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2.1 Constrained Utility
Maximization
Theoretical Tools of
Public Finance
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
2.5 Conclusion
Public Finance and Public Policy Jonathan Gruber Third Edition Copyright © 2010 Worth Publishers
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CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
Addressing when should Govt. intervene and
How should govt. intervene
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. ---quantitative impacts
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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
 FIGURE 2-1
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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
 FIGURE 2-2
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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
 FIGURE 2-4
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2.1
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
Constrained Utility Maximization
Budget Constraints
 FIGURE 2-5
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2.1
Constrained Utility Maximization
Putting It All Together: Constrained Choice
 FIGURE 2-6
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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CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
Constrained Utility Maximization
The Effects of Price Changes: Substitution and Income Effects
 FIGURE 2-7
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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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2.2
CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
Putting the Tools to Work: TANF and Labor Supply
among Single Mothers
Identifying the Budget Constraint
 FIGURE 2-8
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2.2
CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
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
 FIGURE 2-9
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2.2
CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
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?
 FIGURE 2-10
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2.2
CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
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?
 FIGURE 2-11
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CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
2.3
Equilibrium and Social Welfare
welfare economics The study
of the determinants of well-being,
or welfare, in society.
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
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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CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
2.3
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
 FIGURE 2-13
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CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
2.3
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
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
Equilibrium and Social Welfare
Social Efficiency
Consumer Surplus
 FIGURE 2-14
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2.3
Equilibrium and Social Welfare
Social Efficiency
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
Equilibrium and Social Welfare
Social Efficiency
Producer Surplus
 FIGURE 2-15
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2.3
Equilibrium and Social Welfare
Social Efficiency
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 Efficiency
Social Surplus
 FIGURE 2-16
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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 preventing 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
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 worstoff 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.
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2.4
CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
Welfare Implications of Benefit Reductions: The TANF
Example Continued
Efficiency
 FIGURE 2-17
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2.4
CHAPTER 2 ■ THEORETICAL TOOLS OF PUBLIC FINANCE
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.
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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.
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