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 Can we say something quantitative about the effect of a given price change on the consumers welfare?

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

Compensating Variation e* L1L1 L2L2 e1e1 e2e2 I1I1 I2I2 L 1 and I 1 P D = price of DVDs = $20 P C = price of CDs = $15 M = Income = $300. Choice: e 1 C, Music CDs Units peryear Income effect = -3 Substitution effect = Total effect = -6 D, M o vie D VD s, Units per y ear 15 = Substitution Effect + Income Effect = -3 + (-3) L* L 2 and I 2 P D = price of DVDs = $20 P C = price of CDs = $30 M = Income = $300. Choice: e 2 L * and I 1 P D = price of DVDs = $20 P C = price of CDs = $30 M = Income = $450. Choice: e* CV = 450 – 300 = $150

Equivalent Variation L1L1 L2L2 e1e1 e2e2 I1I1 I2I2 L 1 and I 1 P D = price of DVDs = $20 P C = price of CDs = $15 M = Income = $300. Choice: e 1 C, Music CDs Units peryear D, M o vie D VD s, Units per y ear 15 L 2 and I 2 P D = price of DVDs = $20 P C = price of CDs = $30 M = Income = $300. Choice: e 2 L * and I 2 P D = price of DVDs = $20 P C = price of CDs = $15 M = 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? PCPC C Demand 30 15

EV = CV when there is no income effect L1L1 L2L2 e2e2 I1I1 I2I2 L 1 and I 1 P D = price of DVDs = $20 P C = price of CDs = $15 M = Income = $300. Choice: e 1 C, Music CDs Units peryear 620 D, M o vie D VD s, Units per y ear 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 L 2 and I 2 P D = price of DVDs = $20 P C = price of CDs = $30 M = Income = $300. Choice: e 2 EV = CV = $100 8 e1e1 L2*L2* 10 L1*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 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. X PXPX P Y MRS XY Demand Rational choice implies P X /P Y = MRS XY. Therefore, P X = P Y MRS XY. 12 $20

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 CDsWillingness to Pay First100 Second80 Third70 Fourth50

The Demand Curve Price of CD 0Quantity of CDs Demand 1234 The height of the demand curve at any quantity shows the willingness to pay of whoever bought the last unit. CDsWillingness to Pay First100 Second80 Third70 Fourth50 $100 First CD bought at this price 80 Second CD bought 70 3 rd CD 50 4 th 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 $100 Demand 1234 Quantity of Albums Willingness to pay for 1 st CD ($100) The area under the demand curve measures the total willingness to pay for the quantity demanded. CDsWillingness to Pay First100 Second80 Third70 Fourth50

Willingness to pay equals the area under the Demand Curve (b) Price = $70.01 Price of CD $100 Demand 1234 Quantity of CDs Willingness to pay for 1 st CD Willingness to pay for 2 nd CD The area under the demand curve measures the total willingness to pay for the quantity demanded. CDsWillingness to Pay First100 Second80 Third70 Fourth50

Willingness to Pay from the Demand Curve Quantity (a) Willingness to Pay at Price P 1 Price 0 Demand P1P1 Q1Q1 B A C The area under the demand curve measures the dollar value of the DVDs that would compensate for or be equivalent to Q 1 CDs.

Consumer Surplus Consumer surplus Quantity (a) Consumer Surplus at Price P 1 Price 0 Demand P1P1 Q1Q1 B A C Total Payment Consumer Surplus (ABC) + Total Payment (OBCQ 1 ) = Willingness to Pay (OACQ 1 )

How the Price Affects Consumer Surplus Initial consumer surplus Quantity Price 0 Demand A B C DE F P1P1 Q1Q1 P2P2 Q2Q2 The blue shaded area (under the demand curve and between the before and after prices, P 1 and P 2 ) 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. 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 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 < 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 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

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 PCPC 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 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?

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

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

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