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Chapter 2 Theoretical Tools of Public Finance
Theoretical Tools of Public Finance
Chapter 2
2.1 Constrained Utility
Maximization
2.2 Putting the Tools to Work:
TANF and Labor Supply
Among Single Mothers
2.3 Equilibrium and Social
Welfare
2.4 Welfare Implications of
Benefit Reductions: The
TANF Example Continued
theoretical tools The set of
tools designed to understand
the mechanics behind
economic decision making.
empirical tools The set of
tools designed to analyze data
and answer questions raised
by theoretical analysis.
2.5 Conclusion
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
utility function A mathematical function
representing an individual’s set of
preferences, which translates her well-being
from 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 graphical
representations of reality.
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Preferences and Indifference Curves
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Preferences and Indifference Curves
indifference curve A graphical
representation of all bundles of
goods that make an individual
equally well off. Because these
bundles have equal utility, an
individual is indifferent as to
which 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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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Preferences and Indifference Curves
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
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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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Utility Mapping of Preferences
Marginal Utility
marginal utility The additional
increment to utility obtained by
consuming an additional unit of
a 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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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Utility Mapping of Preferences
Marginal Utility
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Utility Mapping of Preferences
Marginal Rate of Substitution
marginal rate of substitution
(MRS) The rate at which a
consumer is willing to trade one
good 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.
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Utility Mapping of Preferences
Marginal Rate of Substitution
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
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 of
any purchase is the next best
alternative 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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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
Budget Constraints
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
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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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
The Effects of Price Changes: Substitution and Income
Effects
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
The Effects of Price Changes: Substitution and Income
Effects
Income and Substitution Effects
substitution effect Holding
utility constant, a relative rise in
the price of a good will always
cause an individual to choose
less of that good.
income effect A rise in the
price of a good will typically
cause an individual to choose
less of all goods because her
income can purchase less than
before.
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2.1
Chapter 2 Theoretical Tools of Public Finance
Constrained Utility Maximization
The Effects of Price Changes: Substitution and Income
Effects
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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Chapter 2 Theoretical Tools of Public Finance
2.2
Putting the Tools to Work: TANF and Labor Supply
Among Single Mothers
Identifying the Budget Constraint
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Chapter 2 Theoretical Tools of Public Finance
2.2
Putting the Tools to Work: TANF and Labor Supply
Among Single Mothers
The Effect of TANF on the Budget Constraint
Effects of Changes in Benefit Guarantee
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Chapter 2 Theoretical Tools of Public Finance
2.2
Putting the Tools to Work: TANF and Labor Supply
Among Single Mothers
The Effect of TANF on the Budget Constraint
How Large Will the Labor Supply Response Be?
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Chapter 2 Theoretical Tools of Public Finance
2.2
Putting the Tools to Work: TANF and Labor Supply
Among Single Mothers
The Effect of TANF on the Budget Constraint
How Large Will the Labor Supply Response Be?
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
welfare economics The study
of the determinants of wellbeing,
or welfare, in society.
Determinants of welfare
Social efficiency
Social welfare
Demand Curves
demand curve A curve
showing the quantity of a good
demanded by individuals at
each price.
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Demand Curves
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Equilibrium
market The arena in which
demanders and suppliers interact.
market equilibrium The combination
of price and quantity that satisfies both
demand and supply, determined by the
interaction of the supply and demand
curves.
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Equilibrium
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Social Efficiency
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Producer Surplus
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Social Surplus
total social surplus (social
efficiency) The sum of consumer
surplus and producer surplus.
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Social Surplus
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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Competitive Equilibrium Maximizes Social Efficiency
First Fundamental Theorem
of Welfare Economics The
competitive equilibrium, where
supply equals demand, maximizes
social efficiency.
deadweight loss The reduction
in social efficiency from denying
trades for which benefits
exceed 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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
From Social Efficiency to Social Welfare: The Role of
Equity
social welfare The level of
well-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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
From Social Efficiency to Social Welfare: The Role of
Equity
equity–efficiency trade-off
The choice society must make
between the total size of the
economic pie and its distribution
among 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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
From Social Efficiency to Social Welfare: The Role of
Equity
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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
From Social Efficiency to Social Welfare: The Role of
Equity
Rawlsian Social Welfare Function
John Rawls suggested that society’s goal should be to maximize the wellbeing 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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2.3
Chapter 2 Theoretical Tools of Public Finance
Equilibrium and Social Welfare
Choosing an Equity Criterion
commodity egalitarianism
The principle that society should
ensure that individuals meet a
set of basic needs, but that beyond
that point income distribution is
irrelevant.
equality of opportunity The
principle that society should
ensure that all individuals have
equal opportunities for success,
but not focus on the outcomes
of choices made.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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Chapter 2 Theoretical Tools of Public Finance
2.4
Welfare Implications of Benefit Reductions: The
TANF Example Continued
Efficiency
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Chapter 2 Theoretical Tools of Public Finance
2.4
Welfare Implications of Benefit Reductions: The
TANF Example Continued
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.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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2.5
Chapter 2 Theoretical Tools of Public Finance
Conclusion
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.
© 2007 Worth Publishers Public Finance and Public Policy, 2/e, Jonathan Gruber
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