Social welfare and price changes

1
Social welfare and price changes

• Udayan Roy
• ECO61 Microeconomic Analysis
• Fall 2008

2
Price changes and consumer well-being

• We have seen that price changes take the consumer
  from one indifference curve to another
• Can we say something quantitative about the
  effect of a given price change on the consumers
  welfare?

3
Consumers well-being

• Can we measure the effect of a price change on
  the consumers well-being?
• Economists use three concepts
• Compensating variation what change in income
  would restore the consumers well-being to what
  it was before the price change
• Equivalent variation what change in the
  consumers income would have an equal effect on
  the consumers well-being as the price change
• Change in consumers surplus area to the left of
  the demand curve between the before and after
  prices

4
Compensating Variation
L1 and I1 PD price of DVDs 20 PC price of
CDs 15 M Income 300. Choice e1
ear
y
22.5
, Units per
L2 and I2 PD price of DVDs 20 PC price of
CDs 30 M Income 300. Choice e2
s
VD
D
vie
o
M
D,
15
L1
L and I1 PD price of DVDs 20 PC price of
CDs 30 M Income 450. Choice e
L2
e
e1
e2
CV 450 300 150
I1
I2
6
9
12
20
15
C
, Music CDs Units per
y
ear
Income effect -3
Substitution effect -3
Total effect -6
Substitution Effect Income Effect -3 (-3)
5
Equivalent Variation
L1 and I1 PD price of DVDs 20 PC price of
CDs 15 M Income 300. Choice e1
ear
y
, Units per
L2 and I2 PD price of DVDs 20 PC price of
CDs 30 M Income 300. Choice e2
s
VD
D
vie
o
M
D,
15
L1
L and I2 PD price of DVDs 20 PC price of
CDs 15 M Income 200. Choice e
L2
e1
e2
EV 300 200 100
I1
I2
8
6
12
20
C
, Music CDs Units per
y
ear
6
Change in consumer surplus

• The area to the left of the demand curve for CDs
  between the before (15) and after (30) prices
  is another dollar measure of the welfare effect
  of the price change
• How does this measure compare to our other two
  measures, CV and EV?

7
EV CV when there is no income effect
L1 and I1 PD price of DVDs 20 PC price of
CDs 15 M Income 300. Choice e1
ear
y

• The indifference curves have been drawn parallel
  to each other
• They have the same slope at any specific value of
  C.
• This is the reason why there is no income effect
  on the consumption of CDs

, Units per
L2 and I2 PD price of DVDs 20 PC price of
CDs 30 M Income 300. Choice e2
20
s
L1
VD
D
vie
o
M
D,
15
L1
EV CV 100
L2
10
e1
L2
The common value of EV and CV in this case is
also equal to the dollar value of the amount of
DVDs that would compensate for or be equivalent
to the changes in the price of CDs.
e2
I1
I2
8
6
20
C
, Music CDs Units per
y
ear
8
Well-being and the demand curve

• When a change in the price of good X has no
  income effect on the consumption of good X, the
  equivalent and compensating variations of the
  price change are consistent dollar measures of
  the effect of the price change on the well-being
  of the consumer
• The EV and CV of a price change can also be
  measured by making use of the demand curve

9
Willingness to pay and the height of the demand
curve
Rational choice implies PX/PY MRSXY.
Therefore, PX PYMRSXY.

• The height of the demand curve tells us a lot
  about the consumers well-being
• When the quantity of good X is 12, the height of
  our demand curve tells us that the price of good
  X is 20
• But the theory of consumer choice tells us that
  this must also be the dollar value of the
  additional amount of good Y that would be just as
  desirable as an additional unit of good X.

10
Willingness to pay

• The consumers willingness to pay for an
  additional CD is measured by the dollar value of
  the additional amount of DVDs that would have an
  equal effect on the consumers well-being

11
The Demand Curve
Price of CD
The height of the demand curve at any quantity
shows the willingness to pay of whoever bought
the last unit.
0
Quantity of CDs
1
2
3
4
12
Area of a Rectangle
Area Width Height
Height
Width
13
Willingness to pay equals the area under the
Demand Curve
(a) Price 80.01
Price of CD
100
The area under the demand curve measures the
total willingness to pay for the quantity
demanded.
80
70
50
0
1
2
3
4
Quantity of
Albums
14
Willingness to pay equals the area under the
Demand Curve
(b) Price 70.01
Price of CD
100
The area under the demand curve measures the
total willingness to pay for the quantity
demanded.
80
70
50
0
1
2
3
4
Quantity of CDs
15
Willingness to Pay from the Demand Curve
(a) Willingness to Pay at Price P1
Price
The area under the demand curve measures the
dollar value of the DVDs that would compensate
for or be equivalent to Q1 CDs.
Quantity
0
16
Consumer Surplus
(a) Consumer Surplus at Price P1
Price
Consumer Surplus (ABC) Total Payment (OBCQ1)
Willingness to Pay (OACQ1)
Total Payment
Quantity
0
17
How the Price Affects Consumer Surplus
The blue shaded area (under the demand curve and
between the before and after prices, P1 and P2)
measures the change in consumer surplus that is
caused by the price change. This is also the
dollar value of the other goodthe one whose
price is unchangedthat would compensate for the
price change. This is also equal to the
compensating and equivalent variations of the
price change when the income effect is zero.
Price
?CS EV CV, when there is no income effect.
Quantity
0
18
Consumer surplus summary

• When the income effect of a price change is zero,
  the change in consumer surplus is equal to the
  dollar amount that is equivalent to and would
  compensate the price change CV ?CS EV
• So, in this case, ?CS is an excellent measure of
  the effect of a price change on the consumers
  well-being
• But even when the income effect is not zero, ?CS
  is a useful approximate measure of the effect of
  a price change on welfare
• CV lt ?CS lt EV, when income effect is positive
  (normal good)
• CV gt ?CS gt EV, when income effect is positive
  (normal good)

19
Market Demand versus Individual Demand

• Market demand refers to the sum of all individual
  demands for a particular good or service.
• Graphically, individual demand curves are summed
  horizontally to obtain the market demand curve.

20
Market Demand as the Sum of Individual Demands
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Effect of a price change on aggregate well-being

• We have seen that, when the income effect of a
  price change is zero, the change in an
  individuals consumer surplus is
• The area to the left of the demand curve between
  the before and after prices
• Equal to EV and CV and is, therefore,
• A meaningful dollar measure of the change in the
  individuals well-being

22
Effect of a price change on aggregate well-being

• Similarly, the area to the left of the aggregate
  demand curve between the before and after prices
  is a meaningful dollar measure of the effect of a
  price change on aggregate well-being
• if you are a utilitarian

PC
Aggregate Demand
C
23
Social welfare

• We have seen that if people have complete and
  transitive preferences, they can rank all
  possible goods bundles
• So, if we know an individuals preferences and
  also how her goods bundle has changed, we can
  tell whether or not she is better off
• But if we know the preferences of all individuals
  and if we know how each persons goods bundle has
  changed, would we know whether society as a whole
  is better off?

24
Utilitarianism

• According to this theory of social welfare,
• Each individual has a utility function that spits
  out a number representing how happy she is with a
  particular goods bundle
• If the sum of the utility numbers of all
  individualstotal utilityincreases (decreases)
  it is meaningful to say that social welfare has
  increased (decreased)
• Therefore, it should be the goal of government
  policy to increase total utility

25
Utilitarianism

• If the EV, CV, and ?CS for an individual is a
  meaningful measure of the effect of a price
  change on that individuals welfare, then
  according to utilitarianism the aggregate value
  of EV CV ?CS is a meaningful dollar measure
  of social welfare
• Indeed, the aggregate value of ?CS is widely used
  in economics as a measure of the change in social
  welfare
• This reflects the widespread popularity of
  utilitarianism in economics

26
John Rawlss liberalism

• Notwithstanding the popularity of utilitarianism
  in economics, there are other theories of social
  welfare
• John Rawls has argued that a societys welfare is
  equal to the utility of the unhappiest member of
  that society
• So, the effect of a price change on a societys
  welfare is, according to Rawls, the change in the
  consumer surplus of the unhappiest person in the
  society
• This is the area to the left of the unhappiest
  persons demand curve, between the before and
  after prices