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Unformatted text preview: Economics 208 Marek Kapiˇ cka Macroeconomics Spring 2011 Problem Set 2 Solution 1 The Effects of Government Spending Consider a model in which people’s preferences are given by ∞ X t =0 β t ln C t (1) where C t is consumption in period t and β ∈ (0 , 1) is the discount factor. The consumption good is produced using the production function Y p t = K α t , where α ∈ (0 , 1) and K t is the capital stock at the beginning of period t . It is assumed that the capital stock fully depreciates between period. Thus, if I t is investment in period t then K t +1 = I t . The initial capital stock K is given. There is a government that spends resources G t every period to produce additional output Y g t = φG t where φ ∈ [0 , 1) measures the efficiency of the government sector. It is assumed that the government spends a fraction g t ∈ [0 , 1) of private output, i.e. G t = g t Y p t . Hence, the resource constraint can be written as C t + K t +1 = K α t [1- g t (1- φ )] (2) 1. Derive the first order conditions for the Pareto problem that maximizes (1)1....
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This note was uploaded on 12/26/2011 for the course ECON 208 taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08