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

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Suppose that the consumerís preferences are given by

refer to image for the rest

U (c, 1) = √c+Vi=c¹/2 +1¹/2
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.
cU (c,l)
1
1* - 2
1* - 1
1*
1* +1
1* + 2

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