Contemporary Labor Economics
11th Edition
ISBN: 9781259290602
Author: Campbell R. McConnell, Stanley L. Brue, David Macpherson
Publisher: McGraw-Hill Education
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Question
Chapter 2, Problem 6QS
To determine
The impact of labor supply when imposing lump-sum tax and proportional tax.
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Suppose a person can work up to 80 hours per week at a pre-tax wage of $20 per hour but faces a constant 20% payroll tax. Assume that under these conditions the person maximizes utility by choosing to work 50 hours each week. The government proposes a negative income tax so that everyone receives $300 per week regardless of how much they work. To pay for the negative income tax, the payroll tax would be increased to 50%. Using the labor-leisure model, graphically show whether a person would be better off if the negative income tax is
adopted and indicate whether hours worked increases or decreases due to the policy.
Consider a person who can work up to 80 hours each week at a pretax wage of $20 per hour but faces a constant 20 percent payroll tax. Under these conditions, the worker maximizes her utility by choosing to work 50 hours each week. The government proposes a negative income tax whereby everyone is given $300 each week and anyone can supplement her income further by working. To pay for the negative income tax, the payroll tax rate will be increased to 50 percent.a. On a single graph, draw the worker’s original budget line and her budget line under the negative income tax.b. Show that the worker will choose to work fewer hours if the negative income tax is a dopted.c. Will the worker’s utility be greater under the negative income tax?
Suppose that following represents the utility function of the individual
U(c,l)=log(c)+log(l)
c = consumption level of the individual and l = leisure, while the market wage is 10 and available time is 20.
1) Find and draw the labor supply function.
2) Suppose that the government introduces a cash grant for the labor (who is in the labor force) in the amount of R. Find and draw the labor supply function? Compare it to the labor supply function you have found in a).
3) Discuss the existence of reservation wage in the settings described in a and b? If your answer is : “there are no reservation wages under those settings”, please introduce a change in the policy described in b) to make sure that the reservation wage would exist.
Chapter 2 Solutions
Contemporary Labor Economics
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- A worker receives a wage rate w and has L hours of leisure every day (the total endowment of hours is 24 hours per day). The government gives a subsidy of rate S of his income. The worker spends all his income. 1. Write a budget constraint of this individual and plot it. 2. Display graphically what is the optimal consumption-leisure choice for this worker. 3. Imagine that instead, the government imposes income tax at rate T . What is the new budget constraint? Display on the same picture. In the new optimum is the consumption higher? Explain the answer in terms of wealth and substitution effects.arrow_forwardA worker has no non-labor income and is earning $14/hour. He maximizes utility by working 40 hours per week. Begin by drawing a graph that illustrates this to be the utility-maximizing solution. The same worker loses his job. He is entitled to unemployment compensation that will pay up to 50% of his weekly earnings. The worker has an opportunity to supplement his unemployment compensation by taking a job that pays $7/hour. Using the same graph, show the worker's new budget line and his utility-maximizing decision as whether to work the new job and how many hours to work. Make sure your graph shows the relevant budget lines and indifference curves.arrow_forwardThe absolute value of the slope of the consumption-leisure budget line is the after-tax wage, w. Other workers earn w for up to 40 hours of work each week, and then w thereafter as at a second job which pays the same hourly wage as than their primary job. Assume a worker has 168 hours per week and chooses to work 40 hours at the primary job and does not work at a second job. Graph the worker’s budget line and leisure and income at the utility-maximizing level. Assume the primary employer offers the worker an opportunity to earn time-and-a-half working overtime. The overtime pay kicks in after the employee works 40 hours. Graph the old and new budget line and indicate both the number of hours worked and the income earned.arrow_forward
- 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. b) 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.arrow_forwardSuppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with workers’ compensation and has decided to cut the wages of its two employees (Albert and Sid) from $23 per hour to $20 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. Albert and Sid's opportunity set is presented below: "The horizontal axis labeled leisure hours ranges from 0 to 30 in increments of 5. The vertical axis is labeled income. A line begins at point A on the vertical axis goes down to the right and ends at the point (25, 0)." What is the value of A when the wage is $23? (Assume a 24-hour work day.) What is the value of A when the wage is $20? (Assume a 24-hour work day.) At the wage of $23 per hour, both Albert and Sid are observed to consume 13 hours of…arrow_forwardConsider 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.arrow_forward
- 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)arrow_forwardSuppose 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?arrow_forwardSuppose 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)arrow_forward
- An individual can earn $12 per hour if he or she works. Assume that a person can work at most 24 hours per day times 30 days per month for a total of 720 hours. Thus, the axis intercepts, in the absence of any program, are 720 × $12 = $8,640 in consumption and 720 hours of leisure.Scenario: Suppose that a new welfare program is introduced where the government guarantees $600 per month in income and reduces the benefit by $1 for each $1 of labor income. Below is the budget constraints that show the monthly income-leisure trade-off. Given his/her 30 hours of works, he/she is qualified for the welfare program. Calculate his welfare benefits (not total monthly income) after considering dollar-for-dollar reduction. $ _______________________________________arrow_forwardAa1) For a non-participant in the labour market, an increase in non-labour income: a) will have an unknown effect because the income and substitution effects oppose one another b) will increase the reservation wage and leave the individual as a non-participant c) will have a large leisure inducing substitution effect d) will reduce hours worked because it is a pure income effect e) will reduce the reservation wage and (depending how big the reduction is) may coax the individual into the labour marketarrow_forwardHow would you demonstrate part c) diagramatically 6. 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. b) 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. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day.arrow_forward
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