U (c,1)=√c+Vi=c²¹/²+ where c is the level of consumption and I is leisure. The consumer has to allocate 5000 hours between leisure and labour (i.e. h = 5000). The real wage rate (w) is 20 per hour and the real nonwage income (™) is 800. (a) Set up the Lagragian and compute the optimal level of consumption and leisure. (b) Confirm that the allocation found in part (a) is in fact optimal by computing the consumption level and the utility if leisure was l* - 2, l* —− 1, l*, l* + 1, l* + 2. IcU (c,l) 1-2 1-1 [" 1+1 1* +2

U (c,1)=√c+Vi=c²¹/²+ where c is the level of consumption and I is leisure. The consumer has to allocate 5000 hours between leisure and labour (i.e. h = 5000). The real wage rate (w) is 20 per hour and the real nonwage income (™) is 800. (a) Set up the Lagragian and compute the optimal level of consumption and leisure. (b) Confirm that the allocation found in part (a) is in fact optimal by computing the consumption level and the utility if leisure was l* - 2, l* —− 1, l, l + 1, l* + 2. IcU (c,l) 1-2 1-1 [" 1+1 1* +2

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter7: Production, Inputs, And Cost: Building Blocks For Supply Analysis

Section: Chapter Questions

Problem 9TY

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