Theoretical Tools of Public
Economics
Part-2
Previous Lecture
• Definitions and Properties
– Utility functions
• Marginal utility: positive (negative) if x is a ‘good’
(‘bad’)
• Diminishing marginal utility
– Indifferences curves
• Downward sloping
• Consumers prefer higher indifference curves
• Do not intersect
Previous Lecture
• Definitions and Properties
– Optimization with constraints
• Utility maximization subject to a budget constraint
Application in Public Economics
(TANF Example-Chapter 2.2)
– Temporary Assistance to Needy Families:
provides a monthly support check to families
with incomes below a threshold level that
varies by state.
– Largely targeted to single-female-headed
households with children.
Application in Public Economics
(TANF Example-Chapter 2.2)
– Suppose Joelle is a single mother who
spends all of her earnings and TANF
benefits on food for her and her children
(consumption denoted by C)
– The cost of working more is spending less
time with her family (time worked denoted by
W or leisure-time denoted by L)
Application in Public Economics
(TANF Example-Chapter 2.2)
– Can use
1. Consumption (C) and time-worked (W): one good
and one bad
2. Consumption (C) and leisure-time (L): two goods
– We will use the second approach and then
calculate the time-worked by subtracting the
leisure-time from the total work hours.
Application in Public Economics
(TANF Example-Chapter 2.2)
– Assume that Joelle can work a maximum of
2000 hours per year at $10/hour.
– Assume further that a unit of food costs $1.
Application in Public Economics
(TANF Example-Chapter 2.2)
•
Budget constraint without TANF
–
With the first approach (using C and W)
C ≤ 10W
Application in Public Economics
(TANF Example-Chapter 2.2)
•
Budget constraint without TANF
–
With the second approach (using C and L)
C ≤ 10(2000 − L )
C + 10 L ≤ 20000
–
In other words, the price of leisure is $10/hour.
Application in Public Economics
(TANF Example-Chapter 2.2)
• The budget constraint without TANF
Application in Public Economics
(TANF Example-Chapter 2.2)
• The budget constraint under TANF
– Scenario-1: Guarantee of $5000 and 50% reduction
rate
Application in Public Economics
(TANF Example-Chapter 2.2)
•
Budget constraints under TANF (Scenario-1)
If
W ≤ 1000
or
1000 < L ≤ 2000
C ≤ 5000 + 10W − 0.5(10W )
C ≤ 5000 + 5(2000 − L )
C + 5 L ≤ 15000
Application in Public Economics
(TANF Example-Chapter 2.2)
•
Budget constraints under TANF (Scenario-1)
If W > 1000 or
0 < L ≤ 1000
C ≤ 10W
C + 10 L ≤ 20000
Application in Public Economics
(TANF Example-Chapter 2.2)
• The budget constraint under TANF
– Scenario-2: Guarantee of $3000 and 50% reduction
rate
Application in Public Economics
(TANF Example-Chapter 2.2)
•
Budget constraints under TANF (Scenario-2)
If
W ≤ 1400
or
1400 < L ≤ 2000
C ≤ 3000 + 10W − 0.5(10W )
C ≤ 3000 + 5(2000 − L )
C + 5 L ≤ 13000
Application in Public Economics
(TANF Example-Chapter 2.2)
•
Budget constraints under TANF (Scenario-2)
If
W > 600 or 0 < L ≤ 600
C ≤ 10W
C + 10 L ≤ 20000
Application in Public Economics
(TANF Example-Chapter 2.2)
•
What if we switch from Scenario-1 to
Scenario-2?
–
–
Substitution effects
Income effects
Application in Public Economics
(TANF Example-Chapter 2.2)
Application in Public Economics
(TANF Example-Chapter 2.2)
•
How do we calculate the magnitude of the impact of
the switch from Scenario-1 to Scenario-2?
Assume that Joelle’s utility function takes the following
forms
•
–
Case 1:
U (C , L ) = 100 ln(C ) + 175 ln( L )
–
Case 2:
U (C , L ) = 75 ln(C ) + 300 ln( L )
–
Case 3:
U (C , L ) = 300 ln(C ) + 75 ln( L )
Application in Public Economics
(TANF Example-Chapter 2.2)
• Case-1
Application in Public Economics
(TANF Example-Chapter 2.2)
• Case-2
Equilibrium and Social Welfare
(Chapter 2.3)
•
Now that we examined the individual level,
what happens at the aggregate level?
–
How does the aggregate labor supply change with
TANF among low income families?
Equilibrium and Social Welfare
(Chapter 2.3)
•
Welfare economics: the study of determinants
of well-being, or welfare, in society.
Equilibrium and Social Welfare
(Chapter 2.3)
•
How do we determine social welfare?
–
First we define the determinants of social efficiency
(the size of the economic pie),
•
•
•
–
Demand curves
Supply curves
Equilibrium
Then we discuss how to introduce equality (how to
distribute the pie)
•
•
Social welfare function
How to choose the social welfare function?
Equilibrium and Social Welfare
Demand Curves
•
Demand curve: A curve showing the
aggregate quantity of a good demanded by
individuals at each price.
Equilibrium and Social Welfare
Demand Curves
Equilibrium and Social Welfare
Demand Curves
•
Elasticity of demand: The percentage change
in the quantity demanded of a good caused by
each 1% change in the price of that good.
Equilibrium and Social Welfare
Demand Curves
•
Elasticity of demand:
–
–
–
–
They are typically negative, since quantity demanded typically
falls as price rises.
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.
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.
–
Analogous to the utility maximization problem
Equilibrium and Social Welfare
Supply Curves
•
Analogous to utility maximization
–
Utility functions Profit functions
•
Profit function:
–
–
–
Total revenue (p*q(K,L)) – Total cost (C(q(K,L))
Price*Production function – Cost function
Maximize with respect to goods Maximize with
respect to inputs and outputs
•
q: output, K (capital) and L (labor) input
Equilibrium and Social Welfare
Supply Curves
•
Analogous to utility maximization
–
Marginal utility Marginal productivity
•
Marginal productivity of K: Keeping all other inputs, the
change in output as a result of a unit change in capital
∂
MPK =
q( K , L )
∂K
–
Diminishing marginal utility Diminishing marginal
productivity
∂
MPK < 0
∂K
Equilibrium and Social Welfare
Supply Curves
•
The optimum quantity of output is achieved at
the point where marginal revenue equals
marginal cost.
–
•
Marginal cost: The incremental cost to a firm of
producing one more unit of a good.
(In a competitive market), All firms with initial
marginal costs lower than the market price will
produce until their marginal costs equal the
market price.
Equilibrium and Social Welfare
Market 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 between
the supply and demand curves.
Equilibrium and Social Welfare
Market Equilibrium
Equilibrium and Social Welfare
Social Efficiency
•
Consumer surplus: the gain to consumers
from trades in a market for consumer goods.
Equilibrium and Social Welfare
Social Efficiency
•
Produces surplus: the benefit that producers
derive from selling a good, above and beyond
the cost of producing that good.
Equilibrium and Social Welfare
Social Efficiency
•
Social surplus: the sum of consumer surplus
and producer surplus
Equilibrium and Social Welfare
Social Efficiency
•
First Fundamental Theorem of Welfare
Economics: the competitive equilibrium, where
supply equals demand, maximizes social
surplus (social efficiency).
Equilibrium and Social Welfare
Social Welfare
•
Social welfare: the level of social well-being in
society; determined both by social efficiency
(the size of the economic pie) and the
equitable distribution of society’s resources
(the distribution of the pie)
•
Second Fundamental Theorem of Welfare
Economics: Society can attain any socially
efficient outcome by suitably redistributing
resources among individuals and then
allowing them to trade freely.
Equilibrium and Social Welfare
Social Welfare
•
Equity-efficiency trade-off: The choice society
must make between the total size of the
economic pie and its distribution among
individuals.
•
How to measure this trade-off?
–
Social welfare functions
Equilibrium and Social Welfare
Social Welfare Functions
•
•
SWF maps the set of individual utilities in
society into an overall society utility function.
Examples:
–
Utilitarian SWF:
SWF = U1 + U 2 + ... + U N
–
Rawlsian SWF:
SWF = min (U1,U 2 ,...,U N )
Equilibrium and Social Welfare
Social Welfare
•
How to choose a SWF?
–
Two different approaches
•
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.
Equilibrium and Social Welfare
TANF Example