pr11ec70204 - following laws of motion k s,t 1 =(1-δ s k...

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Problem Set 11 Econ 702, Spring 2004 April 15, 2004 Problem 1 (Romer Endogenous Growth) Define the decentralized problem in Romer’s endogenous growth model that we went over in class. Get a formula for the balanced growth path in equilibrium and compare to the social planner’s problem (Look at Problem 5 in Homework 10 for the social planner’s problem). Problem 2 (Capital-Skill Complementarity) Consider an economy with two sectors: one producing consumption goods and capital structures and the other producing capital equipment. Output of these two sectors is given by: c t + x st = A t G ( k c st , k c et , u c t , s c t ) (1) x et = q t A t G ( k e st , k e et , u e t , s e t ) (2) where c t is consumption, x st is investment in structures and x et is output of the equipment sector. The superscripts of the input variables denote the sector where they are used (c for consumption and e for equipment). k st and k et are the stocks of capital structures and equipment.
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Unformatted text preview: following laws of motion, k s,t +1 = (1-δ s ) k st + x st (3) k e,t +1 = (1-δ e ) k et + x et (4) The labor inputs are unskilled labor u t and skilled labor s t . The function G is common to both sectors and is given by, G ( k st ,k et ,u t ,s t ) = k α st h μu σ t + (1-μ )( λk ρ et + (1-λ ) s ρ t ) σ ρ i 1-α σ (5) Total output, in consumption units, is defined by, y t = c t + x st + x et q t = A t G ( k st ,k et ,u t ,s t ) (6) Note that this aggregation of output is possible when G is homogenous of degree 1 and common to both sectors. 1 1. Compute the share of skilled and unskilled labor. 2. What does it mean to have σ < 1 or σ > 1 ? 3. What does it mean to have ρ < 1 or ρ > 1 ? 4. Derive the expressions for the prices of factors of production. 2...
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