Chapter 2
Theoretical Tools of
Public Finance
Introduction
Theoretical Tools of Public Finance
„ Theoretical tools are a set of tools used to
understand economic decision making. They are
primarily graphical and mathematical.
„ Empirical tools allow you to examine the theory
with data. (will do in chapter 3)
Jonathan Gruber
Public Finance and Public Policy
Aaron S. Yelowitz - Copyright 2005 © Worth Publishers
CONSTRAINED UTILITY
MAXIMIZATION
„ Constrained utility maximization means that
all decisions are made in order to maximize the
well-being of the individual, subject to his available
resources.
„ Utility maximization involves preferences and a budget
constraint.
„ One of the key assumptions about preferences is
non-satiation–that “more is preferred to less.”
This bundle of goods gives the
highest utility, subject to the budget
constraint.
QCD
(quantity of
CDs)
3
This indifference curve
gives much higher
utility, but is not
attainable.
Constrained Utility Maximization:
Constrained choice
„ What is the highest indifference curve that an
individual can reach, given a budget constraint?
„ Preferences tells us what a consumer wants, and the
budget constraint tells us what a consumer can
actually purchase.
„ This leads to utility maximization, shown
graphically, in Figure 8.
8
Constrained Utility Maximization:
Putting it together: Constrained choice
„ In this figure, the utility maximizing choice occurs where the
indifference curve is tangent to the budget constraint.
2
Y = PM Q M + PC QC
1
This indifference curve is not
utility-maximizing, because
there are bundles that give
higher utility.
0
Figure 8
1
2
3
QM (quantity
of movies)
„ This implies that the slope of the indifference curve equals
the slope of the budget constraint, where the marginal rate
of substitution equals the ratio of prices:
MRS = −
MU M
P
=− M
MU C
PC
Utility Maximization
1
The Effects of Price Changes:
Substitution and income effects
QCD
(quantity of
CDs)
3
Andrea
Increase
is worse
in PM rotates
off, andthe
consumes
budget
constraint
lessinward
movies.
on x-axis.
„ Consider a typical price change in our framework:
„ Increase the price of movies, PM.
2
„ This rotates the budget constraint inward along the
x-axis.
1
„ Figure 10 illustrates this.
0
Figure 10
The Effects of Price Changes:
Substitution and income effects
1
2
3
QM (quantity
of movies)
Increase in the Price of Movies
QCD
(quantity of
CDs)
3
Movement from one indifference
curve to the other is the income effect.
„ A change in price consists of two effects:
„ Substitution effect–change in consumption due to
Movement along the indifference
curve is the substitution effect
2
change in relative prices, holding utility constant.
„ Income effect–change in consumption due to
1
feeling “poorer” after price increase.
„ Figure 11 illustrates this.
0
Decline in QM
due to income
effect
PUTTING THE TOOLS TO WORK
TANF and labor supply among single mothers
„ TANF is “Temporary Assistance for Needy
Families.”
„ Cash welfare for poor families, mainly single
mothers.
„
For example, in New Mexico, family of three
receives $389 per month.
1
2
3
QM (quantity
of movies)
Decline in QM due to
substitution effect
PUTTING THE TOOLS TO WORK
Identifying the budget constraint
„ What does the budget constraint look like?
„ Assume the person can work up to 2000 hours per
year, at a wage rate of $10 per hour, and that TANF
is not yet in place.
„ Price of food is $1 per unit.
„ Assume the two “goods” in utility maximization
problem are leisure and food consumption.
„ Whatever time is not devoted to leisure is spent
working and earning money.
2
PUTTING THE TOOLS TO WORK
Identifying the budget constraint
„ The “price” of one hour of leisure is the hourly
wage rate.
„ Creates a direct tradeoff between leisure and food:
each hour of work brings her 10 units of food.
„ Figure 12 illustrates this.
Food
consumption
(QF)
20,000
1,000 hours of leisure, 10,000 units of food
15,000
1,500 hours of leisure, 5,000 units of food
10,000
Leisure is a “good” just as movies
were … more is preferred to less.
5,000
0
Figure 12
PUTTING THE TOOLS TO WORK
The effect of TANF on the budget constraint
„ Now, let’s introduce TANF into the framework.
TANF has two key features:
„ Benefit guarantee, G – amount that a recipient with
$0 earnings gets.
„
The slope of the
budget constraint is
–w/PF, or -10.
500 hours of leisure,
15,000 units of food
500
1000
1500
2000
Leisure
(hours)
Leisure is a “good” and labor is a “bad.”
PUTTING THE TOOLS TO WORK
The effect of TANF on the budget constraint
„ Assume that benefit guarantee, G, is $5,000 per year.
„ Assume the benefit reduction rate, τ, is 50%.
„ Figure 13 illustrates this.
Benefit reduction rate, t – rate at which benefit
guarantee falls as earnings increases.
Slope on this section of the
budget constraint is -10.
Food
consumption
(QF)
20,000
At 1,000 hours
of work, TANF
benefits fall to
zero.
15,000
PUTTING THE TOOLS TO WORK
The effect of changes in the benefit guarantee
The benefit reduction rate of 50%
reduces the guarantee as earnings
increase. Green area represents
new bundles from TANF.
Slope on this section of the
budget constraint is -5.
10,000
$5000 guarantee
means that a recipient
could now consume
(2000,5000).
5,000
0
Figure 13
500
1,000
1,500
2,000
„ One possible “policy experiment” is reducing the
benefit guarantee level G.
„ What happens when G falls from $5,000 to $3,000,
holding all other parameters constant?
„ Figure 14 illustrates this.
Leisure
(hours)
Introduce Temporary Assistance to Needy Families
3
Food
consumption
(QF)
20,000
PUTTING THE TOOLS TO WORK
How large will the labor supply response be?
The earnings level where TANF
ends falls from $10,000 to $6,000.
15,000
„ What is the expected labor supply response to such
Lowering the guarantee
reduces the initial non-working
bundle to (2000,3000).
10,000
a policy change?
„ It depends on where the single mother initially was
on the budget constraint.
6,000
„ (1) If she initially earned less than $6,000 and more
5,000
3,000
0
Figure 14
Food
consumption
(QF)
20,000
500
1,000 1,400 1,500
2,000
Leisure
(hours)
than $5000 per year, the policy change involves only
an income effect, not a substitution effect.
„ Figure 15 illustrates this.
Lower the Benefit Guarantee
PUTTING THE TOOLS TO WORK
How large will the labor supply response be?
The effective wage rate does
not change for this person.
„ (2) If she initially earned between $6,000 and
15,000
If leisure is a normal good, the
income effect would reduce
leisure (increase work).
10,000
6,000
5,000
3,000
0
Figure 15
500
1,000 1,400
2,000
$10,000 per year, the policy change involves both an
income and substitution effect.
„ The substitution and income effects go in the same
direction.
„ Figure 16 illustrates this.
Leisure
(hours)
Policy Change Generates Income Effect Only
Food
consumption
(QF)
PUTTING THE TOOLS TO WORK
How large will the labor supply response be?
20,000
The effective wage rate
changes for this person.
„ Economic theory clearly suggests that such a benefit
15,000
The change in labor supply
involves both income and
substitution effects.
10,000
6,000
5,000
3,000
0
Figure 16
500
1,000 1,400
2,000
reduction will increase labor supply, but does not
speak to the magnitude of the response.
„ (3) For example, some welfare recipients who were
not initially working continue to choose not to
work.
„ Figure 17 illustrates this.
Leisure
(hours)
Both Income and Substitution Effects From Policy
4
Food
consumption
(QF)
20,000
This person was initially
out of the labor force.
15,000
She continues to stay out
of the labor force, even
with the benefits reduction.
10,000
6,000
PUTTING THE TOOLS TO WORK
How large will the labor supply response be?
„ The actual magnitude of the labor supply response
therefore depends on the preferences of various
welfare recipients.
„
5,000
To the extent the preferences are more like the first
two cases, the larger the labor supply response.
„ Thus, theory alone cannot say whether this policy
3,000
change will increase labor supply, or by how much.
„
0
Figure 17
500
1,000 1,400
2,000
Leisure
(hours)
No Labor Supply Response To Policy Change
EQUILIBRIUM AND SOCIAL WELFARE
„ Welfare economics is the study of the
PM
Intersection of supply and
demand is equilibrium.
EQUILIBRIUM AND SOCIAL WELFARE
Equilibrium
„ In equilibrium, we horizontally sum individual demand
determinants of well-being, or welfare, in society.
„ This involves a normative question: Does the policy
change make society as a whole better off or not?
„ This depends on:
„ Determinants of social efficiency, or size of the
economic “pie.”
„ Redistribution.
Supply
curve of
movies
curves to get aggregate demand.
„ We also horizontally sum individual supply curves to
get aggregate supply.
„ Competitive equilibrium represents the point at
which both consumers and suppliers are satisfied
with the price/quantity combination.
„ Figure 21 illustrates this.
EQUILIBRIUM AND SOCIAL WELFARE
Social efficiency
„ Measuring social efficiency is computing the potential
PM,3
size of the economic pie. It represents the net gain
from trade to consumers and producers.
PM,2
PM,1
Demand
curve for
movies
QM,3
Figure 21
Must analyze available data on single mothers to
figure out the magnitude.
QM,2
QM,1
QM
Equilibrium with Supply and Demand
5
EQUILIBRIUM AND SOCIAL WELFARE
PM
Supply
curve of
movies
Social efficiency
„ Consumer surplus is the benefit that consumers
derive from a good, beyond what they paid for it.
„ Each point on the demand curve represents a
“willingness-to-pay” for that quantity.
„ Figure 22 illustrates this.
The
The consumer
total consumer
surplus
surplus
at Q* is
is
the area between
this triangle.
the demand
curve and market price.
P*
Demand
curve for
movies
0
Figure 22
EQUILIBRIUM AND SOCIAL WELFARE
1
2
Q*
QM
Deriving Consumer Surplus
PM
Supply
curve of
movies
Social efficiency
„ Consumer surplus is determined by market price
Consumer surplus is
larger when demand curve
is more inelastic.
and the elasticity of demand:
With inelastic demand, demand curve is more
vertical, so surplus is higher.
„ With elastic demand, surplus is lower.
„
P*
Demand
curve for
movies
„ Figure 23 illustrates this.
0
Figure 23
EQUILIBRIUM AND SOCIAL WELFARE
1
2
Q*
Consumer Surplus and Inelastic Demand
PM
Supply
curve of
movies
Social efficiency
„ Producer surplus is the benefit derived by
producers from the sale of a unit above and beyond
their cost of producing it.
„ Each point on the supply curve represents the
marginal cost of producing it.
„ Figure 24 illustrates this.
QM
The producers
total producer’s
surplus
surplus
at Q* is
the area between
this triangle.
the demand
curve and market price.
P*
Demand
curve for
movies
0
Figure 24
1
2
Q*
QM
Producer Surplus
6
EQUILIBRIUM AND SOCIAL WELFARE
EQUILIBRIUM AND SOCIAL WELFARE
Social efficiency
Social efficiency
„ Similar to consumer surplus, producer surplus is
determined by market price and the elasticity of
supply:
With inelastic supply, supply curve is more vertical,
so producer surplus is higher.
„ With elastic supply, producer surplus is lower.
„
PM
Providing the first unit
gives a great deal of
surplus to “society.”
Supply
curve of
movies
Social
The area
efficiency
between
is maximized
the supplyat
*, and iscurves
and Q
demand
from
zero to
the sum
of the
Q* represents
the surplus.
consumer
and producer
surplus.
P*
This area represents the
social surplus from
producing the first unit.
0
Figure 25
Demand
curve for
movies
Q*
1
QM
„ The total social surplus, also known as “social
efficiency,” is the sum of the consumer’s and
producer’s surplus.
„ Figure 25 illustrates this.
EQUILIBRIUM AND SOCIAL WELFARE
Competitive equilibrium maximizes social efficiency
„ The First Fundamental Theorem of Welfare
Economics states that the competitive equilibrium,
where supply equals demand, maximizes social
efficiency.
„ Any quantity other than Q* reduces social efficiency,
or the size of the “economic pie.”
„ Consider restricting the price of the good to P´<P*.
„ Figure 26 illustrates this.
Social Surplus
This triangle represents
lost surplus to society,
known as “deadweight
loss.”
PM
Supply
curve of
movies
EQUILIBRIUM AND SOCIAL WELFARE
Competitive equilibrium maximizes social efficiency
„ A policy like price controls creates deadweight
With such a price
restriction, the quantity
falls to Q´, and there is
excess demand.
P*
The social
surplus
from Q’ is P´
this area,
consisting
of a larger
consumer
and
smaller
producer
surplus.
Figure 26
loss, the reduction in social efficiency by restricting
quantity below the competitive equilibrium.
Demand
curve for
movies
Q´
Q*
QM
Deadweight Loss from a Price Floor
7
EQUILIBRIUM AND SOCIAL WELFARE
EQUILIBRIUM AND SOCIAL WELFARE
The role of equity
The role of equity
„ Societies usually care not only about how much
surplus there is, but also about how it is distributed
among the population.
„ Social welfare is determined by both criteria.
„ The Second Fundamental Theorem of Welfare
Economics states that society can attain any
efficient outcome by a suitable redistribution of
resources and free trade.
„ In reality, society often faces an equity-efficiency
tradeoff.
„ Society’s tradeoffs of equity and efficiency are
models with a Social Welfare Function.
„ This maps individual utilities into an overall social
utility function.
EQUILIBRIUM AND SOCIAL WELFARE
EQUILIBRIUM AND SOCIAL WELFARE
The role of equity
The role of equity
„ The utilitarian social welfare function is:
„ Utilitarian SWF is defined in terms of utility, not
SWF = ∑ U i
„ Society not indifferent between giving $1 of income
dollars.
i
„ The utilities of all individuals are given equal weight.
to rich and poor; rather indifferent between one util
to rich and one util to poor.
„ Implies that government should transfer from
person 1 to person 2 as long as person 2’s gain is
bigger than person 1’s loss in utility.
EQUILIBRIUM AND SOCIAL WELFARE
EQUILIBRIUM AND SOCIAL WELFARE
The role of equity
The role of equity
„ Utilitarian SWF is maximized when the marginal
utilities of everyone are equal:
„ The Rawlsian social welfare function is:
MU1 = MU 2 =... = MU i
SWF = min(U1 , U 2 ,..., U N )
„ Thus, society should redistribute from rich to poor
„ Societal welfare is maximized by maximizing the
if the marginal utility of the next dollar is higher to
the poor person than to the rich person.
well-being of the worst-off person in society.
„ Generally suggests more redistribution than the
utilitarian SWF.
8
WELFARE IMPLICATIONS OF BENEFIT
REDUCTIONS: TANF continued
Wage
Equilibrium
Inefficient,with
butgenerous
entails
substantial
TANFredistribution.
benefit.
„ Efficiency and equity considerations in introducing
or cutting TANF benefits.
„ In a typical labor supply/labor demand framework,
these changes shift the labor supply curve for single
parents.
„ Figure 27 illustrates this.
Labor
supply
Labor
supply
Labor
supply
Equilibrium with no
government intervention,
no deadweight loss.
w3
w2
w1
Labor
demand
H3
Figure 27
H2
H1
Hours
worked
Market Equilibrium with Labor Supply and Demand
WELFARE IMPLICATIONS OF BENEFIT
REDUCTIONS: TANF continued
„ Different policies involve different deadweight loss
triangles, but also different levels of redistribution
for the poor.
„ SWF helps determine the right policy for society.
9