Front | Back |
Consider a society with only two people, rich and poor, who have the same utility functions. These functions exhibit diminishing marginal utility. Suppose that taxes are set such that the TOTAL amount of utility that each person loses is the same. Does it follow that the tax will be progressive?
|
No, it does not follow that the tax will be progressive. If both lose the same amount of utility, the rich person will pay more because of diminishing marginal utility of income. But, a progressive tax requires that a higher proportion of income (the average tax rate) be taken from the rich person. This tax plan only requires that the absolute amount be higher, not the proportional amount. For instance, if the marginal utility were decreasing, but very close to constant, then the rich and poor would pay very close to the same amount in taxes. This amount would be a much larger share of the poor person’s income.
|
Use a general equilibrium framework to discuss the possible incidence of a tax on cigs?
|
If a tax is placed on cigarettes, markets other than the cigarette market will be affected. A tax on cigarettes is effectively a tax on the resources used to make them. The tax will reduce the quantity of cigarettes purchased, therefore decreasing the purchase of the resources used to produce cigarettes. If production of cigarettes is primarily labor intensive, then the tax primarily affects people who earn their incomes from labor in other sectors of the economy. The labor from the production of cigarettes will flow into other segments, increasing the supply of labor and decreasing the wages paid to labor in all sectors. The same thing would happen to capital if cigarette production were capital intensive.
|
In an effort to reduce alochol consumption, the govt is considering a $1 tax on each gallon of liquor sold. Suppose that the demand curve is Qd = 500,000-20,000P and supply curve is Qs=30,000P.
a. Compute how the tax affects the price paid by consumersand the price received by producers. b. How much revenue does the tax raise for the govt? How much of the revenue comes from consumers, and how much from producers?> c.Suppose that the demand for liquor is more elastic for younger drjinkers than for older drinkers. Will the liquor tax be more less or equally effective at reducing liquor consumption among young drinkers? |
A) Before-tax equilibrium: P = $10 and Q = 300,000. QD=QS so 500,000-20,000P=30,000P and 500,000=50,000P. P=10, Q=30,000*10=300,000.
(b) After-tax equilibrium: P = $10.60 and Q = 288,000, producers receive $9.60. So 500,000-20,000P=30,000(P-1) and 530,000=50,000P, so P=10.6, Q=30,000*(10.6-1) = 288,000. (c) Revenue = $288,000. Consumers bear 60 percent of the tax burden and producers bear 40 percent. So, $172,800 comes from consumers and $115,200 from producers. (d) With a more elastic demand curve, quantity consumed will decrease even more as a result of the tax, so the liquor tax will be more effective at reducing consumption among young drinkers. |
Suppose that the income tax in a certain nation is computed as a flat rate of 5 percent, but no tax is levied above 50,000 in taxable income. Taxable income in turn is computed as the individuals income minus $10,000 so everyone gets a $10,000 reduction. What are marginal and avg tax rates for each of the following threee workers?
a. part time worker with annual income of 9000 b. retail sales with annual income of 45000 c. advertising exec with income of 600000 Is the tax progressive, proportional or regressive with respect to income. |
A) A part-time worker with annual income of $9,000 pays no taxes since everyone gets a $10,000 deduction. Her marginal tax rate is 0% and her average tax rate is 0%.
(b) A retail salesperson with annual income of $45,000 has taxable income of $35,000 and pays $1750 in taxes (5 percent of taxable income). As a percentage of income, the average tax rate is 3.89% ($1750 is 3.89% of $45,000). Her marginal tax rate is 5%. (c) An advertising executive with annual income of $600,000 pays $2,500 in taxes since no tax is levied above $50,000 in taxable income. As a percentage of income, the average tax rate is 0.42%. Her marginal tax rate is 0%. The tax is initially progressive, but because of the cap on taxable income, becomes regressive. |
In 2007, President on whiskey brandy and cognac by $1.79 per liter and increased tax on cigs by 20 cents per pack. Regarding the liquor tax, one said "its unfair because ithe consumer is the one who pays. On cig tax, one said "they wont stop smoking". Diagram models for the liquor and cig markets in Venezuela that are consistent with these observations.
|
The comment regarding the tax on cigarettes implies that the demand for cigarettes is fairly inelastic (reasonable assumptions since cigarettes are addictive). When the demand is inelastic, much of the tax will be paid by the consumer. The statement on the tax on liquor implies that the demand for liquor is perfectly inelastic, so that all the tax is passed to the consumer. This is unlikely.
|
Suppose the government adopts a Haig-Simons comprehensive income definition. Will this make employers more or less likely to offer employer-provided pension plans or health insurance coverage? Why or why not?
|
Less likely. Because pension contributions and health insurance are included in Haig-Simon income, employers would no longer be able to make a tax-deductible contribution to either the pension fund or to providing health insurance. Workers still might like having employers provide pensions (for psychological reasons, or because of employer matches), and insurance (because of the advantage of lower premiums from group rates) but there’s no longer the tax break.
|
A welfare program provides a $7500 “guaranteed subsidy” even if enrollees aren’t working, but with a 50% implicit tax, leading to a break-even point of $15,000. A new reform is implemented that provides just a $4000 guarantee, with a new break-even point of $8,000. An NPR reporter states that “this reform will surely cause a decline in total income (earnings plus transfers) for welfare recipients.” Is this true, false or uncertain? Explain USING A GRAPH and (briefly) in words.
|
Uncertain. The individual begins at point A with utility U0, and one can certainly imagine the individual moving to point B (if they have preference described by U1), where income is indeed lower. (Note – I have just drawn B as having zero hours of work, but it could have positive hours too.). However, it is also possible that the individual may just leave the program entirely, and end up earning more if her preferences are U2, ending up at point C. But according to our standard theory, while the person is earning more, she is still worse off (because of the loss of leisure).
|
Hilda S. is a single mother with cash income of $600 per month. Initially she receives $200 per month in food stamps. A new program is initiated: Rather than receive the food stamps, Hilda receives a special discount card that allows her to receive a 50% discount on every dollar of food she purchases. (i) Show her new budget line. Will this new program discourage or encourage food consumption? Briefly explain your answer using the graph. (ii) Does this new “in-kind” program entail any distortions or efficiency costs as the result of the food discount? Show graphically and explain.
|
The effect on Hilda’s consumption of food depends on her preferences. I’ve drawn some effects below, ignore the dotted red line – but the solid red line is the new budget. The old budget is BCK. As you can see, if Hilda was consuming a lot of food to begin with, this new program would probably increase her food consumption, both because of an income effect (the subsidy could be larger) and the substitution effect, which would push her to increase consumption of food at the margin, from E to F. The effects are more ambiguous if she consumes little food, because then the income effects (less subsidy $) might dominate the substitution effect (consume more food), leading to a movement from C to D. Note that this variable quantity subsidy is more likely to introduce distortions at the margin than the traditional food stamp program (unless you think there should be a subsidy for food at the margin!)
|
“The Rawlsian social welfare function implies that governments should redistribute away from the richest members of society to everyone else. By contrast, the utilitarian (Benthamite) approach implies that free markets should be left alone to maximize social welfare.” Evaluate each of these two sentences; are they true, false, or uncertain?
|
This is false along at least two dimensions. First, the Rawlsian social welfare function is not about taking money away from the richest citizens, it’s all about taking money from everyone but the poorest groups, and giving that money to the poorest. Under the Rawls formulation, it doesn’t matter whether the money comes from the lower middle class or Bill Gates, the important thing is that the lowest income people experience a rise in their living standards. Second, the utilitarian approach does NOT imply that free markets should be left alone. It only says that society should seek to maximize the sum of individual utility. Thus in some cases, a free-market outcome, by expanding the size of the enchilada, could improve social welfare, but in other cases, where the poor are hurt, free markets would reduce utilitarian social welfare.
|
Suppose that the govt introduces an income maintenance program for low income people that offers a basic grant of $200 per month but that for any earnings above $100 the grant is reduced dollar for dollar.
a.assume lois can earn $10/hour and has no other income. Sketch her annual budget constraint with and w/o the program.At how many hours is grant reduced to zero. b.According to economic theory, what would happen to Lois's hours worked and total income if the govt instituted this welfare plan? c. Suppose that the gov't decides to keep the monthly base grant at $200, but to lower the implicit marginal tax rate on earnings to 66.67%. Draw new budget constraint. d. Relattive to first plan, how will this new plan affect Lois's hours of work and total income. |
A. Without the program in effect, Lois’s budget constraint is the line AD. With the program in effect, her budget constraint is ABCD. The grant is reduced to zero if Lois works 30 hours per month since her hourly wage rate is $10 and she can exempt the first $100 in earnings.
b. Many low-wage earners, including Lois, would be better off working zero hours with this kind of program in place, as shown in Figure 13.6. c. If the implicit marginal tax rate on the grant is 66.67 percent, then Lois can work 40 hours before losing the full $200 grant. |
Section 8 program for housing assistance discussed in this chapter in effect shifts out the demand curve for low-income houusing in a given community. Draw supply and demand diagrams that are consistent with these outcomes:
a.Price of low-inc housing gets bid up, there is no increase in the stock of low--inc housing. b. There is no increase in the price of low-inc housing and there is an increase in the stock of low-inc housing. c. There is an increase in the price of low-inc housing and there is an increase in the stock of low-inc housing. Which is most consistent with the research by Sinai and Waldfogel that is discussed in this chapter. |
In all cases, the demand curve for housing slopes downward.
a. If the price of low income housing gets bid up but there is no increase in the stock of housing, then the supply curve is perfectly inelastic, e.g., vertical. See graph below. b. If there is no increase in the price of housing, but there is an increase in the stock of housing, then the supply curve is perfectly elastic, e.g., horizontal. See graph below. c. If there is an increase in both the price and quantity of housing, then the supply curve slopes upward. See graph below. According to Sinai and Waldfogel, there is partial crowding out, consistent with case c above. Although the underlying housing stock itself is probably quite inelastic in the short-run, the number of rental homes can be more elastic as (potential) landlords convert vacation homes or vacant homes into rental units. |
Consider Eleanor who qualifies for the earned income tax credit as depicted in figure 13.8 suppose she can earn$8 an hour. Taking into account the EITC and ignoring other aspects of the tax and transfer systems:
a. How much do her earnings increase when her labor supply increases from 0 to 1,000 hours per year? b. How much do her earnings increase when her labor supply increases from 1,000 to 1,500 hours per year? c. How much do her earnings increase when her labor supply increases from 1,500 to 2,000 hours per year? |
(a) When Eleanor’s hours (earnings) go from 0 to 1,000 ($0 to $8,000), she qualifies for an additional earned income tax credit (EITC) worth $3,200 (=0.4*8,000). Thus, her income goes up from $0 to $11,200. The implicit tax rate is -40% (or a subsidy).
(b) When Eleanor’s hours (earnings) go from 1,000 to 1,500 ($8,000 to $12,000), she still does not qualify for the maximum EITC (according to Figure 13.8 in the textbook). She receives $4,800 ($12,000 x 0.4). The earnings between $0 and $12,060 face a subsidy, thus her hourly wage faces a subsidy of 40 percent. Her income goes up from $11,200 to $16,800. The implicit tax rate is -40% (or a subsidy). (c) When Eleanor’s hours (earnings) go from 1,500 to 2,000 ($12,000 to $16,000), she moves into the range where the EITC is at its maximum of $4,824 ($12,060 x 0.4). Her income goes up from $16,800 to $20,824. The implicit tax rate is 0% because her EITC is neither increasing nor decreasing. |
Suppose there are two people Simon and Charity who must split a fixed income of $100. For Simon Marginal utility of income is MUs = 200-2Is and for Charity it is MUc = 400-6Ic.
a. What is the optimal distribution of income if the social welfare function is additive? b. What is the optimal distribution if society values aonly the utility f Charity? What if the reverse is true? c. Finally commonent on how answers change if Marginal utility of income for both of them is constant? |
A. To maximize W, set marginal utilities equal; the constraint is Is + Ic = 100. So, 400 - 2Is = 400 - 6Ic, substituting Ic = 100 - Is gives us 2Is = 6 (100 – Is). Therefore, Is = 75, Ic = 25.
b. If only Charity matters, then give money to Charity until MUc = 0 (unless all the money in the economy is exhausted first). So,400-6 Ic = 0; hence, Ic = 66.67. Giving any more money to Charity causes her marginal utility to become negative, which is not optimal. Note that we don’t care if the remaining money ($33.33) is given to Simon or not. If only Simon matters, then, proceeding as above, MUs. 0 if Is = 100; hence, giving all the money to Simon is optimal. (In fact, we would like to give him up to $200.) c. MUs = MUc for all levels of income. Hence, society is indifferent among all distributions of income. |
President Russia proposed replacing in kind subsidies such as free public transportation and rent free appts for gov't workers with cash subsidies of between 20 and $120 per month. It led to widespread complaints among Russian citizens that the cash subsidies were not large enough. What is the perk worth"? Use an indifference curve analysis to show how to convert an in kind subsidy into a cash subsidy that leaves people equally well off.
|
Suppose the government is initially providing an in-kind benefit of 10 units of free public transportation, worth $2 each, so the cost of the subsidy is $20. Without the subsidy, income is $40. With no subsidy, the consumer maximizes utility at point A, and with an in-kind benefit of 10 units of free public transportation, the consumer maximizes utility at point B. A cash subsidy equal to $20 would allow the consumer to reach point B as well, so the government could convert an in-kind subsidy valued at $20 to a cash subsidy of $20 and leave people equally well off.
Another possibility is that the utility-maximizing point for a cash subsidy differs from the utility-maximizing point for an in-kind subsidy, as illustrated in the next graph. In this case, an in-kind subsidy, costing $20, would allow the consumer to move from point A’ to point C’, while a cash subsidy of $20 would make the consumer better off at point B’. In order to make the consumer equally well off, the cash subsidy should be a little less than $20. |
An economy consists of two individuals, Lynne and Jonathan whose utility levels are given by Ul and Uj.
a. Suppose that social Welfare function is W = Ul + Uj True or false, society is indifferent between giving a dollar to Lynne and a dollar to Jon. b. Suppose instead that social welfare function is W = Ul + 8Uj T or F, sociaty values Jon's happiness more than Lynne's c. Now function is W = min[Ul,Uj] T or F, in this society the optimal distribution of income is complete equality. |
A. False. Society is indifferent between a util to each individual, not a dollar to each individual. Imagine that UL=I and UJ=2I. Then each dollar given to Jonathan raises welfare more than the same dollar given to Lynne.
b. True. The social welfare function assumes a cardinal interpretation of utility so that comparisons across people are valid. c. False. Departures from complete equality raise social welfare to the extent that they raise the welfare of the person with the minimum level of utility. For example, with the utility functions UL=I and UJ=2I, the social welfare function W=min[UL,UJ] would allocate twice as much income to Lynne than Jonathan. |