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NotesECN741-page62

# NotesECN741-page62 - the truth about his ability in the...

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ECN 741: Public Economics Fall 2008 Let’s assume we have such a tax system. Then the consumer FOCs are 1 c 1 = R (1 - τ k ) . 5 c 2 h + . 5 c 2 l w c 1 = y 1 w c 2 h = y 2 h Also note that c 2 h = R (1 - τ k ) k 2 + wy 2 h + T 2 h c 2 l = R (1 - τ k ) k 2 + T 2 l Question: How do we pick taxes to implement efficient allocations ( c * 1 , c * 2 h , c * 2 l , y * 1 , y * 2 h , K * 2 ) in the equilibrium? Why don’t we try the simplest way to do this. And choose the following taxes 1 - τ k = [0 . 5 c * 2 h + 0 . 5 c * 2 l ] - 1 h 0 . 5 c * 2 h + 0 . 5 c * 2 l i and T 2 h = c * 2 h - R (1 - τ k ) K * 2 - wy * 2 h T 2 l = c * 2 l - R (1 - τ k ) K * 2 This way the equilibrium allocations satisfy all of the optimality conditions listed above. They are also feasible and hence should implement the efficient allocations. What is missing? The taxes above guarantee that the individual saves the correct amount “if” he plans to tell
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Unformatted text preview: the truth about his ability in the second period. Also, they guarantee that the individual tells the truth “if” he saves the correct amount. Question: What if the individual saves more than K * 2 and plan to lie about their ability if they happen to be the able type? We ﬁrst show that this double deviation is feasible and improves individuals welfare. Consider three diﬀerent plan by the agent 62...
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