hw5 - Homework 5 ECON 4721H: Money and Banking, Fall 2011...

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Unformatted text preview: Homework 5 ECON 4721H: Money and Banking, Fall 2011 Due Wednesday, November 23, at the beginning of class Problem 1: Bank Runs Consider an economy in which consumers live for three periods (called period 1 , 2 , and 3 ). Each consumer has an endowment of 20 goods when young, and nothing when middle-aged and when old. Assume that consumers eat the half of their endowment in the rst period, and save the other half. Utility from consumption depends on what "type" a consumer is, as follows: u ( c 1 ,c 2 ,c 3 ) = log [ c 2 ] for type 1 impatient log [ c 2 + c 3 ] for type 2 patient There are 200 consumers, and half will become each type. However, consumers only learn their type in period 2 . Assume no one else can observe the types (an agent knows her type only). There are two assets available in the economy, money and capital, o ering the following rates of return: One-Period Return Two-Periods Return Fiat Money 1 1 Capital . 9 1 . 5 1) Suppose a consumer, on her own, saves half her goods in each asset in period 1 . After nding out her type, she consumes all the savings in the appropriate period. Calculate the consumption the consumer would receive in either period. 2) Suppose a competitive bank o ers demand deposit contracts to all consumers, specifying interest rates r 1 and r 2 for deposits withdrawn in periods 2 and 3 , respectively. Which assets, and in what amounts, would the bank need to hold in order to o er...
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This note was uploaded on 02/07/2012 for the course ECON 4721H taught by Professor Tanaka during the Fall '11 term at Minnesota.

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hw5 - Homework 5 ECON 4721H: Money and Banking, Fall 2011...

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