Department of Economics Microeconomic TheoryUniversity of California, Berkeley Economics 101AFebruary 7, 2007 Spring 2007Economics 101A: Microeconomic TheorySection Notes for Week 41 Labor Supply Example: Earned Income Tax CreditThe Earned Income Tax Credit (EITC) is a governmental subsidy program designed toincrease the income of low income households. The program works approximately as follows:- If you earn between $0 and $7,500 per year, then you receive a subsidy equal to 34% ofyour earnings.- If you earn between $7,500 and $13,500 you receive a subsidy of 34% of $7,500 (whichis equal to $2,550).- If you earn between $13,500 and $28,955 you the subsidy is taxed away at a rate of16.5%.- If you earn above $28,955 the EITC does not affect you.Assume the price of goods, px= 1. Let’s examine the budget constraint of a worker whoearns a wage of w dollars per hour and has no non-labor income (y = 0).Draw the graph.How will the EITC program affect the labor supply decision of a worker? The answer dependsupon how much income they would have earned at their optimum number of hours had thesubsidy not been present. The effects can be broken down as follows:- Those who would have earned between $0 and $7,500 (the phase-in region for thesubsidy) will face a higher marginal wage rate (w + $0.34) implying that they face ahigher price of leisure (substitution effect will cause them to work more) and also thatthey will earn more (income effect will cause them to work less). Thus, the net effectdepends upon the relative sizes of the two effects.- Those who would have earned b etween $7,500 and $13,500 receive a lump sum of $2,550,thus their marginal wage will still be w. The income effect will cause these workers towork less.- Workers who would have earned between $13,500 and $28,955 (the phase-out region)face a marginal tax rate of w − $0.165 implying that their implicit price of leisure hasgone down (the substitution effect will cause them to work less) however their incomehas gone up (so the income effect will also cause them to work less).- Finally depending upon the curvature of the worker’s indifference curves some workerswho would have earned above $28,955 may decide to reduce their hours in order toopt-in to the subsidy program.12 Consumption Savings DecisionsSuppose a consumer has preferences of consumption of goods today, C1and consumption ofgoods next period, C2that can be expressed by the utility function U (C1, C2) =√C1+β√C2where 0 < β < 1 reflects the degree to which the consumer prefers consumption today relativeto consumption of goods next period. Then the consumer’s utility maximization problem(UMP) can be expressed asmaxC1,C2pC1+ βpC2s.t. p1C1+p2C21 + R= Y1+Y21 + Rwhere p1, p2are the price of consumption goods in periods 1 and 2, Y1, Y2are income inperiods 1 and 2, and R is the net interest rate for borrowing or saving between periods 1and 2.For simplicity, we will assume that p1= p2= 1.Solve the UMP. The LaGrangian isL(C1, C2, λ) =pC1+ βpC2− λC1+C21 + R− Y1−Y21 + Rthus the FOC’s are∂L∂C1=12C−121− λ = 0∂L∂C2=12βC−122−λ1 + R= 0∂L∂λ= C1+C21 + R− Y1−Y21 + RThus the tangency condition is1 + R =C−121βC−122=1β·rC2C1solving for C2we getC2= β2(1 + R)2C1and plugging into the budget constraintC1[1 + β2(1 + R)] = Y1+Y21 + RFinally, we arrive at the ordinary demand function for consumption in period 1.C1(R, Y1, Y2) =Y1+Y21+R1 + β2(1 + R)C2(R, Y1, Y2) = (β2(1 + R)2) ·Y1+Y21+R1 + β2(1 + R)2If we would like to analyze the savings behavior of savers we can set Y2= 0 foricing theconsumer to save some of their income from period one. Then savings areY1− C1= Y1−Y11 + β2(1 + R)= Y1·β2(1 + R)1 + β2(1 + R)similarly if we would like to analyze the borrowing behavior of borrowers we can set Y1= 0forcing the consumer to borrow if they want to consume anything in period 1. Then savings(the negative of borrowings) are−C1= −Y21+R1 + β2(1 + R)= −Y2·11 + R + β2(1 +
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