Part A: Exercises

Question 1 [Comparing Redistributive Programs]

We discussed different approaches to raising the standard of living of the poor. Consider the following policy suggestions:

1)  wage subsidies: employers are subsidized by the government to pay higher wages to low wage employees.

2)  a means-tested cash welfare program: all individuals are guaranteed a minimum standard of living and that minimum grant is reduced as their earnings rise.

3)  categorical welfare: certain groups, such as single mothers or disabled individuals, receive cash or in-kind assistance.

a) Some people claim that a wage subsidy is the optimal means for raising the income of the  poor, since it necessarily increases the incentive for working by raising the wage that they are paid. Is this argument correct? Why or why not? [Hint: consider both substitution effects and income effects in your answer.]

b) How do the incentives for working under a means-tested cash welfare program compare to      those of a wage subsidy?  Remember that under a means-tested cash welfare program individuals are entitled to a certain benefit guarantee (G) that is taxed away at some rate (t) as earnings (E)    increase (where B = G – tE). Consider this question for both the poor and for other groups.           Illustrate your answer in figures and explain.

c) Describe advantages and disadvantages of categorical welfare (that is based on, e.g., single     motherhood or blindness) relative to the cash welfare system. What rule should guide the            government as it decides what the appropriate categories are to use in designing these programs; that is, which types of categorical definitions will minimize the distortions from the system?  Do you know of empirical evidence on the question of whether categories used to establish welfare eligibility affect behavior? [Hint: for the latter part, we briefly discussed one example in class,   and you can also rely on the textbook here.]

d) Imagine that you are designing a means-tested cash transfer program to combat poverty. That is, you are choosing a guaranteed benefit level and an implicit tax rate (benefit reduction rate) at which this grant will be taken away as income rises. What are the efficiency and equity              implications of choosing different grant levels and different tax rates? (Here you should just      provide a short discussion.)

Question 2 [Welfare Programs and Work Disincentives]

There are three types of individuals who differ in their marginal valuations of leisure. Individuals have utility functions that can be described as follows:

Un  = ln xn  + nln (1− ln ) ,

where x is consumption, l is labor supply, and n indicates type. A third of all individuals falls into each of the three following categories of types: n = 1/2, n = 1, n = 2. Labor supply is bounded between 0 and 1. The price of private consumption is 1, and the wage rate is also equal to 1 for all individuals. All individuals have non-labor income equal to 1/4. The following exercises explore the potential work disincentives of welfare programs in this economy.

In each of the following parts of the question, please explain your results graphically as well as algebraically.

a) In the absence of a welfare program, how much labor will individuals of each type supply?

b) The government has realized the distribution of consumption across individuals is very unequal. It decides to establish a welfare program to achieve more equity in this economy. The program guarantees all individuals who choose to take up welfare transfers a grant of 1/4. However, this grant is taxed away at a rate of one-for-one with labor earnings; that is, the benefit reduction rate (or the implicit tax rate) is 1 (100%). How much labor does each type choose to supply under this program?

c) After introducing the welfare program, the government is surprised by how high welfare outlays are. The administration decides to improve the labor supply incentives of the welfare program by reducing the implicit tax rate on earnings to 1/2 (i.e., by allowing individuals to keep half of labor earnings and still participate in welfare). How much labor does each type of individual choose to supply under this program? What happens to total government outlays? (In your answer you can assume there is one person of each type.)

Question 3 [In-Kind Welfare Program]

Winters are very cold in Chillhood. Unfortunately, low-income residents cannot afford to spend very much on clothing, and they therefore suffer disproportionately during the winter. In response to their discomfort, the mayor institutes a new program – “Warm Winter for All” – under which every resident is entitled to one warm coat (with a store value of $100) that can be obtained from an official in City Hall. Individuals must personally collect their winter coats. Since the winter is quite cold, a large number of people are likely to want free coats. Even people who do not need new coats might be tempted to get one at City Hall, since individuals can sell their coats to the local store for $100 each.

a) One of the city’s residents is an econ major financial analyst who earns $200 per hour. The analyst considers the length of the line (assumed to be known) before deciding whether or not to get a coat. Under what conditions will the analyst decide to get a coat? What is the effective price the analyst pays to obtain the coat (here in the form of opportunity costs)?

b) The analyst earns the top wage in this town. Assume that there are 200 residents, each of whom earns different wages ranging from $1/hour to $200/hour. (That is, one person earns $1/hour, one person earns $2/hour, one person earns $3/hour, and so on, up to the analyst who earns $200/hour.) The mayor’s social media account reports that the line for coats is always the same length: one must stand in line for H hours. Which people will decide to stand in line for coats? Graph the value of a coat, and its effective price, as a function of the wage rate of the potential coat recipient. Your graph should have wage on the horizontal axis and $ on the vertical axis.

c) Now suppose that H is a simple function of the number of people standing in line: H = N/4, in which N is the number of people who line up for coats this winter. What is the equilibrium length of the coat line? Which people decide to obtain coats? What are their net benefits (that is, the benefit of a coat minus the effective price of a coat)? [Hint: The marginal person will be just indifferent between the option of waiting in line and getting a coat and the option of opting out of the Warm Winter for All Program. Because of the setup of the problem, that person’s wage will be equal to N, the number of people who wait in line.]

d) The welfare system is often criticized for stigmatizing low-income people, by making them wait in line at welfare offices (and endure various other indignities). Is there a function served by making people wait in line for income assistance? Is such a system purely inefficient or can it increase social welfare?

Question 4 [Social Welfare Functions]

A neighborhood consists of three families, indexed by a, b, and c. Family “a” has an income of $80, family “b” has an income of $110, and family “c” has an income of $120. The town intends to build a public playground for the use of the families’ children which will be financed with a local tax paid to the town. The playground will cost $60 to build, and the arrangement is that each family would pay $20 in taxes if the playground is built. The utility functions of the neighborhood

families are:

      =       =

      =

20 +  

  +   +  

61 + 2

where  is family ’s utility level,  is family ’s after-tax income, and  is a constant. Note that  could be a positive or negative constant.  is a variable that indicates whether or not     there is a playground:  = 0 if there is no playground, and  = 1 if there is a playground.

a) If the project is undertaken, what effect will it have on the utilities of families a, b, and c?

b) If the town had an additive utilitarian social welfare function, would it undertake the project?

c) If the town had a Rawlsian social welfare function, would it undertake the project? [Hint: the answer depends on the potential values of  .]

II. Short-Answer and Multiple-Choice Questions

1.        There is an ongoing debate regarding the way that your state links the receipt of welfare benefits to attending job training sessions. A recent study has found that the job training has little to no effect on the earning prospects of your welfare recipients. One politician argues that for this reason, the job-training requirement should be eliminated. Others are not so sure. What do you think?

2.         Assume that utility functions (with diminishing marginal utility) are the same across all individuals, depend on income only, and that the amount of income in the economy is  fixed. An additive social welfare function implies which of the following?

A)  The well-being of the worst off member is maximized.

B)   The sum of individual utilities is maximized.

C)   The marginal utilities of everyone in society should be equalized in the optimal allocation.

D)  No redistribution should occur.

E)   Both b and c are correct.

3.         A Rawlsian social welfare function implies which of the following?

A)  The well-being of the worst off member is maximized.

B)   The sum of individual utilities is maximized.

C)   The marginal utilities of everyone in society are equal.

D)  No redistribution should occur.

E)   Both b and c are correct.

4.         Suppose someone criticizes the federal measure of the poverty line by saying that it      should, but does not, account for Medicaid receipts. This is an example of which of the following criticisms of the federal poverty line?

A)  It is based on an oversimplified definition of family size.

B)   The bundle has changed.

C)   Differences in cost of living across areas are ignored.

D)  It is inconsistent with international measures.

E)   The definition of income is incomplete since it does not include the monetized value of in-kind benefits.

5.         Does taxing the wealthy to give benefits to the poor necessarily increase social welfare? Explain.

6.         Suppose that the government is currently considering whether to implement a childcare subsidy program for low-income families. Is this childcare subsidy different from a      wage subsidy to low-income families with children? Explain.

7.         Suppose someone criticizes the federal measure of the poverty line by saying it should, but does not, account for differences in housing prices faced by different families. This is an example of which of the following criticisms of the federal poverty line?

A)  It is based on an oversimplified definition of family size.

B)   The bundle has changed.

C)   Differences in cost of living across areas are ignored.

D)  It is inconsistent with international measures.

E)   The definition of income is incomplete since it does not include the monetized value of in-kind benefits.

8.         The share of a nation’s total income that accrues to the poor relative to the rich is a measure of which of the following?

A)  the poverty line

B)   relative income inequality

C)   the iron triangle of welfare programs

D)  absolute deprivation

E)   allocative inefficiency

9.         Which of the following describes welfare programs that are provided only to people qualifying on the basis of income and asset levels?

A)  in-kind welfare

B)   categorical welfare

C)   means-tested welfare

D)  non-hedonic welfare

E)   cash welfare

10.       Which of the following describes the paradox of ordeal mechanisms?

A)  Welfare systems not only make the high-income individuals worse off, they reduce the overall well-being of low-income individuals in the long run.

B)   By their making the receipt of welfare benefits less attractive and less generous, it is possible that the worse off can actually be made better off.

C)   By their effectively targeting low-income individuals, those individuals are made worse off for having received welfare because of the corresponding reduction in self-worth.

D)  Welfare programs make the high-income individuals better off, even though they are the ones who are taxed to fund the welfare program.

E)   None of the above is correct.

11.       Which of the following describes welfare programs that deliver certain goods to recipients?

A)  in-kind welfare

B)   categorical welfare

C)   means-tested welfare

D)  non-hedonic welfare

E)   cash welfare

12.       Suppose that welfare is restricted to unmarried mothers who have a least one child. This type of welfare could be best characterized as which of the following?

A)  in-kind welfare

B)   categorical welfare

C)   means-tested welfare

D)  non-hedonic welfare

E)   cash welfare

13.       The cash welfare benefit for individuals with no other income that may be reduced as income increases is referred to as the ____________; the schedule that shows how     welfare benefits will be withheld as other income is earned is the ___________.

A)  benefit guarantee; work requirement

B)  benefit reduction rate; benefit guarantee

C)   work requirement; benefit reduction rate

D)  benefit guarantee; benefit reduction rate

E)   benefit reduction rate; work requirement

14.       Which of the following is true if the benefit reduction rate of a welfare program is reduced?

A)  Total labor supply will go up.

B)   Some who were working may work less.

C)   Total labor supply may go up or down.

D)  Both b and c are correct.

E)   None of the above is correct.

15.       The equity-efficiency tradeoff means that the result of obtaining __________ in equality is to also obtain __________ in the so-called size of the pie.

A)  no change; a decrease

B)   no change; an increase

C)   a decrease; a decrease

D)  an increase; a decrease

E)   none of the above

16.       Suppose that reducing the benefit guarantee for a given benefit reduction rate will definitely encourage work and lower costs but will also lower the amount of        redistribution. This is an example of:

A)  relative income inequality.

B)   the iron triangle of welfare programs.

C)   absolute deprivation.

D)  allocative inefficiency.