Hello! I just wanted someone to look over my answers for these labor economics questions, and possibly help with the questions that do not have answers/are starred. Thank you!
2. Many states offer child-care grants for low-income single mothers (e.g. New York), as opposed to (or in addition to) standard cash grants. The primary purpose of this type of policy is to invoke single mothers, who likely need to be compensated with a high wage to offset childcare costs, into the labor force. First, consider the daily labor supply decision of Sarah, who has preferences dictated by U(C, L) = 202/311/3, who faces a wage rate of w = $8 and earns non-labor income of V = $200. (a) Sarah's marginal rate of substitution is given by MRSL,C = C/2L. Compute her reserva- [2 pts] tion wage. Will she work at the market wage rate? MRS : 2. 3 . C2/8.)-2/3 C= 200 MRS : C L: 20 2 . z . c / 3 . L'/ 3 2 L Reservation was is $4.16 and Sarah's MRS - 200 = 4. 16 wage rate is $8 so yes she will 2 x 20 work at market waal because it is higher than the reservation wage . Page 3(b) What is Sarah's optimal bundle of leisure hours and consumption dollars? [4 pts] (1 200 4 7 ( 2n - L) c= Ww (an-L) W= MRS 8 : 260 1 8 (an=) 146 200+192 - 86 auL . 892 LEW. 53 hows C 200 + 7 (24 -10.33) c= $241.36 200 1 61. 36 Now, consider Sarah's twin sister Tara, who has a child. Like Sarah, Tara has non-labor income of V-$200, a wage rate of w = $8, and preferences represented by U(C, L) = 209/31,1/3 However, Tara faces a "fixed cost" to participating in the labor force. If she does not participate (choosing h = 0), she does not have to pay for childcare. If she chooses to participate and work A > 0 hours, she must pay Po =$100 each day for childcare. (c) What is her non-labor income if she does not participate in the labor force? What is her [2 pta] effective non-labor income if she does participate in the work force and has to pay for child care? If Tara dats not participate her non-labor incent will be $200. and if she does decide to participate then she will have to pay 3100 childean so ker non -laber inset will be 1 200 - $160 . $160. (d) On the graph below, plot Tara's budget constraint, and label it B". (Hint: Think carefully [2 pta] about how much consumption income she has, less her childcare costs, at 0 labor hours, 1 labor hour, 0.01 labor hours, etc.). AsNon- participant B. Participant PAY W/ SUBSIDY IC. IC, Figure & Tara's' Budget get De is consumption w/ childcare, B. is consumption w/a childcare (e) Using indifference curves (you don't need to use her preferences, just general, convex in- [2 pts] difference curves), illustrate why Tara would likely prefer to stay out of the work force, as opposed to entering the work force and incurring the childcare costs.(f) Now, suppose the government offers a $100 childcare payment to Tara which she receives [2 pts] if, and only if, she works A > 0 hours. Plot her new budget constraint, and label this constraint B'. Briefly explain how this effectively gives her the same labor force incentives as Sarah; in other words, explain why this would lead her to return to the labor force
