Macro Homework3

# Macro Homework3

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Assignment 3 Economics 202-01 Macroeconomic Theory I Question 1 Suppose we allow for installation costs, the utility function and production function are given by U ( c t ) = ln c t (1) y t = F ( k t ) = Ak α t (2) In addition, the resource constraint and capital accumulation are given by y t = c t + 1 + φ 2 i t k t i t and (3) 4 k t +1 = i t - δk t , (4) where φ 0. (a) Write the First Order Conditions for consumption, capital, investment, and Lagrange multipliers for the optimal solution. (b) Derive the equation for Tobin’s q. (c) Using (a) and (b), derive the Euler equation in terms of Tobin’s q, capital, and con- sumption. (c) Determine the steady state levels for Tobin’s q, capital, investment, and consumption. (d) Determine the effects of a permanent productivity increase (i.e. 4 A > 0). Question 2

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