Econ 387L: Macro II Spring 2006, University of Texas Instructor: Dean Corbae Problem Set #6- Due 2/28/06 1. Consider an economy with a representative household that chooses per capita consumption and per capita future capital holdings each period to maximize lifetime utility given by: U = ∞ X t =0 β t c 1 − σ t 1 − σ for β ∈ (0 , 1) , σ>0 . The production function in this economy is: y t = Ak t where the parameter A>0 can be thought of as including depreciation of physical capital and k0 is given. This technology gives this class of growth models its name “AK”. (a) Write down the social planner’s problem. (b) Derive the Euler equation describing the optimal allocation of capital. (c) To justify the constant returns assumption, we typically interpret the capital stock as a broad measure that includes not only physical capital, but also human capital and intangible capital. Does an economy like this continue to invest and grow for ever? What conditions on parameters do we need to make this a bounded problem? (Hint: consider separately the case
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