True or False. Explain why. Deniz’s preferences for consumption and leisure is as follows: U(C,L)=C2L Deniz has 100 hours in the week available to split between work and leisure. She earns $10 per hour after taxes. She also receives $260 worth of welfare benefits each week. Deniz’s optimal amount of leisure time will be 45 whereas labour supply will be 55.
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True or False. Explain why.
Deniz’s preferences for consumption and leisure is as follows:
U(C,L)=C2L
Deniz has 100 hours in the week available to split between work and leisure. She earns $10 per hour after taxes. She also receives $260 worth of welfare benefits each week. Deniz’s optimal amount of leisure time will be 45 whereas labour supply will be 55.
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- Rebecca's wage is $10 per hour, and she can work up to 60 hours per week. The table and the budget constraint graph show the trade-off that she faces between income and leisure in one week of potential work at this wage. Her manager raises her wage to $15 per hour. Change the graph below to illustrate her new income-leisure budget constraint. The line and the individual endpoints are movable. Assume that nothing else changes. Hours Leisure time Income ($) (hours) worked at $10/hour 0 200 400 600 0 20 40 60 60 40 20 0 Income ($) 1000 900 800 700 600 500 400 300 200 100 0 0 10 20 30 40 50 60 70 80 90 Leisure (hours)Fill in the blanks and round to 2 decimals where needed. Katie has 75 hours per week to allocate to leisure or work. She has a job that pays $30 per hour, she has $150 nonlabour income per week and the price of the (composite) consumption good is p=$1. Her preferences are given by U(C,L) = ½ C L. Katie's reservation wage is $ 30 and she prefers to work 87.5 hours per week. If Katie's nonlabour income rises to $210, she would prefer to work 68 hours per week. If Katie's hourly wage was to rise to $40, she would prefer to work 72 hours per week (with the original Yn=150). Considering the change in hours in response to the wage rise, the effect clearly dominates the effect.The following utility function represents Rose's preference over consumption and leisure u(c, l) = √c + 4√l. Rose receives a real wage of 15 and a non-wage income of 2. As a qualified recipient, Rose gets an additional non-wage income of 5 from the government through a cash transfer program. What is Rose's optimal choice of labor supply?
- Winona has 80 hours to divide between leisure and labor. Her utility function is u(r,c) = f(r) + c, when r represents hours of leisure,c represents dollars of consumption, and f is strictly concave. Winona’s wage is w0= $15/hr. initially, then it rises to w1= $20/hr. (i) Explain what happens to Winona’s labor supply when the wage rises,and why. (ii) Explain how the answer to (i) would change if Winona were to win a lottery.(i) Keith’s marginal utility of leisure is C – 20 and his marginal utility of consumption is L – 50. There are 110 hours in the week available to split between work and leisure. Keith receives £250 of welfare payments each week regardless of how much he works (assume he spends all of his welfare payments on consumption). What is Keith’s reservation wage? (ii) Suppose Danny receives the same welfare payments each week as Keith and has the same number of available hours (110). However, Danny’s indifference curve is flatter than Keith’s. How would his reservation wage compare to Keith’s? Why?Akua gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 110 hours. Her utility function is U (C, L) = C × L. Akua receives 660 GHS each week from her great-grandmother—regardless of how much she works. a. What will be Akua’s marginal rate of substitution. b. What will be Akua’s reservation wage? (Explain in detail)
- Refer to the following diagram. Point A is 24 hours, C is 14 hours, D is 8 hours, and E is 6 hours. Income B₂ 0 D -Leisure If the current wage rate results in a budget constraint of AB2, how many hours will the individual work?Jeff, Alan, and Katie all work for the same employer at an hourly wage rate of wo-$24. All three of them have T=100 hours of weekly time endowment and non-labor income of IN=$0. Their preferences over consumption and leisure are as follows: = cl² Jeff: U (c, l) Alan: U(c, l) = min {c, 241} Katie: U(c, l) = c +221 Based on the consumption-leisure model, solve for Jeff, Alan, and Katie's optimal consumption and leisure choices: (c†, lj), (C‚ lå), and (ck, lk), respectively. For each worker, graphically illustrate their optimal consumption and leisure choices by drawing the indifference curve and budget constraint and labeling their respective optimal bundle (use separate graphs for each worker). What are the optimal working hours for each worker?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 line. b. What is Shelly’s marginal rate of substitution when L = 100 and she is on her budget line? c. What is Shelly’s reservation wage? d. Find Shelly’s optimal amount of consumption and leisure.
- Consider two individuals, Carole and Mo, who each have a job opportunity that pays a wage of $20 per hour and allows them to choose the number of hours per week they'd like to work. Carole has stronger preferences for leisure than Mo. Ultimately, both Carole and Mo choose to work more than zero hours per week. Draw (and upload) one graph that includes: • Carole and Mo's income-leisure constraint • Carole's utility-maximizing indifference curve (Uc) and choice of leisure hours (Lc) • Mo's utility-maximizing indifference curve (UM) and choice of leisure hours (LM) [Note: There are multiple, though similar, ways to draw this graph. Focus on ensuring that the constraint, indifference curves and hours worked align with the information provided above.]Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.On average, people sleep 8 hours per day meaning that each individual has 16 hours per day to allocate between labour and leisure. Assuming that the wage rate is $15 per hour and there are non-labor income is zero. The utility function of an individual is given by U(Y, L) = YL and for simplicity, the price index for real income is 1. a. Determine the budget constraint. b. Determine the marginal rate of substitution. c. What are the optimal labor and leisure hours? d. At the optimal relationship, what is the utility level for the individual?