309 Social Security Fall12

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ECO309: Public FinanceChapters 11-12: Social Security and Income Redistribution

Tanvir Hussain

1

1 Assistant ProfessorDepartment of Economics and Social Sciences

BRAC University

Tanvir Hussain (THN) Public Finance 1 / 14
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What is Available in the Market?

Annuity pay a lump-sum premium and, in return, receive a fixed annual amount forever.

Understandably, larger the premium, bigger the annual payment.

Life Insurance pay an annual amount to the insurance company and receive a one time(lump-sum) payment upon death.

Both the above are fairly similar they are both used as tools for consumption smoothing.Assuming a certain degree of risk aversion, an individual wants to reduce consumption during

high-earning years in order to increase consumption possibilities during low-earning years.1

Obviously, there will be problems of asymmetric information in these markets. One majorproblem is that of adverse selection:

In case of annuities, the expected profit for the seller depends, critically, on what his/her belief (oraverage estimate) about the buyers life expectancy. The buyer will always know more about his/her

true life expectancy. In time, the seller will only confront a market full of people with higher thanaverage life expectancies.

Read about other justifications from the book, e.g., lack of foresight and paternalism.

1Recall, from macroeconomics, the lifecycle-permanent income hypothesis.

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Distributional Objectives

2. Intra-generational redistribution of income:

(a) Life expectancy issues African-Americans gain less lifetime benefits than comparable Whites

(b) Single males gain lower lifetime benefits than single-earner couples(c) Double-earner couples gain lower lifetime benefits than single-earner couples

Are these redistributive goals are desirable for the society in general? Depends on valuejudgements.

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Intertemporal Budget Constraint

A simple two period model, period 0 (present) and period 1 (future). Consumption today is c0and consumption in future is c1. A is the current endowment point. Lifetime (or intertemporal)budget constraint is defined by:

c0+ c11 +r

=I0+ I11 +r

lifetime consumption must equal lifetime income

where, r is the market interest rate. This budget line is shown below:

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Figure 1: Intertemporal budget constraint

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Intertemporal Choice

Optimality depends on the location of intertemporal indifference curves (along the budget line).

An optimal to the left and above A means consumer saves in period 0

An optimal to the right and below A means consumer borrows in period 0

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Intertemporal Choice with Social Security

How does the introduction of social security payment (or tax) affect things? The consumer has tomake social security contribution equal to $T now, which means the endowment point, effectively,moves to point R. The optimal could, still, be at point E1, but, one major difference from before.

With social security, private savings is only (IT0 c

0), which is less than before.

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Figure 3: Intertemporal choice and crowding out

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Pattern of Effects

Literature suggests that, in the presence of social security, the following behavioral effects havebeen observed among people:

1 Wealth substitution effect: The crowding out of private savings due to the presence ofsocial security is known as the wealth substitution effect. In figure 3, private savings isreduced (or crowded out) by the amount (I0 IT0 ) because of social security.

2 Retirement effect: social security may induce people to retire early. Therefore, they wouldwant to save more to finance a higher number of retirement years.

3 Bequest effect: parents may have bequest motive to leave higher savings for future

generations. Parents may recognize the fact that childrens social security payments are justdistributing their current incomes to future generations.

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Income Redistribution

This section focuses on the distribution of income; more specifically, should the government get

involved in income redistribution policies? Economists have displayed some tendency to stayaway from addressing concerns about distributional issues; but, two obvious problems with thisway of thinking:

1 Decisions based (purely) on the grounds of economic efficiency will not always be desirablefrom a normative standpoint.

2 More importantly, economists can ignore normative (or value judgement) questions, but,policy makers (or politicians) cannot.

So, at some point, economists do have to look at normative issues, otherwise, their quantitativeanalyses alone will not get the policy makers attention. At a minimum, economists should beable to forecast the distributional impacts of their prescribed policies.

Read the textbook section on distribution and measurement of income. It describes some ofthe pertinent features of the United States Census data on income and associated indicators.

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Income Redistribution: Rationales

Utilitarian view: standard theory of welfare economics suggests that societys welfare

depends on the welfare of individual members:2

W =F(U1, U2, ......, Un) (2)

where, Ui is the utility function of individual iwith a total ofn individuals living in thesociety. The utilitarian view argues that F(Ui) >0, that is, an increase in any one personsutility will increase overall welfare (ceteris paribus).

A special case of equation(2)is the additively separable social welfare function:

W =U1+ U2+ ......+Un (3)

Suppose the governments problem is to:

Maximize: W =n

i=1

Ui (4)

2Assuming a social welfare function can be reached based on individual preferences.

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Government Welfare Maximization

Under the following set of assumptions, maximization of the additive social welfare function yieldsclear results:

1 Utility functions are identical across individuals, where, utility only depends on income.Definitely, a troublesome assumption; always impossible to determine whether individualshave identical utility functions. One defense is that the government should act as ifindividual functions are identical.

2 Each utility function exhibitsdiminishing marginal utility of income. A technical assumptionnecessary for redistributive policies to have any impact on social welfare.

3 Aggregate income (total endowment) is fixed for the society as a whole. Another technicalassumption, simply asserts that the size of the pie is not changing as government

redistributing income.

Assuming the above are true, the maximization problem in equation (4) yields the result that thegovernment should redistribute income so as to attain complete equality of income acrossindividuals.

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Optimal Distribution of Income

Consider a simple two person society with Paul and Peter. The horizontal distance (OO)measures the total available income, that is, any point along the horizontal axis shows acombination of Pauls and Peters income. The two vertical axes measure the marginal utilities,

which are both downward sloping. And, because the utility functions are identical, the MUPetercurve is a mirror image of the MUPaul curve.

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O i l Di ib i d
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Optimal Distribution contd.

Imagine that, initially, Paul has income Oa and Peter has income Oa, which means Peter is

richer than Paul. Are there possibilities of increasing social welfare by way redistributingincome between Peter and Paul?

Consider that the government is thinking of redistributing income abfrom Paul to Peter.What are the implications? Geometrically:

Pauls gain in total utility = area abfePeters loss in total utility = area abdc

Net gain in social welfare = (abfe abdc) = area cefd

Individually, of course, Peter is worse off and Paul is better off, but, social welfare isincreasing. Social welfare continues to change (increase or decrease) until income I isreached where:

MUPaul = MUPeter

IncomePaul = IncomePeter

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309 Social Security Fall12

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