Econ 321 Notes 2 – Welfare Economics
Adam Smith : ….every individual . . . endeavors as much as he can . . . to direct . . . industry so that its
produce may be of the greatest value . . . neither intend[ ing] to promote the public interest, nor know[
ing] how much he is promoting it. . . . He intends only his own gain, and he is in this, as in many other
cases, led by an invisible hand to promote an end that was no part of his intention.. . . By pursuing his own
interest he frequently promotes that of society more effectually than when he really intends to promote it.
First fundamental theorem of welfare economics:
The market equilibrium of an ideal market system yields an efficient (Pareto optimal) allocation of
resources.
P
MC
The net benefits (Total benefit – Total
cost) is maximized at q* level of
production (consumption)
Remember total benefit equals to the
area under MB curve and similarly
total cost is the area under MC curve.
C
Either more than q* and less than q*
yields smaller net benefit to the
society.
B
MB
q`
O
q*
Clearly competitive markets will
produce q* level of production
(consumption)
Thus competitive markets maximize
net benefit (social welfare)
q``
Q
ANOTHER REPRESENTATION OF EXCHANGE EFFICIENCY
MBN
MBB
When the MB is the same for both
individuals, we have the exchange
efficiency. The sum of areas under the MB
curves (total benefit) maximized.
Remember at competitive markets
equilibrium occurs ( Nihan consumes at qn
and Bahattin at qb) where MBn = MBb
P
On
MBn
Efficicient amount of
consumption by Nihan
MBb
Os
Efficient amount of consumption by Bahattin
Total available amount
qn
qb
Q
P
Econ 321 Notes 2 – Welfare Economics
EDGEWORTH DIAGRAM
Bahattin’s consumption of biscuits
Oa
Bahattin’s
cosnonsumption
of tea
f
Nihan’s consumption of
tea
t
h
g
Contract curve
Om
Nihan’s
consumption
of biscuit
Assume initially we are at point f. If we move from point f to point t Nihan’s utility stays constant (at
the same indifference curve), however Bahattin is better off (at a higher indifference curve). The
movement from point f to t is called Pareto Improvement. At point t we cannot make Bahattin off
without hurting Nihan (making her worse off). So we completed the Pareto Improvement
opportunities, thus point t is called Pareto Optimum (efficient) point. Similarly g is another Pareto
Optimum point. Every point on Contract Curve is also Pareto Optimum.
Pareto efficiency: If you cannot make anybody better off without hurting somebody else, you are at
Pareto efficient point.
Marginal rate of substitutions of tea and biscuit is the same both Nihan and Bahattin at Pareto
Optimum points.. (slopes of their indifference curves) Marginal rate of substitutions is a person’s
willing to exchange x for y. For an allocation point to be efficient, it must be the case for both
individuals to have same marginal rate of substitutions. (Notice that at each Pareto Optimum point
indifference curves of Nihan and Bahattin are tangent to each other, thus their slopes and MRSs.)
Now the question is whether we are going to be able to reach this Pareto Optimum point with the
free markets.
Remember from old economics courses that utility maximizing individuals will the consumption
bundle such that their indifference curves are tangent to budget lines.
Econ 321 Notes 2 – Welfare Economics
Tea
mbahattin
Ptea
X*Tea
Biscuit
X*Biscuit
Bahattin
Notice that for Bahattin utility
maximizing consumption bundle
(X*Tea, X*Biscuit) is where budget
line is tangent indifference curve.
At this point indifference curves
slope is equal to budget line’s
slope
mbahattin
Ptea  Ptea
mbahattin Pbiscuit
Pbiscuit
mbahattin
Pbiscuit
Tea
Utility maximizing Nihan also
choose the consumption bundle
where her own utility curve is
tangent to her own budget line.
(Notice that her indifference
curves and income levels can be
different than Bahatttin’s).
mnihan
Ptea
X*Tea
X*Biscuit
mnihan
Pbiscuit
At her best consumption point
the slope of the indifference
curve is:
Biscuit
mnihan
Ptea  Ptea
mnihan Pbiscuit
Pbiscuit
Nihan
So free markets with utility maximizing individuals (and firms)
are going to reach us to the point where the slopes of
indifferences curves (marginal rate of substitutions) of every
individual in the society are equal to each other.
Notice that this is the point at which social welfare maximizing
point on Edegeworth Box.
Econ 321 Notes 2 – Welfare Economics
First fundamental theorem of welfare economics: The market equilibrium of an ideal market system
yields an efficient (Pareto optimal) allocation of resources.
In the Edgeworth diagram discuss what happens if the government seizes some portion
of one individual’s endowment and give it to the other one. It is still going to be efficient.
Point g is better than point f. But what about point h, is h better than f. (certainly more efficient)
Redistribution of income.
Bahattin’s consumption of biscuits
Oa
Bahattin’s
cosnonsumption
of tea
f
Nihan’s consumption of
tea
t
g
h
Contract curve
Om
Nihan’s
consumption
of biscuit
Which point is better f or g? Both points are Pareto Optimum (efficient). However, at point g the
income is shared between Nihan and Bahattin more fairly. Generally societies prefer more even
income distribution, thus point g is better than point h. (though they are equally efficient)
What about comparison of point h and point f?
The fact that markets fail is not enough reason for government intervention. There have to be
policies that solve these problems or at least lowers the magnitude of them.
Efficiency is not the only concern of the society. (Efficiency vs. equity)
Econ 321 Notes 2 – Welfare Economics
UTILITY POSSIBILITIES SCHEDULE
Utility of farmers
A
B
C
D
Utility of consumers
Which one is better D or C?
Which one is better A or B?
Which one is better A or C?
Assume that Friday and Crusoe have identical utility functions described by following
UTILITY FUNCTIONS FOR FRIDAY AND CRUSOE
# Of Oranges
Utility
Marginal Utility
1
11
11
2
21
10
3
30
9
4
38
8
5
45
7
6
48
3
7
50
2
8
51
1
Draw the utility function. Fill in the marginal utility data in the table above, and draw the marginal
utility function
2) Assume that there are 8 oranges to be divided between Friday and Crusoe. Assume that social
welfare is the sum of the utility of two individuals. What is the social welfare maximizing allocation of
oranges?
3) Draw the utility possibilities schedule.
4) Assume Crusoe initially has 6 oranges and Friday 2. Assume that for every 2 oranges taken away
from Crusoe, Friday gets only 1, an orange being lost in the process. What does the utility possibilities
schedule look like? What is the social welfare maximizing allocation of oranges?
Efficiency in Production Economy
Above we analyzed that with free markets the goods are going to be allocated between the
individuals in a way such that social welfare is maximized. However, real life is more complex than
this simple world. Below we are going to study the efficiency of production with profit maximizing
firms.
Econ 321 Notes 2 – Welfare Economics
Lets assume there are only two goods, biscuit and tea, and two production inputs, capital and labor,
to manufacture those two goods. There are fixed amount of labor and capital in the world and we
want to maximize social welfare (total production). How should we allocate capital and labor
between tea and biscuit production?
Labor used in tea production
Tea
Capital used in
tea production
f
Capital used in biscuit
production
t
g
Biscuit
Labor used in
biscuit
production
consumption
of biscuit
assume
that initially
Lets
we are at point f. Black and blue curves are isoquant curves
(which shows the possible combination of input uses which yield the same of
production output) for the tea and biscuit production. It is obvious from the graph that
if we reallocate the capital and labor use between tea and biscuit production and reach
to point t, we are going to be able increase tea production without lowering biscuit
production. (Or move to point g and increase both production levels).
Thus at optimum level the slopes of isoquants of tea and biscuit production are equal
to each other.
Econ 321 Notes 2 – Welfare Economics
Capital
TCbiscuit
r
K*Tea
Labor
L*Biscuit
Biscuit production
TCbiscuit
w
Notice that for profit maximizer
(or cost minimizer) biscuit
producers are going to use the
capital and labor inputs in a way
that isoquant curves are tangent to
isocost line. At this point isocost
curve’s slope is equal to isocost
line’s slope
TCbiscuit
w
r

TCbiscuit r
w
w: wage rate of labor
r: rental rate (price) of capital
TCbiscuit: Total cost of biscuit
production
Capital
Similar to biscuit producers tea
producers are also going to
choose capital labor use where
their own isoquant curves are
tangent to isocost lines. (Notice
that their indifference curves
and Total Costs can be different
than biscuit producers).
TC tea
r
K*Tea
Labor
L*Tea
TC tea
w
At this best possible point the
slope of isoquant curve:
TCtea
r w
TCtea r
w
Tea production
So free markets with profit maximizing firms are going to reach
us to the point where the slopes of isoquant curves (marginal rate
of technical substitutions) of every good (and firm) in the society
are equal to each other.
Notice that this is the point at which social welfare maximizing
point on Edegeworth Box.
Econ 321 Notes 2 – Welfare Economics
Second fundamental theorem of welfare economics: Society can attain any Pareto Efficient
allocation of resources by making a suitable assignment of initial endowments and then letting
people freely trade with each other.