handoutgcp - Simple Statement of Government Commitment...

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Simple Statement of Government Commitment Problems Draws on Stokey (1989, AER, p. 134-9). 1 Environment Continuum (unit measure) of identical households and one “big” govern- ment Each household (hh) chooses x X . Government (govt.) chooses y Y to maximize household utility. If X is chosen by all hh, y is feasible for the govt if ( X,y ) Z Y Hh preferences represented by w ( x, X, y ) which is the utility of a hh if it chooses x , all other hhs choose X , and the govt chooses y. 2 Static First best ( X f ,y f ) = arg max ( X,y ) Z w ( X, X, y ). Characterization by foc: X : w 1 + w 2 =0 (1) y : w 3 3 Static Ramsey Equilibrium (RE) Timing: govt chooses y Y before hhs choose x X . Work backwards: Given y ,hhch oo s e s x (which yields a decision rule η ( y )). Consistency and optimality requires: η ( y ) = arg max x X w ( x, η ( y ) )( 2 ) Given η ( y ) , govt chooses y : y r =a r gm a x y Y w ( η ( y ) ( y ) 3 ) s.t. ( η ( y ) ) Z In general X f 6 = X r η ( y ), so Ramsey outcomes are not necessarily f rst best since x : w 1 (4) y :( w 1 + w 2 ) η 0 ( y )+ w 3 . 1
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4 Static No Commitment Equilibrium (NCE) Timing: hh chooses x X before govt chooses y Y . Work backwards: Given X n ,govtchooses y . ϕ ( X n ) = arg max y Y w ( X n ,X n ,y )( 5 ) s.t. ( X n ) Z Since each hh is small, it realizes that its impact on the govt is in f nites- imal. It expects that if all other hhs choose X n , the govt will choose ϕ ( X n ) . Consistency and optimality requires X n =argmax x X w ( x, X n ( X n )) (6) In general X r 6 = X n since in the RE, the government takes into account its in F uence on hh, while in the NCE it does not: x : w 1 =0 (7) y : w 3 .
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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.

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handoutgcp - Simple Statement of Government Commitment...

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