This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good. Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week. Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).
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This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good.
Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week.
Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).
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- An individual values both consumption and leisure. Suppose the individual has 1600 hours per week they can allocate between leisure and work. IF the individual works, they make a wage of $25 per hour. The individual's utility function is given as a function of leisure time, L and consumption, c: U(L, c) = L^(1/2)c ^ (1/2) a) Draw the individual's budget constraint for leisure and consumption. b) How much leisure time will the individual have when utility maximizing? c) Consider a Universal Basic Income policy like the one proposed by Andrew Yang that would give all individuals a lump -sum, unconditional cash transfer of $1,000 each month. How much leisure time will the individual have when utility maximizing with the cash transfer? d) Now suppose, instead of a cash transfer, a minimum wage of $40 per hour is implemented. How much leisure time will the individual have when utility maximizing with the cash transfer? e) What change in leisure time can be attributed to the substitution…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)Jack's marginal utility of consumption is MUc = L - 6, and the marginal utility of leisure is MUL=C-40. Jack does not have any nonlabor income, i.e., V = 0. Jack faces a $48 an hour wage rate. Jack's total number of hours available per week is 150. What is Jack's optimal choice of consumption? (calculate to 2 decimal places)
- John works in a shoe factory. He can work as many hours per day as he wishes at a wage rate w. Let C be the amount of dollars he spends on consumer goods and R. be the number of hours of leisure that he chooses. John's preferences are represented by U(C, R) = CR utility function Question 2 Part a John earns $8 an hour and has 18 hours per day to devote to labor or leisure, and he has $16 of nonlabor income per day. Draw John's indifference curves, budget constraints and solve for his optimal consumption and leisure choices.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.Question 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? (b) Determine the MRS of leisure for labour (c) Draw a leisure-influenced labor curveTerry’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 Draw a leisure-influenced labor curveConsider a consumer who could earn $400 per week and has 50 weeks available each year to allocate between work (H) and nonmarket time (L). They have no non-labour income. Their utility function is U = C2L , where C is the value of consumption goods. What is their optimal choice for the number of weeks in nonmarket time and consumption? Show this in a diagram. Suppose the government introduces a policy that (i) offers no benefits to people who do not work, (ii) offers a wage subsidy on earnings at a rate of 25%, with a maximum benefit of $5000, and (iii) the benefit is subject to reduction at a rate of 25% for every dollar earned above $20,000 in the year. Show the person’s new budget constraint in a new diagram, and discuss how the person’s optimal choice might change (you do not have to calculate this, but point to where it is likely on the new budget constraint). Discuss how income and substitution effects play a role.
- Nora's utility function is given by U = In(C) + In(L), where U is utility, C is consumption, and L is leisure. The total time Nora has is T = 1 and is a utility maximizer. Before the Covic pandemic, the wage rate is 10, and Nora has no non-labor income. When the pandemic hit and part of the economy was locked down, Nora's wage rate decreased to 8. However, the government provided income support by sending out a non-labor income of 5 to everyone, including Nora. Nora still has a total amount of time T = 1 for leisure and work during the pandemic. Which of the following statements is correct? O Before the pandemic, Nora's labor supply is 0.2. O Before the pandemic, Nora spent time equal to 0.2 O Before the pandemic, Nora's consumption was 9. O During the pandemic, Nora's labor supply is 0.5. leisure. O During the pandemic, Nora was better off for having a higher utility level. O During the pandemic, Nora's labor supply is unchanged becauses income effects were perfectly offset by the…Task 4: leisure or work? The consumer choice is not restricted to the choice of consumption goods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has a wage per hour of 10 euros. With her earned income she consumes. That is, C = wH per day. She also decides how many hours to work of take leisure time each day. H = 24 – N, where H is work and N is leisure. Her utility is given by C1-o U(C, N) + B log(N) 1- o (a) Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif- ferent curve. What is the labor supply function? (b) If o > 1, what is the shape of the labor supply? How does it relate with the income andSuppose that the cost of living increases, thereby reducing the purchasing power of your income. If your money wage doesn’t increase, you may work more hours because of this cost-of-living increase. Is this response predominantly an income effect or a substitution effect? Explain.