Theoretical Tools of Public Finance

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© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber 1 of 43

Theoretical Tools of Public Finance

2.4 Welfare Implications of Benefit Reductions: The TANF Example Continued

2.3 Equilibrium and Social Welfare

2.2 Putting the Tools to Work: TANF and Labor Supply Among Single Mothers

2.1 Constrained Utility Maximization

Chapter 2

2.5 Conclusion

theoretical tools The set oftools designed to understandthe mechanics behind economic decision making.

empirical tools The set oftools designed to analyze dataand answer questions raised by theoretical analysis.

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Constrained Utility Maximization2 . 1

utility function A mathematical function representing an individual’s set of preferences, which translates her well-beingfrom different consumption bundles into units that can be compared in order to determine choice.

constrained utility maximization The process of maximizing the well-being (utility) of an individual, subject to her resources (budget constraint).

models Mathematical or graphicalrepresentations of reality.

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Preferences and Indifference Curves

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indifference curve A graphicalrepresentation of all bundles of goods that make an individualequally well off. Because these bundles have equal utility, an individual is indifferent as towhich bundle he consumes.

Indifference curves have two essential properties, both of which follow naturally from the more-is-better assumption:

1. Consumers prefer higher indifference curves.

2. Indifference curves are always downward sloping.

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Utility Mapping of Preferences

Underlying the derivation of indifference curves is the notion that each individual has a well-defined utility function.

A utility function is some mathematical representation

U = f(X1, X2, X3, …),

where

X1, X2, X3, and so on

are the goods consumed by the individual and

f

is some mathematical function that describes how the consumption of those goods translates to utility.

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Marginal Utility

marginal utility The additionalincrement to utility obtained byconsuming an additional unit ofa good.

This utility function described exhibits the important principle of diminishing marginal utility: the consumption of each additional unit of a good makes an individual less happy than the consumption of the previous unit.

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Marginal Utility

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Marginal Rate of Substitution

marginal rate of substitution(MRS) The rate at which a consumer is willing to trade onegood for another. The MRS is equal to the slope of the indifference curve, the rate at which the consumer will trade the good on the vertical axis for the good on the horizontal axis.

/ M CMRS MU MU

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Marginal Rate of Substitution

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Budget Constraints

budget constraint A mathematical representation of all the combinations of goods an individual can afford to buy if she spends her entire income.

opportunity cost The cost ofany purchase is the next bestalternative use of that money,or the forgone opportunity.

When a person’s budget is fixed, if he buys one thing he is, by definition, reducing the money he has to spend on other things. Indirectly, this purchase has the same effect as a direct good-for-good trade.

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Budget Constraints

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Putting It All Together: Constrained Choice

Marginal analysis, the consideration of the costs and benefits of an additional unit of consumption or production, is a central concept in modeling an individual’s choice of goods and a firm’s production decision.

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The Effects of Price Changes: Substitution and Income Effects

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Income and Substitution Effects

substitution effect Holdingutility constant, a relative rise inthe price of a good will alwayscause an individual to chooseless of that good.

income effect A rise in theprice of a good will typicallycause an individual to chooseless of all goods because herincome can purchase less thanbefore.

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Income and Substitution Effects

normal goods Goods for which demand increases as income rises.

inferior goods Goods for which demand falls as income rises.

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Putting the Tools to Work: TANF and Labor Supply Among Single Mothers

2 . 2

Identifying the Budget Constraint

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2 . 2

The Effect of TANF on the Budget ConstraintEffects of Changes in Benefit Guarantee

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2 . 2

The Effect of TANF on the Budget ConstraintHow Large Will the Labor Supply Response Be?

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Equilibrium and Social Welfare2 . 3

Demand Curves

welfare economics The studyof the determinants of wellbeing,or welfare, in society.

demand curve A curve showing the quantity of a gooddemanded by individuals ateach price.

Determinants of welfareSocial efficiency

Social welfare

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Demand Curves

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Demand Curves

Elasticity of Demand

elasticity of demand The percentage change in the quantity demanded of a good caused by each 1% change in the price of that good.

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Demand Curves

Elasticity of Demand

There are several key points to make about elasticities of demand:

They are typically negative, since quantity demanded typically falls as price rises.

They are typically not constant along a demand curve. A vertical demand curve is one for which the quantity demanded does

not change when price rises; in this case, demand is perfectly inelastic. A horizontal demand curve is one where quantity demanded changes

infinitely for even a very small change in price; in this case, demand is perfectly elastic.

The effect of one good’s prices on the demand for another good is the cross-price elasticity, and with the particular utility function we are using here, that cross-price elasticity is zero. Typically, however, a change in the price of one good will affect demand for other goods as well.

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Supply Curves

supply curve A curve showing the quantity of a good that firms are willing to supply at each price.

marginal productivity The impact of a one unit change in any input, holding other inputs constant, on the firm’s output.

marginal cost The incremental cost to a firm of producing one more unit of a good.

profits The difference between a firm’s revenues and costs, maximized when marginal revenues equal marginal costs.

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Equilibrium

market The arena in which demanders and suppliers interact.

market equilibrium The combinationof price and quantity that satisfies both demand and supply, determined by the interaction of the supply and demand curves.

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Equilibrium

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Social Efficiency

Social efficiency represents the net gains to society from all trades that are made in a particular market, and it consists of two components: consumer and producer surplus.

consumer surplus The benefit that consumers derive from consuming a good, above and beyond the price they paid for the good.

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Social Efficiency

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Producer Surplus

producer surplus The benefit that producers derive from selling a good, above and beyond the cost of producing that good.

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Producer Surplus

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Social Surplus

total social surplus (socialefficiency) The sum of consumersurplus and producer surplus.

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Social Surplus

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Competitive Equilibrium Maximizes Social Efficiency

First Fundamental Theoremof Welfare Economics Thecompetitive equilibrium, wheresupply equals demand, maximizessocial efficiency.

deadweight loss The reductionin social efficiency from denyingtrades for which benefitsexceed costs.

It is sometimes confusing to know how to draw deadweight loss triangles. The key to doing so is to remember that deadweight loss triangles point to the social optimum, and grow outward from there.

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From Social Efficiency to Social Welfare: The Role of Equity

social welfare The level ofwell-being in society.

Second Fundamental Theorem of Welfare Economics Society can attain any efficient outcome by suitably redistributing resources among individuals and then allowing them to freely trade.

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equity–efficiency trade-offThe choice society must makebetween the total size of theeconomic pie and its distributionamong individuals.

social welfare function (SWF) A function that combines the utility functions of all individuals into an overall social utility function.

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Utilitarian SWF

With a utilitarian social welfare function, society’s goal is to maximize the sum of individual utilities:

SWF = U1 + U2 + . . . + UN

The utilities of all individuals are given equal weight, and summed to get total social welfare.

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Rawlsian Social Welfare Function

John Rawls suggested that society’s goal should be to maximize the well- being of its worst-off member. The Rawlsian SWF has the form:

SW = min (U1, U2, . . ., UN)

Since social welfare is determined by the minimum utility in society, social welfare is maximized by maximizing the well-being of the worst-off person in society.

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Choosing an Equity Criterion

commodity egalitarianismThe principle that society shouldensure that individuals meet aset of basic needs, but that beyond that point income distribution is irrelevant.

equality of opportunity Theprinciple that society shouldensure that all individuals haveequal opportunities for success,but not focus on the outcomesof choices made.

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Welfare Implications of Benefit Reductions: The TANF Example Continued

2 . 4

Efficiency

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Welfare Implications of Benefit Reductions: The TANF Example Continued

2 . 4

Equity

Governments have programs such as TANF because their citizens care not only about efficiency but also about equity, the fair distribution of resources in society. For many specifications of social welfare, the competitive equilibrium, while being the social efficiency-maximizing point, may not be the social welfare-maximizing point.

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Conclusion2 . 5

This chapter has shown both the power and the limitations of the theoretical tools of economics.

On the one hand, by making relatively straightforward assumptions about how individuals and firms behave, we are able to address complicated questions such as how TANF benefits affect the labor supply of single mothers, and the implications of that response for social welfare.

On the other hand, while we have answered these questions in a general sense, we have been very imprecise about the potential size of the changes that occur in response to changes in TANF benefits.

Theoretical Tools of Public Finance

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