Consider the following consumer problem's facing a proportional income tax. Utility function over consumption (C) and leisure (L) U(C,L)= 3 ln(C)+ 2 ln(L) Total hours : H=40 Labor hours :NS =H-L Proportional income tax rate = 0.2 Production function: Y =zND Total factor productivity : z =4 The representative consumer maximizes utility, the representative firm maximizes profit, and the government balances budget . What is the tax revenue at equilibrium.?
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Consider the following consumer problem's facing a proportional income tax.
Utility function over consumption (C) and leisure (L)
U(C,L)= 3 ln(C)+ 2 ln(L)
Total hours : H=40
Labor hours :NS =H-L
Proportional income tax rate = 0.2
Production function: Y =zND
Total factor productivity : z =4
The representative consumer maximizes utility, the representative firm maximizes profit, and the government balances budget .
What is the tax revenue at equilibrium.?
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- Consider the following consumer problem's facing a proportional once tax. Utility function over consumption (C) and leisure (L) U(C,L)= 3 ln(C)+ 2 ln(L) Total hours : H=40 Labor hours :NS =H-L Proportional income tax rate = 0.2 Production function: Y =zND Total factor productivity : z =4 The representative consumer maximizes utility, the representative firm maximizes profit, and the government balances budget . What is the tax revenue at equilibrium.?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?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?
- All individuals have the same utility function over consumption, C, and leisure, L, given by U = C1/3L2/3, Denote the wage rate by w. The total time available for labour and leisure is equal to 12. The price of consumption is PC=1. Denote the amount of labour supplied as N. 1)Find the Labour supply function. 2)The government introduces a tax t=0.2 on wage, such that the after-tax wage is (1-t)w. How much tax revenue does the government collect on everyone? What is the effect on labour supply? 3)The government chooses instead to collect a fixed lump-sum T from everyone. What is the effect on labour supply?Assume that the production technology is such that each unit of output requires one unit of labor and that the government has a revenue requirement of one unit of labor. Also assume that there is a single consumer. a. Using a diagram, describe how the optimal tax on the consumption good is determined. Now assume that the consumer has preferences given by U = log(x) + log(10 + ), where x is consumption and is labor supply. b. By maximizing utility subject to the budget constraint qx + w = 0, construct the consumer’s offer curve. c. Treating the equations of the production frontier and the offer curve as a simultaneous system, determine the optimal tax rate.Assume a consumer has a utility function given by u(x,y)=x+y , with an income of $100. Consider a $1 per-unit tax on good 1. Suppose a lump sum tax raises the same amount of income as the per-unit tax. How much income must it raise?
- A consumer derives utility from two goods (x and y), and her utility function is in the form u(x,y) = xy. Her income is 120 TL, and the prices of x and y are both 1 TL: a) Suppose that a tax of 1 TL per unit is levied on good x. How will this alter her utility maximizing market basket of goods? b) Suppose that instead of the per unit tax in (a), an income tax of the same total tax revenue is levied on the consumer. What is her utility maximizing market basket? c) Show your analysis in part (a) and (b) on a graph.d. Holding Donald's income and Pd constant at $120 and $1 respectively, what is Donald's demand curve for carrots? e. Suppose that a tax of $1 per unit is levied on donuts. How will this alter Donald's utility maximizing market basket of goods? f. Suppose that, instead of the per unit tax in (e), a lump sum tax of the same dollar amount is levied on Donald. What is Donald's utility maximizing market basket? g. The taxes in (e) and (f) both collect exactly the same amount of revenue for the government, which of the two taxes would Donald prefer? Show your answer numerically and explain why Donald prefers the per unit tax over the lump sum tax, or vice versa, or why he is indifferent between the two taxes.1) An individual utility function is given by U(x,y) = x·y. Derive this individual indirect utility function. Using this individual indirect utility function, compute her level of utility when I = $800, px = $20 and py = $40. It is equal to 200 utils. 2) An individual utility function is given by U(x,y) = x·y. Let I = $800, px = $20 and py = $40. Suppose that a tax t of $10 per unit is imposed on good x. Assume that the full burden of this excise tax is borne by this consumer, i.e. the new price this individual faces for good x is p’x = px + t = $20+ $10 = $30. Use the indirect utility function you derived earlier to compute this person new utility level with this excise tax. It is equal to 133.33 utils. Question: An individual utility function is given by U(x,y) = x·y. Let I = $800, px = $20 and py = $40. Suppose that a tax t of $10 per unit is imposed on good x. Assume that the full burden of this excise tax is borne by this consumer, i.e. the new price this individual faces for…
- Consider a one period model in which a representative agent maximises the utility function: u(c,l) = lnc + 5lnl subject to the budget constraints: c = (1-t)w(1-l) + v where c is consumption and l is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments. A. Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? B. Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1. C. In this particular example, what are the contributions of the income and substitution effects?Suppose in Fiscalville there is no tax on the first $10,000 of income, but a 20 percent tax on earnings between $10,001 and $20,000 and a 30 percent tax on income between $20,001 and $30,000. Any income above $30,000 is taxed at 40 percent. If your income is $50,000, how much will you pay in taxes? Determine your marginal and average tax rates. Is this a progressive tax? Explain.Many economists believe that a more effective way to supplement the income of the poor is through a negative income tax. Under this scheme, everyone reports his or her income to the government; individuals and families earning a higher income will pay a tax based on that income, while low-income individuals and families receive a subsidy, or negative tax. Assume that the only qualification required to receive a tax credit is low income. Suppose the government uses the following equation to compute a family’s tax liability: Taxes Owed = (1/4 of Income)−$6,000 For each of the incomes listed in the following table, determine the tax liability for a family with that income level. (Note: If a family receives a subsidy because its income is too low, be sure to indicate the tax liability as negative.) Income Tax Liability (Dollars per year) (Dollars per year) 0 12,000 24,000 60,000 True or False: Any family with an annual income more than…