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Social welfare and price changes. Udayan Roy ECO61 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

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social welfare and price changes

Social welfare and price changes

Udayan Roy

ECO61 Microeconomic Analysis

Fall 2008

price changes and consumer well being
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
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

L1 and I1

PD = price of DVDs = $20

PC = price of CDs = $15

M = Income = $300.

Choice: e1

Compensating Variation

ear

y

22.5

L*

, 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

15

6

9

12

20

C

, Music CDs Units per

y

ear

Income effect = -3

Substitution effect = -3

Total effect = -6

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

equivalent variation

L1 and I1

PD = price of DVDs = $20

PC = price of CDs = $15

M = Income = $300.

Choice: e1

Equivalent Variation

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

10

L*

e1

e2

e*

EV = 300 – 200 = $100

I1

I2

8

6

12

20

C

, Music CDs Units per

y

ear

change in consumer surplus
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

30

15

Demand

C

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

EV = CV when there is no income effect

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

well being and the demand curve
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
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 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.

PX

$20

PYMRSXY

Demand

X

12

willingness to pay
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
the demand curve

$100

80

70

50

Demand

The Demand Curve

Price of CD

First CD bought at this price

Second CD bought

3rd CD

4th CD

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

0

1

2

3

4

Quantity of CDs

area of a rectangle
Area of a Rectangle

Area = Width × Height

Height

Width

willingness to pay equals the area under the demand curve

Demand

Willingness to pay for 1st CD ($100)

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

Quantity of

0

1

2

3

4

Albums

willingness to pay equals the area under the demand curve1

Demand

Willingness to pay for 1st CD

Willingness to pay for 2nd CD

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

Quantity of CDs

0

1

2

3

4

willingness to pay from the demand curve

A

P1

B

C

Demand

Q1

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

consumer surplus

A

Consumer

surplus

P1

B

C

Demand

Q1

Consumer Surplus

(a) Consumer Surplus at Price P1

Price

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

Total Payment

Quantity

0

how the price affects consumer surplus

A

Initial

consumer

surplus

C

P1

B

F

P2

D

E

Demand

Q1

Q2

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 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.

Price

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

Quantity

0

consumer surplus summary
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 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.
effect of a price change on aggregate well being
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 being1
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
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
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
utilitarianism1
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
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
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