4721_HW4 - Copy - Econ 4721: Money and Banking, Fall 2008...

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Unformatted text preview: Econ 4721: Money and Banking, Fall 2008 Homework 4 Due Monday, December 8, 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. 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, offering the following rates of return: One-Period Return Two-Periods Return Fiat Money 1 1 Capital . 9 1 . 5 (a) Suppose a consumer, on her own, saves half her goods in each asset in period 1. After finding out her type, she consumes all the savings in the appropriate period. Calculate the consumption the consumer would receive in either period.consumer would receive in either period....
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