Suppose George views leisure as a normal good. He works at a job that pays w an hour. Use a labor-leisure analysis to compare the effects on the hours he works from a marginal tax rate on his wage, x, or a lump-sum tax (a tax collected regardless of the number of hours he works), T. If the per-hour tax is used, he works 10 hours and earns (1-x)10w. The government sets T = a10w, so that it earns the same from either tax. The budget constraint without taxes L¹ is illustrated in the figure to the right. Let the price of a unit of consumption be $1.00 such that 10w units of consumption correspond to income of $10w. 1.) Use the line drawing tool to draw the new budget constraint with an income tax. Label this line 'L''. 2.) Use the line drawing tool to draw the new budget constraint with a lump-sum tax. Label this line 'LL. Carefully follow the instructions above, and only draw the required objects. Y, Goods per day 10w 10w(1-tax rate) Time constraint 10: L, Leisure hours per day

Suppose George views leisure as a normal good. He works at a job that pays w an hour. Use a labor-leisure analysis to compare the effects on the hours he works from a marginal tax rate on his wage, x, or a lump-sum tax (a tax collected regardless of the number of hours he works), T. If the per-hour tax is used, he works 10 hours and earns (1-x)10w. The government sets T = a10w, so that it earns the same from either tax. The budget constraint without taxes L¹ is illustrated in the figure to the right. Let the price of a unit of consumption be $1.00 such that 10w units of consumption correspond to income of $10w. 1.) Use the line drawing tool to draw the new budget constraint with an income tax. Label this line 'L''. 2.) Use the line drawing tool to draw the new budget constraint with a lump-sum tax. Label this line 'LL. Carefully follow the instructions above, and only draw the required objects. Y, Goods per day 10w 10w(1-tax rate) Time constraint 10: L, Leisure hours per day

Economics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506725

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter28: Income Inequality And Poverty

Section: Chapter Questions

Problem 9CQ

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answer please, additional information has been given. 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. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases but labour supply de Using the concept of the marginal rate of substitution, explain why this is a likely outcome. e) Now assume that, starting from the optimal point in d), your wage increases to £18 per hour. Explain why the impact of this change is ambiguous, and relate to the long-run historical experience of wage growth in rich countries.
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 her income (i.e. her income is (1+s) times what it would be without the subsidy). The worker cannot save, and initially faces no tax. She consumes a single consumption good, c. 1. Write a budget constraint for this individual and plot it. 2. Suppose that the worker has well-behaved preferences, i.e. she likes more consumption and leisure rather than less, she dislikes working, and she has decreasing marginal utility in consumption and leisure. a. Display graphically what the optimal consumption-leisure choice for this worker (no need for exact numbers as we don’t know the utility function; give intuition) 3. Imagine that instead of a subsidy rate, s, 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…
Suppose that a consumer can earn a higher wage rate for working overtime. That is, for the first q hours the consumer works, he or she receives a real wage rate of w1, and for hours worked more than q he or she receives w2, where w2 > w1 . Suppose that the consumer pays no taxes and receives no nonwage income, and he or she is free to choose hours of work. (a) Draw the consumer’s budget constraint, and show his or her optimal choice of consumption and leisure. (b) Show that the consumer would never work q hours, or anything very close to q hours. Explain the intuition behind this. (c) Determine what happens if the overtime wage rate w2 increases. Explain your results in terms of income and substitution effects. You must consider the case of a worker who initially works overtime, and a worker who initially does not work overtime.
Mark can work up to 80 hours each week at a pre-tax hourly wage of $20 but faces a constant 20 percent tax on his earnings. Thus, Mark maximizes his utility by choosing to work 50 hours per week. The government proposes a negative income tax whereby everyone is given $300 per week and anyone can supplement their income further by working. To pay for the negative income tax, tax on earnings will be increased to 50 percent. On a single graph, draw Mark's original budget line and his budget line under the negative income tax. Show that Mark will work fewer hours if the negative income tax is implemented Will Mark's utility be greater under the negative income tax? Discuss your answer.
Suppose a consumer’s preferences over two goods x_1 and x_2 are given by u = Square root (X_1,X_2). Her income is M and the two goods cost p1 and p2 per unit respectively. a) Derive her utility at the optimal consumption point as a function of prices and income. b) Now suppose the government imposes a proportional tax t on the value of the good x_1 (such as VAT). If the consumer approaches the government for income compensation to remain as well off as before the tax (i.e. compensating variation in income), how much money would she ask for? c) If instead, the government decides to maintain consumer’s utility level not through lump-sum transfer but by introducing a proportional subsidy S on the price of good 2, then what should be the size of the subsidy? d) Based on your answer in part c) discuss how much would it cost for the government to introduce both a tax and a subsidy at the same time? Can you think of any situation when this policy would make sense?
Willy the Worker has unavoidable personal commitments taking 8 hours per day. He can choose to work or to play (i.e., take leisure, a normal good) in the remaining hours. Being a graduate in Economics, he can charge $100 per hour for his consulting services when he chooses to work. The government's income tax system has a 0% tax rate for daily incomes from $0 to $ $600 per day; above $600 per day, the tax rate is 20%. Willy has a certain Utility Function U(L, I) where L = leisure playtime and I = Income. His Marginal Rate of Substitution is known to be derived from this equation: MRSL/I=2I/L. (Note that the "price" of Income is $1.) Willy thinks he pays enough taxes via the excise taxes on things he buys. So he decides to work the maximum number of hours he can without paying any income taxes. According to our Indifference Theory model, is Willy maximizing his satisfaction with his "no tax" choice, or should he work fewer hours?
In this hypothetical economy, there are two consumers living over two periods of life. Ann’s incomes are $50,000 in both periods. Meanwhile, Bob earns nothing in the first period but $105,000 in the second period. Both of them can borrow or lend at the interest rate r. For simplicity, assume that there are no taxes. a) Assume that both Ann and Bob consume $50,000 in the first period and $50,000 in the second period. Write down the lifetime budget constraint for each consumer then calculate the interest rate r. Describe the economic behavior of each consumer. b) Suppose the interest rate increases. What will happen to Ann’s consumption in the first period? Is Ann better off or worse off than before the interest rate rises? Explain your answer using an appropriate diagram c) What will happen to Bob’s consumption in the first period when the interest rate increases? Is Bob better off or worse off than before the interest rate increases? Explain your answer using an…
In this hypothetical economy, there are two consumers living over two periods of life. Ann's incomes are $50,000 in both periods. Meanwhile, Bob earns nothing in the first period but $105,000 in the second period. Both of them can borrow or lend at the interest rate r. For simplicity, assume that there are no taxes. a)Assume that both Ann and Bob consume $50,000 in the first period and $50,000 in the second period. Write down the lifetime budget constraint for each consumer then calculate the interest rate r. Describe the economic behaviour of each consumer. b) Suppose the interest rate increases. What will happen to Ann's consumption in the first period? Is Ann better off or worse off than before the interest rate rises? Explain your answer using an appropriate diagram c) What will happen to Bob's consumption in the first period when the interest rate increases? Is Bob better off or worse off than before the interest rate increases? Explain your answer using an appropriate diagram.
Consider a single mother with the utility function U = 2/3 log(x) + 1/3 log(), where x is consumption and is leisure. The mother can work up to 100 hours per month. Any of the 100 hours that are not worked are leisure hours. She earns a wage of $10 per hour and pays no taxes. The consumption price is normalized to $1. To be able to work, she has to incur a child care cost of $5 for every hour worked. a. Suppose that there is no tax and welfare benefits. How many hours will she work and what will be her consumption level? Draw the graph depicting her budget set with consumption on the vertical axis and leisure on the horizontal axis. b. Suppose that the government introduces a negative income tax (NIT) that guarantees an income of $200 per month. The benefit is taken away one for one as earnings increase. Draw the new budget set. Compute the new number of hours worked and consumption level. Has consumption increased and is the mother better off? Why or why not? c. Now…
Exercise 5 (Borrowing Constraints and Consumption Taxes). Consider a two-period economy in which households face the borrowing constraint S p 1 ≥ 0. Suppose that the constraint is binding. In period 1, the household receives an exogenous endowment of goods Y1 = 50, and the government levies a proportional tax on consumption at the rate τ1 = 0.25 and has expenditures in goods and services in the amount G1 = 2. Firms borrow in period 1 at the interest rate r and use the funds to invest in physical capital, denoted I1. Investment becomes productive in period 2. The investment schedule is I1 = 12.5 (1 + r) ^2 1. Calculate private consumption in period 1 (C1), government saving in period 1 (S g 1 ), and national saving in period 1 (S1). 2. Calculate the equilibrium real interest rate (r).
Consider the utility function for a worker according to leisure, l, and consumption, c: where consumption has the price p and the wage has the price w. The state can implement an income tax, t, for the worker where 0 < t < 1 such that his after-tax hourly wage is w(1 - t). What is the biggest tax revenue that the state can get?
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.