4) Consider the following scenario: Juliet faces 200 Total Hours to devote to Labor or Leisure. She faces a wage of $10 and has no non-labor income. Her preferences are given by the utility curve U(C,L)=C% L% a. What are her optimal hours worked and consumption choice? b. What is Juliet's reservation wage? c. Now assume the government is offering a "take-it-or-leave-it" grant of $625 for anyone who isn't working. What is her optimal hours worked and consumption choice in this scenario? d. Now assume instead the government is offering $625 for non-working individuals, but taxes it away at a rate of 50% for each dollar earned. Graph the budget constraint and find the new optimal hours worked and consumption choice. e. Between (a), (b), and (c) which scenario has Juliet the most well-off? Between (b) and (c) which scenario is most costly (in terms of grants paid) to the government?

4) Consider the following scenario: Juliet faces 200 Total Hours to devote to Labor or Leisure. She faces a wage of $10 and has no non-labor income. Her preferences are given by the utility curve U(C,L)=C% L% a. What are her optimal hours worked and consumption choice? b. What is Juliet's reservation wage? c. Now assume the government is offering a "take-it-or-leave-it" grant of $625 for anyone who isn't working. What is her optimal hours worked and consumption choice in this scenario? d. Now assume instead the government is offering $625 for non-working individuals, but taxes it away at a rate of 50% for each dollar earned. Graph the budget constraint and find the new optimal hours worked and consumption choice. e. Between (a), (b), and (c) which scenario has Juliet the most well-off? Between (b) and (c) which scenario is most costly (in terms of grants paid) to the government?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.1P

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Consider 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.
Suppose that the owner of Boyer Construction is feeling the pinch of incrs associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours? (LO2, LO3, LO7)
Suppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours? (LO2, LO3, LO7)
The weekly preferences over consumption (C) and leisure(L) are defined by u(C, L) = √C + 3√L. The person receives a weekly allowance of m from The hourly wage is $18 per hour, and the person can work up to50 hours each week (T = z + L = 50), where z is the number of hours spent working). a)How many hours will the person work if her allowance is m= $450 per week b) What is the smallest allowance m for which the person will stopworking altogether (z∗ = 0) for a wage of w = 18?
4. 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)
Suppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours?
Jasmine can work as much as 64 hours per week. She receives $200 per week in non-wage income. Her utility function for leisure and consumption is U(R, C) = 320R(1/2) + 2C , where R is hours of leisure and C is consumption. The price of consumption is unity. (a) What is Jasmine's reservation wage? (b) How much will Jasmine work when the wage is $20 per hour?
(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?
21. Let U=x 2 +y 2 is the utility function of a worker who has 10 hours that to be allocatedbetween labour supply (L) and leisure (x). Let y is a consumption good whose price is 1.Wage rate (w) is Rs 1 and non-wage income is 20. Find out L.a) 10 b) 0 c) 5 d) 8 e) none 22. On the basis of the above question, hen w=0 and non-wage income is 40, find out L.a) 10 b) 0 c) 5 d) 8 e) none
Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1. a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation. b) Suppose that Susan’s preferences over carrots and leisure are expressed by the following utility function: U(C,L) = min{C, 10L}. Calculate Susan’s optimal consumption bundle, both algebraically and graphically. Calculate the value of MRS at the optimal choice. c) Suppose instead that Susan’s preferences are such that indifference curves in the L-C space are strictly convex to the origin, and that she chooses to work 5…
Consider a couple (a husband and a wife) that jointly represents their collective preferences between combinations of household production time (X) and purchased goods and services (Y) according to the formula W = X2Y, where W represents the level of welfare. Suppose the maximum time available in a day is 16 hours and currently the wife devotes 6 hours to market work (H) at a wage of $16 per hour. a. What is the level of welfare associated with the wife’s current situation? b. How much additional purchasing power would the wife contribute if her market work hours increased to 8? c. How much of an increase in purchased goods and services would be necessary to compensate for the additional 2 hours of lost household production? d. Should this couple choose to have the wife increase her market work by 2 hours? e. If this couple is raising a child, suppose that combinations of household production and purchased goods are now ranked according to the formula U = X3Y. Would the additional 2…
Consider two individuals with endowments of T 5 60 hours (per week) of leisure, nonlabour income of Y, and a wage of $7.50 per hour. At this wage, assume that workers are constrained by their employers to work 40 hours per week, or not at all. a. On a carefully labelled diagram, show the equilibrium for a worker for whom 40 hours is the optimum labour supply and a worker who would like to work 20 hours, but still prefers the 40-hour week to not working. Compare the mar- ginal rates of substitution for these individuals at 40 hours per week. b. The average part-time wage is $7 per hour, in contrast to $7.50 wage for full-time workers. Using the above model, provide an explanation for this difference in wage rates.