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a) Assume Jamaal can work up to 60 hours per week at a rate of$10per hour, and that because of a government subsidy, Jamaal has$200in unearned income per week. Draw Jamaal's budget constraint showing how much Leisure (L) and Consumption (Y) he can have. Label both axes with values and titles. Call this Line A. Assume that Jamaal is a leisure lover and at his preferred bundle he works for 10 hours. Label this point A and draw an indifference curve for this bundle labeledU A​ . How much does he earn? (b) Now assume that the cost of child care for Jamaal's daughter is$100per week which he pays only if he works any hours>0. Re-draw his budget constraint on the same graph and label it Line B. What effect will this cost likely have on the amount of labor Jamaal supplies assuming both consumption and leisure are normal goods? Talk about this in terms of income and substitution effects. If Jamaal preferred to work 10 hours in the case of no child care costs, how many hours do you think he will work now? (c) Now assume that Jamaal's employer is willing to pay$3.33of Jamaal's child care expenses for every hour he works, but only if he works 30 hours or more. Now re-draw Jamaal's budget constraint and label it clearly as Line C. Given what you drew for your previous indifference curves, how do you think this will affect Jamaal's consumption of Leisure and Market Goods? Will he work more, less or the same? Explain why.Thanks in advance!Skip questionStart SolvingExitExitQnA

Question

a) Assume Jamaal can work up to 60 hours per week at a rate of10perhour,andthatbecauseofagovernmentsubsidy,Jamaalhas10per hour, and that because of a government subsidy, Jamaal has200in unearned income per week. Draw Jamaal's budget constraint showing how much Leisure (L) and Consumption (Y) he can have. Label both axes with values and titles. Call this Line A. Assume that Jamaal is a leisure lover and at his preferred bundle he works for 10 hours. Label this point A and draw an indifference curve for this bundle labeledU A​ . How much does he earn? (b) Now assume that the cost of child care for Jamaal's daughter is100perweekwhichhepaysonlyifheworksanyhours>0.Re−drawhisbudgetconstraintonthesamegraphandlabelitLineB.WhateffectwillthiscostlikelyhaveontheamountoflaborJamaalsuppliesassumingbothconsumptionandleisurearenormalgoods?Talkaboutthisintermsofincomeandsubstitutioneffects.IfJamaalpreferredtowork10hoursinthecaseofnochildcarecosts,howmanyhoursdoyouthinkhewillworknow?(c)NowassumethatJamaal′semployeriswillingtopay100per week which he pays only if he works any hours>0. Re-draw his budget constraint on the same graph and label it Line B. What effect will this cost likely have on the amount of labor Jamaal supplies assuming both consumption and leisure are normal goods? Talk about this in terms of income and substitution effects. If Jamaal preferred to work 10 hours in the case of no child care costs, how many hours do you think he will work now? (c) Now assume that Jamaal's employer is willing to pay3.33of Jamaal's child care expenses for every hour he works, but only if he works 30 hours or more. Now re-draw Jamaal's budget constraint and label it clearly as Line C. Given what you drew for your previous indifference curves, how do you think this will affect Jamaal's consumption of Leisure and Market Goods? Will he work more, less or the same? Explain why.Thanks in advance!Skip questionStart SolvingExitExitQnA

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Solution

(a) Jamaal can work up to 60 hours per week at a rate of 10perhour.Thismeanshismaximumearningsfromworkwouldbe10 per hour. This means his maximum earnings from work would be 600 (60 hours * 10/hour).Addinghisunearnedincomeof10/hour). Adding his unearned income of 200, his total income would be 800.Thisishisbudgetconstraint.Ifhechoosesnottoworkatall,hewouldhave60hoursofleisureand800. This is his budget constraint. If he chooses not to work at all, he would have 60 hours of leisure and 200 of consumption. If he works all 60 hours, he would have 0 hours of leisure and 800ofconsumption.Thiscreatesadownwardslopinglinefrom(60,200)to(0,800)onagraphwithLeisureonthex−axisandConsumptiononthey−axis.ThisisLineA.IfJamaalchoosestowork10hours,hewouldearn800 of consumption. This creates a downward sloping line from (60, 200) to (0, 800) on a graph with Leisure on the x-axis and Consumption on the y-axis. This is Line A. If Jamaal chooses to work 10 hours, he would earn 100 (10 hours * 10/hour),andwithhisunearnedincome,hewouldhave10/hour), and with his unearned income, he would have 300 for consumption. This point, (50, 300), is point A.

(b) If child care costs 100perweek,thisreducesJamaal′stotalincometo100 per week, this reduces Jamaal's total income to 700 if he works any hours. This shifts his budget constraint down to a line from (60, 200) to (0, 700), which is Line B. This cost would likely reduce the amount of labor Jamaal supplies, as both consumption and leisure are normal goods. The income effect suggests that as income decreases, he will work more to compensate for the loss of income. However, the substitution effect suggests that as the price of leisure decreases (since he effectively gets paid less per hour of work due to the child care cost), he will consume more leisure and work less. The overall effect depends on which effect is stronger. If Jamaal preferred to work 10 hours without child care costs, he might choose to work less now due to the substitution effect.

(c) If Jamaal's employer pays 3.33ofhischildcareexpensesforeveryhourheworksover30hours,thischangeshisbudgetconstraintagain.Forthefirst30hours,hisbudgetconstraintisthesameasinpart(b).Foreveryhourover30,heearns3.33 of his child care expenses for every hour he works over 30 hours, this changes his budget constraint again. For the first 30 hours, his budget constraint is the same as in part (b). For every hour over 30, he earns 10 but also gets 3.33towardschildcare,effectivelyearning3.33 towards child care, effectively earning 13.33 per hour. This creates a kinked budget constraint, with Line C being a line from (60, 200) to (30, 500) to (0, 900). Given his previous indifference curves, this might encourage Jamaal to work more than 30 hours, as the effective wage rate is higher. However, if he strongly prefers leisure, he might still choose to work less than 30 hours.

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