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# taxexample - E CON 714 M ACROECONOMIC T HEORY II TA T IM L...

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E CON 714: M ACROECONOMIC T HEORY II TA: T IM L EE A PRIL 9, 2010 Tax Announcements (by Rody Manuelli) Consider a simple two planner economy. The first planner picks taxes (denoted by the flat tax rate τ ) and makes transfers to the representative agent (denoted v ). The second planner takes the tax rates and transfers as given . That is, even though YOU know the connection between tax rates and transfers, the second planner does not, she takes the sequence of tax rates and transfers as given and beyond her control. The problem she faces is max { c t , x t , k t + 1 } t = 0 t = 0 β t u ( c t ) subject to c t + x t ( 1 - τ t ) f ( k t ) + ν t , k t + 1 ( 1 - δ ) k t + x t , k 0 0 given, ( c t , x t , k t + 1 ) ( 0, 0, 0 ) t 0. Assume the functions u and f are nice and smooth. 1. Assume that 0 < τ t = τ < 1 (constant tax rates), and that v t = τ f ( k t ) (remember that we know this, but the second planner takes v t as given at the time she maxi- mizes). Show that there exists a steady state, and that for any initial condition k 0 > 0 the economy converges to the steady state.

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taxexample - E CON 714 M ACROECONOMIC T HEORY II TA T IM L...

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