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Homework 2 solution

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University of Minnesota Department of Economics Econ 4331w: Economic Development Homework Assignment 2 - Answer Key Exercise 1 a) (5 points) Describe the …nal goods producing sector in the Romer model. Is there perfect or imperfect competition? Write down the problem of the …rm in this sector and derive the …rst order conditions for optimality. Answer: This sector produces the …nal good using intermediate goods and sells that good to consumers. There RA are a large number of perfectly competitive …rms using the CRS production function Y = L1 xj dj. The Y 0 …rm’ problem is s Z A Z A 1 pj xj , max LY xj dj wLY LY ;xj 0 0 and the …rst order conditions are [LY ] [xj ] : (1 : ) LY L1 Y A xj dj …show more content…

1 X 1+n t 1 1+r = PA = = 1+n (1 + r) t=0 1 + r 1 + r 1 1+r 1+r r n and …nally, we get PA = r n : Exercise 4 There are three approaches to calculation GDP: the expenditure approach, the income approach and the product approach. All three approaches give the same result. In particular, if you add the income of all agents in the economy (the income approach) it should equal the value of the …nal goods produced in the economy (the product approach). This exercise will help you show that this is the case in the Solow model and in the Romer model. a) (2.5 points) Write down the problem of the …rm in the Solow model and obtain the …rst order conditions for optimality. Answer: In the Solow model the problem of the …rm is 1 max K (AL) wL K;L rK, and the …rst order conditions are [K] : K [L] : (1 1 1 (AL) ) K A1 L r = 0, w = 0. b) (5 points) Using the results from part a, obtain the interest rate, r, as a function of Y =K and the wage, w, as a function of Y =L. 1 Answer: This is just simple algebra using the fact that Y = K (AL) : 1 r = w = K (AL) Y )r= . K K 1 K (AL) (1 ) ) w = (1 L 4 ) Y . L c) (2.5 points) Add the capital income, rK, to the labor income, wL, and show that it is equal to the value of the …nal

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