handoutbanking - A Primer on Banking From Diamond, D. and...

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APr imeronBank ing From Diamond, D. and P. Dybvig (1983) “Bank Runs, Deposit Insurance, and Liquidity”, Journal of Political Economy , Vol. 91, p. 401-19. 1 Environment Three periods t =0 , 1 , 2 . Unit measure of ex-ante (i.e. t = 0) identical agents All agents have 1 unit of the good at t = 0 and prefer to consume either at t =1or t =2 . Storage technologies 1. Productive Storage technology: 1 unit of goods invested at t =0y ie lds R> 1 units at t =2 . If the storage is interrupted at t =1 , the salvage value is the initial investment. t =0 t =1 t =2 11 R 2. Pillow Storage technology: 1 unit of goods invested at t = 1 yields 1 unit at t =2 . t =1 t =2 11 Storage in this technology is unobservable. Agents face an iid preference shock ( θ ) which is realized at t =1and determines their type: 1. Early consumers: prob ( θ =1 )= π with preferences u ( c 1 ) . That is, they only want to consume at t =1 . 2. Late consumers prob ( θ =2)=(1 π ) with preferences u ( c 2 ) . That is, they only want to consume at t =2 . Given that these shocks are iid and there is a continuum of agents, π and (1 π ) also denote the population fractions of early and late consumers in the economy. Assume u 0 ( c ) > 0 ,u 0 (0) = , u 0 ( )=0 , and CRRA > 1. Consumption is unobservable. 2 Autarkic Allocation At t =1 , choose W =1i f θ =1and W =0i f θ =2 . This generates c A 1 =1and c
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3 Planner’s problem when type is observable (First Best) max ( c 1 ,c 2 ) R + , ( S,W ) [0 , 1] πu ( c 1 )+(1 π ) u ( c 2 ) s.t.S + πc 1 = W (1 π ) c 2 = R (1 W )+ S where the two constraints are resource feasibility at t =1and t = 2 respectively and the objective function should not be considered expected utility but the sum of utilities for each agent in the economy. Since the short return between
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This note was uploaded on 08/06/2008 for the course ECON 387 taught by Professor Corbae during the Spring '07 term at University of Texas at Austin.

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handoutbanking - A Primer on Banking From Diamond, D. and...

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