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- Tatum is a mother of Anny (1 year old). Tatum derives utility from income Y (i.e. a disposable income that she can spend on consumption goods other than childcare) and leisure L according to the utility function U(Y,L)=Y*L . She has non-labour income of $300 per day. Her time endowment is 16 hours per day that can be spent either on Leisure (which mostly consists of caring for Anny) or labour market work. If Tatum works she has to leave Anny in the child care. Tatum’s wage is $30 per hour, while the childcare cost $5 per hour. Tatum only uses childcare when she works. Compute how many hours Tatum will work under these circumstances. Round your answer to the second decimal point.Suppose your weekly allowance from your parents is $100 and your part-time job pays $10 per hour. The slope of the line plotting the relationship between the hours worked per week (the horizontal axis) and the income per week (the vertical axis) is $. (Enter your response as an integer.) Suppose you start with 10 hours of part-time work and then decide to increase your time working by 3 hour(s). By how much will your weekly income increase? $. (Enter your response as an integer.) Suppose you start with 10 hours of work and then decide you need additional income of $20 per week. How many additional hours would you have to work? hours. (Enter your response as an integer.)(Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor. a) How many consumptions does he choose? How many hours of leisure does he choose? b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect. c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?
- Given the utility function: U = ln c + l + ln c’ + l’ and the budget constraint: w(ℎ−l)+(w′(ℎ−l′))/(1+r)=c+(c′)/(1+r) (see pictures of function and constraint) where c = current consumption, c' = future consumption, l = current leisure, l' = future leisure, and r is the market interest rate.Suppose that the current wage, w = 20 and the future wage w' = 22. a) What is the optimal value of current consumption, c? b) What is the optimal valueof future consumption, c’*?Katie Kwasi's utility function is U(x₁, x₂)=5(In x₁)+x₂. Given her current income and the current relative prices, she consumes 10 units of x₁ and 15 units of x₂. If her income doubles, while prices stay constant, how many units of x₁ will she consume after the change in income? a)10 b)20 c)15 d)5Question 3: Shelly's preferences for consumption and leisure can be expressed as: U(C, L) = (C-200) × (L-80) This utility function implies that Shelly's marginal utility of leisure is C -200 and her marginal utility of consumption is L - 80. There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works. (a): Graph Shelly's budget constraint. (b): What is Shelly's marginal rate of substitution when L = 100 and she is on her budget line? Question 4: The utility function of a worker is represented by U(C, L) = C x L. Suppose this person currently has a weekly income of $600 and choose to enjoy 70 hours of leisure per week. How many ad- ditional dollars of income would it take to entice the worker to work 10 more hours?
- Terry’s utility function over leisure (L) and other goods (Y ) is U(L, Y ) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? Determine the MRS of leisure for labour (b) Draw a leisure-influenced labor curveWhat is the optimal number of work hours for the student whose utility function for other goods (X) and leisure (L) is U (C,L) = CL, and who has $50 of nonlabor income per week and the possibility to work at $5 per hour. Assume that after studying for class & other activities, the student has only 50 hours per week remaining to choose between work and leisure.Terry’s utility function over leisure (L) and other goods (Y) is U (L, Y) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a) What is the number of hours he would like to have for leisure? (b) Determine the MRS of leisure for labour (c) Draw a leisure-influenced labor curve
- Angela has utility over consumption (C) and leisure (L) that is given by U(C,L)= (C0.5)+6(L0.5) where consumption is measured in dollars and leisure is measured in hours. Each week, Angela has 168 hours to devote to either leisure or working. Suppose Angela is offered a job that pays $10 per hour (such that, if she were to work every hour of the week, she would earn $3,024). If Angela has no income besides that which she earns from working, her budget constraint over consumption and leisure is C +18L = 3,024 Solve for the levels of consumption and leisure that maximize Angela's utility subject to her budget constraint. Angela's utility-maximizing consumption is $ 0 168 utility-maximizing number of leisure hours is in the blanks, and please round to the nearest whole numbers if necessary.) Her hours. (Enter only numbersFind the marginal utility of an additional unit of good z for a consumer with utility function u (a, y) = zi yi when their current consumption level is 2 and y = 16.An individual derives utility from consumption spending C and leisurel according to the following utility function: U(C,1)=C"1¹-a where 0>a>1. Leisure time in hours is given by: 1=T-H where T is hours of total time available and H is hours of work. The consumer's real income is given by: C=w (T-1)+N where w is real wage and N is real non-labour income. d) Verify that the second-order conditions for a constrained maximum are met. Reduce your answer (which should only be function a, w, N, and T) to the lowest terms.
