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ps10macro2sp08 - Econ 387L Macro II Spring 2008 University...

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Econ 387L: Macro II Spring 2008, University of Texas Instructor: Dean Corbae Problem Set #10- Due 4/17/08 I. Consider an economy populated by a largen number of identical people who live from period 0 through T (where T is possibly in fi nite). In each period a nonstorable consumption good is produced from labor Y t = N t . Part of the output is used for government consumption and the other part for private consumption. The per capita level of government consumption G t is exogenously given and varies over time. The national income identity is C t + G t = N t where C t and N t denote per capita private consumption and labor input. The government raises revenue from a proportional tax on labor income τ t with after-tax income given by (1 τ t ) N t . The government also issues public debt in the form of one period discount bonds with face value of one unit of the consumption good. Let B t denote public debt outstanding (so that B t +1 > 0 is the amount of government borrowing undertaken at time t to fi nance government expenditure above tax revenue). To accomodate
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