upon which event occurs in the second period, as summarized in the following table: Event H Event L probability of occuring π H = 0 . 5 π L = 0 . 5 return on asset a r H = 1 . 25 r L = 1 . 25 return on asset b r H = 2 r L = 0 . 5 The consumer cares about expected utility from consumption, defined as ln ( c 1 ) + β [ π H ln ( c 2 ,H ) + π L ln ( c 2 ,L )] where β = 0 . 5 and c 2 ,H and c 2 ,L are consumption in Event H and consumption in Event L , respec- tively. (a) Investment plan 1: Invest all 20 goods in asset a . Calculate the expected rate of return on this investment plan and the expected utility for the consumer using the formula above.
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