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eco200_labor&intertemporalchoice_fall2009

eco200_labor&intertemporalchoice_fall2009 - ECO 200...

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ECO 200: Microeconomic Theory Lecture notes on labor-leisure choice and intertemporal consumption 1 Fall 2009 Carlos J. Serrano 1 Lecture notes updated on Oct. 12 at 11.40am 1
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Summary Choice of labor and leisure E ff ects of a change in the wage rate E ff ects of a change in the income tax rate Intertemporal consumption E ff ects of an increase in future consumption taxes E ff ects of RRSP accounts in future consumption 2
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1 The choice of labor and leisure 2 The decision of how many hours to work is an important choice made by individuals. It has implications in design of the optimal taxation of income; and more broadly in the level of GDP in the economy. We model the choice by assuming that consumers enjoy leisure L as well as the consump- tion of goods. Instead of listing the goods individually, we simplify the model considering that the utility function is a function of income and leisure (   ) Income is produced by working (24 ) hours at wage per hour. Furthermore, non- wage income 0 occurs independently of any choice made by the individual. Non-wage income can be negative as in contractual debt obligations. The buget constraint of the individual is = (24 ) + 0 The maximization problem of the individual is max  { (   ) }  = (24 ) + 0 The consumer maximizes utility at some point, where the indi ff erence curves are tangent to the budget line. The slope of the budget line is . To solve the maximization problem. The lagrangian is L = (   ) ( (24 ) 0 ) The fi rst order conditions are  = 0   = 0 2 Some the contents are based on material form "The structure of economics: a mathematical analysis" by Silberberg and Suen. 3
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where  is the marginal utility of good {   } From the above equations we get that   = 1 or   =  which implies that the marginal value of leisure, in terms of forgone income, is the wage rate. If a person can choose how many hours to work, then the decision not to work an additional hour implies giving up an hour’s income, . Alternatively, we can write the optimality condition as  1 =  1.1 What is the e ff ect on and of an increase in the wage rate ? A unique implication over the direction of and does not exist. When increases, the opportunity cost of leisure increases. This implies that the individual will rise the number of hours work, substituting away from leisure. However, this is just a substitution e ff ect.
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