exam2006 - Final exam, AREP 263 Fall 2006 You have three...

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Final exam, AREP 263 Fall 2006 You have three hours to work on this exam — closed book, closed notes. Please return the exam to me or to my mailbox in 207 Giannini by 5 PM on Friday. Answer all questions. You cannot avoid using mathematics to answer these questions. However, DO NOT GET BOGGED DOWN IN ALGEBRA. It is su cient to provide a clear statement of the algebraic manipulations that you would perform, and the nature of the result that you would obtain. I hope that there are no typos or ambiguities in the following questions. If you f nd a problem of this sort, just be sure to let me know what assumptions you have made. Question 1. Consider the following two-sector model, with total stock of labor = 1. The amount of labor in the manufacturing sector at time t is equal to L ( t ) . The value of output in the manufacturing sector is Lf ( L ) with f 0 ( L ) > 0 The increasing returns to scale in the sector are external to the f rm, so each worker receives the wage w = f ( L ) . The value of output in the agricultural sector is (1 L ) a ; the agricultural wage is the constant a .A s s um e t h a t f (0) <a<f (1) .T h e F ow of labor into the manufacturing
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exam2006 - Final exam, AREP 263 Fall 2006 You have three...

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