Econ 321 Notes 2 – Welfare Economics

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Oct 10, 2013 (4 years and 2 months ago)

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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. . . . H
e 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

rea
lly 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
re
sources.



ANOTHER REPRESENTATION OF EXCHANGE EF
FICIENCY





MB
N

MB
B

O
n

O
s

Tot
al available amount

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 q
n

and Bahattin at q
b
)
where MB
n
= MB
b



Efficicien
t amount of
consumption by Nihan

Efficient

amount of consumption by Bahattin

P

MB
b

MB
n

q
n

q
b

Q

P

P


O

Q

C

B

The net benefits (Total benefit


Total
cost) is maximized at q* level of
production (consumption)


Remember total benefit equals to the
area unde
r MB curve and similarly
total cost is the area under MC curve.


Either more than q* and less than q*
yields smaller net benefit to the
society.


Clearly competitive markets will
produce q* lev
e
l of production
(consumption)


Thus competitive markets maximi
ze
net ben
e
fit (social welfare)


q` q* q``

MC

MB

Econ 321 Notes 2


Welfare Economics


EDGEWORTH DIAGRAM





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 o
ff (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 cal
led
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 po
int.



Marginal rate of substitutions of tea and biscuit is the same both Nihan and Bahattin at Pareto
Optimum

points.. (slope
s

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 curve
s

of Nihan and Bahattin are tangent to each other, thus their slopes and MRSs.)




Now the q
uestion 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 bud
get lines.


f

O
m

O
a

Nihan
’s consumption of

tea

Nihan
’s
cons
u
mption
of biscuit

Bahattin
’s consumption of biscuits

Bahattin
’s
cosnonsumption

of tea

Contract curve

g

h

t

Econ 321 Notes 2


Welfare Economics


T
ea

Biscuit

X*
Biscuit

X*
Tea



Notice that for Bahattin utility
maximizing cons
umption 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


Bahattin

T
ea

X*
Tea

X*
Biscuit

Biscuit



Nihan

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).


At her best con
sumption point
the slope of the indifference
curve is:


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 inc
ome.




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 po
int 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 l
owers the magnitude of them.


E
fficiency is not the only concern of the society. (Efficiency vs. equity)







f

O
m

O
a

Nihan
’s consumption of

tea

Nihan
’s
cons
u
mption
of biscuit

Bahattin
’s consumption of biscuits

Bahattin
’s
cosnonsumption

of
tea

Contract curve

g

h

t

Econ 321 Notes 2


Welfare Economics

UTILITY POSSIBILITIES SCHEDULE


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 fun
ction. 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 i
s 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 th
e 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
ind
ividuals 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.

A

B

C

Utility of consumers

Utility of farmers

D

Econ 321 Notes 2


Welfare Economics

Lets assume there are only two goods, biscuit and te
a, 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 bi
scuit production?


f

Biscuit

Tea


Capital used in biscuit
production

Labor used in
biscuit
production
cons
u
mption
of biscuit

Labor used in tea production

Capital used in
tea production

g

t

Lets assume that initially we are at point f. Black and blue curves are isoquant curves
(which shows th
e 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

Labor

L*
Biscuit

K*
Tea

Notice that for profit maximizer
(or cost minimizer) biscuit
producers are going to use the
capi
tal 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



w:

wage rate of labor

r:

rental rate (price) of capital

T
C
biscuit:

Total cost o
f biscuit
production


Biscuit production

Tea production

Similar to biscuit producers t
ea
producers are also going to
choose capital labor use where
their own isoquant curves are
tangent to isocost lines.
(Notice
that
their

indif
ference curves
and Total Costs

can be different
than biscuit producers
).


At

this best possible point the
slope o
f isoquant curve:


So free
markets wit
h profit maximizing firms

are going to reach
us to the point w
here the slopes of isoquant

curves (marginal rate
of
technical
substit
utions) 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.



Capital

Labor

K*
Tea



L*
Tea

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 lett
ing
people freely trade with each other.