NotesECN741-page63 - ECN 741 Public Economics Fall 2008...

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ECN 741: Public Economics Fall 2008 PLAN 1: Save K * 2 ( K 1 + wy * 1 - c * 1 ) Produce y * 2 h if θ 2 = 1 and zero if θ 2 = 0 PLAN 2: Save K * 2 ( K 1 + wy * 1 ) Produce zero in the second period Note first that, because incentive compatibility in planner’s problem binds, individual is indifferent between PLAN 1 and PLAN 2. Also, 1 c * 1 < R (1 - τ k ) . 5 c * 2 h + . 5 c * 2 l < R (1 - τ k ) 1 c * 2 l PLAN 3: Save K * 2 + . Consume c * 2 l + R (1 - τ k ) . and produce zero. Define function g ( ) g ( ) = log( c * 1 - ) + log( c * 2 l + R (1 - τ k ) ) - [log( c * 1 ) + log( c * 2 l )] and note that
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