Download Welfare Economics

Session 2
Welfare Economics
Welfare Economics
Welfare Economics – branch of economic theory
concerned with the social desirability of alternative
economic states
Pure Economy Exchange
• Assume a given amount of commodities exist
– No Production
– Two people and two commodities
• Problem is to efficiently allocate these commodities
among households
– An allocation of existing commodities is efficient if no one
household can be made better off without making some
other household worse off
Edgeworth Box
• A device used to depict the distribution of
two goods in a two good –two person
world.
• We look at the possible distribution of
apples and fig leaves between Adam and
Eve.
• Constructed from utility functions from two
households
– Utility functions have the usual properties…
• Every point in the Edgeworth box is a
feasible allocation
• Size of Edgeworth box determined by the
total initial endowment.
Edgeworth Box
Eve
y
0’
Fig leaves per year
r
v
u
0
Adam
w
s
x
Apples per year
Edgeworth Box
Edgeworth Box
• Adam and Eve , each has a set of
indifference curves that reflect their
preferences for fig leaves and apples.
• Adam is happier the farther he can move
toward the top-right corner of the box.
• Eve attains higher utility as she moves
toward the lower-left corner
Indifference curves in Edgeworth Box
Eve
r
0’
E1
Fig leaves per year
E2
E3
A3
A2
A1
s
0
Adam
Apples per year
Edgeworth Box
Making Adam better off without Eve
Eve
becoming worse off
0’
r
Fig leaves per year
Eg
g
h
A Pareto
Efficient
Allocation
p
Ap
Ah
Ag
s
0
Adam
Apples per year
Edgeworth Box
Making Eve better off without Adam
Eve
becoming worse off
0’
r
Fig leaves per year
Eg
g
p
Ep1
p1
A Pareto
Efficient
Allocation
Ag
s
0
Adam
Apples per year
Edgeworth Box
Making both Adam and Even better off
Eve
0’
r
Fig leaves per year
Eg
g
• Pareto efficient
• Pareto improvement
Ep2
p
p2
p1
Ap2
Ag
s
0
Adam
Apples per year
Edgeworth Box
Starting from a different initial point
Eve
0’
r
Fig leaves per year
Eg
g
k
p4
Ep2
p
p3
p2
p1
Ap2
Ag
s
0
Adam
Apples per year
Edgeworth Box
The Contract Curve
Eve
0’
r
Fig leaves per year
Eg
g
The
contract
curve
p4
Ep2
p
p3
p2
p1
Ap2
Ag
s
0
Adam
Apples per year
Edgeworth Box
Pareto-Efficient Allocation
• Allocation where there is no way to make
all households better off
• No way to make some households better
off without making someone else worse off
– All gains from trade are exhausted…
• Definition of Pareto-Efficient Allocation:
– Allocation for which it is not possible to
make any person better off without
making someone else worse off…
Pareto Efficiency in Consumption
•
•
•
•
MRSAdamaf
= MRSEveaf
A point at which the indifference curves for
Adam and Eve are barely touching
(tangent).
The slopes of the indifference curves are
equal.
Pareto efficiency is used as a standard for
evaluating the desirability of an allocation
of resources.
If the allocation is not Pareto efficient, it is
wasteful.
Pareto improvement
• A reallocation of resources that makes one
person better off without making anyone
worse-off.
• Contract curve- The locus of all Pareto
efficient points.
Fig leaves per year
Production Possibilities Curve
C
│Slope│ =
marginal rate of
transformation
w
y
0
C
x
z
Apples per year
Marginal Rate of Transformation
• MRTaf = Marginal rate of transformation of
apples for fig leaves
• MRTaf = MCa/MCf
• MRT is the rate at which the economy can
transform one good into another good- it is
the slope of the PPF.
• MC-Marginal cost- is the incremental cost
of producing one more unit of output
Efficiency Conditions with Variable Production
Adam
Eve
MRTaf = MRSaf = MRSaf
Adam
Eve
MCa/MCf = MRSaf = MRSaf
The First Fundamental Theorem of
Welfare Economics
– In a perfectly competitive price system,
correspondence between Paretoefficient allocation of resources and
perfectly competitive price system is
exact
• Market forces in a competitive market
lead to (Pareto) efficient outcomes.
• Thus, if supply equals demand
(equilibrium), prices are at equilibrium,
and consumers cannot be made
The First Fundamental Theorem of
Welfare Economics
MRSAdam
af = Pa/Pf
MRSEve
af = Pa/Pf
MRSaf = MRSaf
Adam = P Eve
MCa/MC
f
a/Pf
MRTaf = Pa/Pf
Pa/Pf = MCa/MCf
• A competitive economy automatically
allocates resources efficiently.
2nd Fundamental theorem:
Efficiency versus Equity
0’
Fig leaves per year
r
p3
p5
q
s
0
Adam
Eve
Apples per year
Edgeworth Box
Efficiency versus Equity
• Point p5 is Pareto efficient but q is not.
• But society may prefer point q becoz it
provides a more equal distribution of the
two goods.
• The main argument is that Pareto
efficiency alone is not enough to rank
alternative allocations.
• Explicit value judgements are required on
the fairness of the distribution of utility
Adam’s utility
Utility Possibilities Curve
U
p3
p5
q
U
Eve’s utility
Utility Possibilities Curve
• A graph showing the maximum amount of
Adam’s utility given each level of utility attained
by Eve.
• We derive it from the contract curve
• All points on or below the utility possibilities
frontier are attainable by society.
• All points on UU are Pareto efficient, although
they represent different distributions of real
income btn Adam and Eve.
• Which distribution is the best?
• We assume social welfare function
• W = F(UAdam, UEve)
Adam’s utility
Social Indifference Curve
W = F(UAdam, UEve)
Increasing
social
welfare
Eve’s utility
Social Indifference Curve
• The welfare function embodies society’s
preferences on the relative deservedness
of Adam and Eve.
• Society’s welfare depends on the utilities
of each of its members.
• Society is better off when any of its
members becomes better off.
• The social welfare function leads to a set
of social indifference curves between
people’s utilities.
Adam’s utility
Maximizing Social Welfare
i
iii
ii
Eve’s utility
2nd Fundamental theorem
• Point iii is preferred to i and ii becoz it is
both efficient and fair.
• Govt intervention may be necessary to
achieve a fair distribution of utility.
• Society can attain any Pareto efficient
allocation of resources by making a
suitable assignment of the initial
endowments and then letting people freely
trade with each other.
Market Failure
• An economy can be inefficient becoz of 2 reasons:
Market Power and Nonexistence of Markets
• Market Power
– Monopoly- firms are price makers not price takers
violating the 1st Theorem. P can be >MC
• Nonexistence of Markets
– E.g. there is no market for poverty insurance.
– There are 3 types of inefficiencies from non-existent
markets:
• asymmetric information - one part in a transaction has
information that is not available to others
• Externality- one person’s behaviour affects the welfare of others
– MC<MSC
• public good – A good that is non-rival and non-excludable in
consumption.
Buying into Welfare Economics
• Individualistic outlook
– merit goods
• Results orientation
• Coherent framework for analyzing policy
– Will it have desirable distributional
consequences?
– Will it enhance efficiency?
– Can it be done at a reasonable cost?