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ps7macro2sp06

# ps7macro2sp06 - Econ 387L Macro II Spring 2006 University...

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Econ 387L: Macro II Spring 2006, University of Texas Instructor: Dean Corbae Problem Set #7- Question I Due 3/10/06, II Due 3/21/06 I. Consider the following version of the Lucas asset pricing model. Preferences are given by U ( c t ) = ln( c t ) . Each household is endowed with project that generates dividends y t D R ++ where D is a fi nite set. The dividends follow a markov process with π ( y t +1 | y t ) = prob ( y t +1 = y 0 | y t = y ) . The government spends amount g t = ε t y t per capita where ε t [0 , 1) which does not enter preferences. Government spending follows a markov process φ ( ε t +1 = ε 0 | ε t = ε ) . The only assets traded are shares (or titles) to trees. 1. Assume that all goverment expenditures are fi nanced by a lump sum tax τ t per household which is independent of the shares owned by the household. Calculate the equilibrium share price function. 2. Assume that there is an income tax on dividends. Speci fi cally dividends are taxed at the rate τ t y t so that τ t units of the time t good are collected on dividends. Assume a balanced

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