Social welfare and price changes

Udayan RoyECO61 Microeconomic Analysis

Fall 2008

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 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

Compensating Variation

e*

L1

L2

e1e2

I1

I2

L1 and I1

PD = price of DVDs = $20

PC = price of CDs = $15M = Income = $300.

Choice: e1

C, Music CDs Units peryearIncome effect = -3 Substitution effect = -3

6 9 12 20

Total effect = -6

D, M

ovie

DV

Ds,

Uni

ts p

erye

ar

15

= Substitution Effect + Income Effect = -3 + (-3)

L*

L2 and I2

PD = price of DVDs = $20

PC = price of CDs = $30M = Income = $300.

Choice: e2

L* and I1

PD = price of DVDs = $20

PC = price of CDs = $30M = Income = $450.Choice: e*

22.5

15

CV = 450 – 300 = $150

Equivalent Variation

L1

L2

e1e2

I1

I2

L1 and I1

PD = price of DVDs = $20

PC = price of CDs = $15M = Income = $300.

Choice: e1

C, Music CDs Units peryear6 12 20

D, M

ovie

DV

Ds,

Uni

ts p

erye

ar

15

L2 and I2

PD = price of DVDs = $20

PC = price of CDs = $30M = Income = $300.

Choice: e2

L* and I2

PD = price of DVDs = $20

PC = price of CDs = $15M = Income = $200.Choice: e*

EV = 300 – 200 = $100

8

e*

L*

10

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?

PC

C

Demand

30

15

EV = CV when there is no income effect

L1

L2

e2

I1

I2

L1 and I1

PD = price of DVDs = $20

PC = price of CDs = $15M = Income = $300.

Choice: e1

C, Music CDs Units peryear6 20

D, M

ovie

DV

Ds,

Uni

ts p

erye

ar

15

• 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 = $30M = Income = $300.

Choice: e2

EV = CV = $100

8

e1

L2*

10

L1*20

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 consumer’s 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.

X

PX

PYMRSXY

Demand

Rational choice implies PX/PY = MRSXY. Therefore, PX = PYMRSXY.

12

$20

10

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

The Demand CurvePrice of CD

0 Quantity of CDs

Demand

1 2 3 4

The height of the demand curve at any quantity shows the willingness to pay of whoever bought the last unit.

CDs Willingness to Pay

First 100

Second 80

Third 70

Fourth 50

$100 First CD bought at this price

80 Second CD bought

70 3rd CD

50 4th CD

12

Area of a Rectangle

Height

Width

Area = Width × Height

Willingness to pay equals the area under the Demand Curve

(a) Price = $80.01

Price of CD

50

70

80

0

$100

Demand

1 2 3 4 Quantity ofAlbums

Willingness to pay for 1st CD ($100)

The area under the demand curve measures the total willingness to pay for the quantity demanded.

CDs Willingness to Pay

First 100

Second 80

Third 70

Fourth 50

Willingness to pay equals the area under the Demand Curve

(b) Price = $70.01Price of CD

50

70

80

0

$100

Demand

1 2 3 4 Quantity of CDs

Willingness to pay for 1st CD Willingness to pay for 2nd CD

The area under the demand curve measures the total willingness to pay for the quantity demanded.

CDs Willingness to Pay

First 100

Second 80

Third 70

Fourth 50

Willingness to Pay from the Demand Curve

Quantity

(a) Willingness to Pay at Price P1

Price

0

Demand

P1

Q1

B

A

C

The area under the demand curve measures the dollar value of the DVDs that would compensate for or be equivalent to Q1 CDs.

Consumer Surplus

Consumersurplus

Quantity

(a) Consumer Surplus at Price P1

Price

0

Demand

P1

Q1

B

A

C

Total Payment

Consumer Surplus (ABC) + Total Payment (OBCQ1) = Willingness to Pay (OACQ1)

How the Price Affects Consumer Surplus

Initialconsumer

surplus

Quantity

Price

0

Demand

A

BC

D EF

P1

Q1

P2

Q2

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.

CS = EV = CV, when there is no income effect.

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

C

Aggregate Demand

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