Homework1-2 - EC 302 Intermediate Macroeconomics Antonio...

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EC 302 – Intermediate Macroeconomics Antonio Doblas-Madrid, Ph.D. - Page 1 of 2 - HOMEWORK 1 D UE ON W EDNESDAY , F EBRUARY 10 TH 2016, AT 4:20 PM P LEASE UPLOAD YOUR ANSWERS TO THE D2L DROP BOX . Problem 1 — The Solow Growth Model (50 points) Consider a closed economy with the following production function 1 , t t t Y AK N where , t t Y K and t N denote, respectively, GDP (a.k.a. output, or income), capital, and labor at time . t Suppose that, for all periods 0,1, t labor is constant at 40 and that the total factor productivity (TFP) parameter A is constant and equal to 5 and 0.4. The economy starts with a capital stock equal to 40, i.e., 0 40. K Since this is a closed economy, net exports are zero. Furthermore, we assume that government purchases are also zero. Thus, GDP is split between consumption t C and investment . t I Assume that, every period, consumption is (1 ) 0.75 s 75% of GDP, and the remaining 0.25 s 25% is devoted to investment. Capital depreciates at the rate of 0.04 4% . For our purposes, what this means is that after each period, 4% of the capital stock disappears. (This represents the fact that some machines break, others
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