MIT14_02F09_lec23

# MIT14_02F09_lec23 - 14.02 Bank Runs Fall 2009 1 Bank runs...

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14.02 Bank Runs Fall 2009

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1 Bank runs Diamond and Dybvig (1983) Three periods T = 0 ; 1 ; 2 Continuum of agents Preferences u ( c 1 + 2 ) where idiosyncratic shock = ( 0 with probability ± 1 with probability 1 ± ± (&late consumer±)
Agents have an endowment normalized to 1 At time 0 , each agent invests without knowing his shock No aggregate uncertainty: exactly ± fraction of agents will have = 0 Technology: if an agent invests 1 at time 0 , he can get: 1. x if he chooses to liquidate a fraction x at time 1 2. R (1 ± x ) ² (1 ± x ) if he liquidates 1 ± x at time 2

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Autarky: single agent will choose how much to consume in two periods max x;c 1 ;c 2 E [ u ( c 1 ( ) + 2 ( ))] c 1 ( ) ± x c 2 ( ) ± R (1 ² x ) optimal to choose c 1 (1) = 0 ;c 2 (1) = R c 1 (0) = 1 ;c 2 (0) = 0
Banks: risk sharing arrangement max E [ u ( c 1 ( ) + 2 ( ))] E [ c 1 ( )] ± x E [ c 2 ( )] ± R (1 ² x ) optimal c 1 (1) = 0 ;c 2 (0) = 0 and u 0 ( c 1 (0)) = Ru 0 ( c 2 (1))

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Assumptions Assumption 1: high coe¢ cient of relative risk aversion R > 1
use C 1 for c 1 (0) and C 2 for c 2 (1) resource constraint at time 2 imposes (1 ± 1 ) R = (1 ± ) C

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MIT14_02F09_lec23 - 14.02 Bank Runs Fall 2009 1 Bank runs...

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