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NotesECN741-page61

# NotesECN741-page61 - y 2 h> c 2 l = R(1-τ k k 2 T 2 l c...

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ECN 741: Public Economics Fall 2008 Individuals have the same endowment of k 1 = K 1 and choose how much to work and how much to save. Government taxes savings at rate τ k . Government makes transfers T 2 h and T 2 l to individual who produce y 2 h and zero output in the second period. Transfers can be negative. Competitive equilibrium is allocations ( c 1 ,y 1 ,c 2 h ,y 2 h ,c 2 l ,k 2 ) and policy ( τ k ,T 2 h ,T 2 l ) such that: 1. Given the policy, allocations solve consumer problem max c 1 ,c 2 h ,c 2 l ,y 1 ,y 2 h ,k 2 log( c 1 ) - y 2 1 2 + 0 . 5 ± log( c 2 h ) - y 2 2 h 2 ² + 0 . 5[log( c 2 l )] sub. to c 1 + k 2 = Rk 1 + wy 1 c 2 h = R (1 - τ k ) k 2 + wy 2 h + T 2 h , if y 2 h > 0 c 2 h = R (1 - τ k ) k 2 + T 2 l , if
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Unformatted text preview: y 2 h > c 2 l = R (1-τ k ) k 2 + T 2 l c 1 ,c 2 h ,c 2 l ,y 1 ,y 2 h ,k 2 ≥ 2. Markets clear c 1 + K 2 = RK 1 + wy 1 . 5 c 2 h + 0 . 5 c 2 l = RK 2 + 0 . 5 wy 2 h k 1 = K 1 k 2 = K 2 Note that the government budget constraint is satisﬁed in equilibrium Rτ k K 2 = 0 . 5 T 2 h + 0 . 5 T 2 l We want the tax system be such that y 2 h > . Then it is necessary that log( c 2 h )-y 2 2 h 2 ≥ log( c 2 l ) 61...
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