208-2011-PS5 - Economics 208 Macroeconomics Marek Kapika c...

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Economics 208 Marek Kapiˇ cka Macroeconomics Spring 2011 Problem set 5 1 Bank Runs Consider an economy with three periods t = 0 , 1 , 2. Individuals are endowed with one unit of the consumption good at t = 0. There are two types of assets. An investment in the liquid (“short”) asset yields a rate of return 1 next period. A time zero investment in the illiquid (“long”) assets gives a return F > 1 in t = 2. If the investment in the long asset is interrupted in period t = 1 then the return is f = 1. (Since the long asset yields the same return as the short asset when interrupted, we will assume that in period zero everything is invested in the long asset.) There are two types of agents. With probability λ the agent is an “early” type and cares only about consumption at t = 1. With probability 1 - λ , the agent is “late” and cares about the sum of consumption in both periods t = 2. In the aggregate, λ and 1 - λ also represent fractions of each type of
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