Download Prices and Welfare

Social welfare and price changes
Udayan Roy
ECO61 Microeconomic Analysis
Fall 2008
Price changes and consumer wellbeing
• 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
consumer’s welfare?
Consumer’s well-being
• Can we measure the effect of a price change on
the consumer’s well-being?
• Economists use three concepts:
– Compensating variation: what change in income
would restore the consumer’s well-being to what it
was before the price change
– Equivalent variation: what change in the consumer’s
income would have an equal effect on the consumer’s
well-being as the price change
– Change in consumer’s surplus: area to the left of the
demand curve between the before and after prices
L1 and I1
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $300.
Choice: e1
D, Movie DVDs, Units per year
Compensating Variation
22.5
L*
L2 and I2
PD = price of DVDs = $20
PC = price of CDs = $30
M = Income = $300.
Choice: e2
15
L1
L* and I1
PD = price of DVDs = $20
PC = price of CDs = $30
M = Income = $450.
Choice: e*
L2
e*
e1
e2
I1
CV = 450 – 300 = $150
I2
6
Income effect = -3
9
12
20
C, Music CDs Units peryear
Substitution effect = -3
Total effect = -6 = Substitution Effect + Income Effect = -3 + (-3)
15
L1 and I1
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $300.
Choice: e1
D, Movie DVDs, Units per year
Equivalent Variation
L2 and I2
PD = price of DVDs = $20
PC = price of CDs = $30
M = Income = $300.
Choice: e2
15
L1
L* and I2
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $200.
Choice: e*
L2
10
L*
e1
e2
e*
I1
I2
6
8
12
20
C, Music CDs Units peryear
EV = 300 – 200 = $100
Change in consumer surplus
PC
30
15
Demand
C
• 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?
L1 and I1
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $300.
Choice: e1
D, Movie DVDs, Units per year
EV = CV when there is no
income effect
•
•
20 L1*
•
15
L1
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
L2 and I2
PD = price of DVDs = $20
PC = price of CDs = $30
M = Income = $300.
Choice: e2
EV = CV = $100
L2
e1
10
L2*
e2
I1
I2
6
8
20
C, Music CDs Units peryear
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.
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
Willingness to pay and the height of
the demand curve
• The height of the demand
curve tells us a lot about the
PX
consumer’s well-being
• When the quantity of good X
is 12, the height of our
demand curve tells us that the $20
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.
Rational choice implies
PX/PY = MRSXY. Therefore,
PX = PYMRSXY.
PYMRSXY
Demand
12
X
Willingness to pay
• The consumer’s 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 consumer’s well-being
CDs
Willingness
to Pay
First
100
Second 80
Third
70
Fourth 50
10
The Demand Curve
Price of CD
$100
First CD bought at this price
80
Second CD bought
Willingness
to Pay
First
100
Second 80
Third
70
Fourth 50
3rd CD
70
4th CD
50
Demand
0
CDs
1
2
3
4
The height of the
demand curve at any
quantity shows the
willingness to pay of
whoever bought the last
unit.
Quantity of CDs
Area of a Rectangle
Area = Width × Height
Height
Width
12
Willingness to pay equals the area
under the Demand Curve
CDs
Willingness
to Pay
First
100
Second 80
Third
70
Fourth 50
(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
Demand
0
1
Willingness to pay for 1st CD ($100)
2
3
4
Quantity of
Albums
Willingness to pay equals the
area under the Demand Curve
CDs
Willingness
to Pay
First
100
Second 80
Third
70
Fourth 50
(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
Demand
0
Willingness to pay for 1st CD
1
2
3
4 Quantity of CDs
Willingness to pay for 2nd CD
Willingness to Pay from the Demand Curve
(a) Willingness to Pay at Price P1
Price
A
The area under the demand
curve measures the dollar value
of the DVDs that would
compensate for or be equivalent
to Q1 CDs.
P1
B
C
Demand
0
Q1
Quantity
Consumer Surplus
(a) Consumer Surplus at Price P1
Price
A
Consumer Surplus (ABC) +
Total Payment (OBCQ1) =
Willingness to Pay (OACQ1)
Consumer
surplus
P1
B
C
Total
Payment
0
Demand
Q1
Quantity
How the Price Affects Consumer Surplus
Price
A
Initial
consumer
surplus
P1
P2
0
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 good—the one whose price is
unchanged—that 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.
C
B
F
D
E
Q1
Q2
CS = EV = CV, when
there is no income
Demand effect.
Quantity
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 consumer’s 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 < CS < EV, when income effect is positive (normal
good)
– CV > CS > EV, when income effect is positive (normal
good)
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.
Market Demand as the Sum of Individual
Demands
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
individual’s 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
individual’s well-being
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
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 individual’s 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 person’s
goods bundle has changed, would we know
whether society as a whole is better off?
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
individuals—total utility—increases (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
Utilitarianism
• If the EV, CV, and CS for an individual is a
meaningful measure of the effect of a price
change on that individual’s 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
John Rawls’s liberalism
• Notwithstanding the popularity of utilitarianism
in economics, there are other theories of social
welfare
• John Rawls has argued that a society’s welfare is
equal to the utility of the unhappiest member of
that society
• So, the effect of a price change on a society’s
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 person’s
demand curve, between the before and after prices