Consumer s Surplus. Molly W. Dahl Georgetown University Econ 101 Spring 2009

Transcription

1 Consumer s Surplus Molly W. Dahl Georgetown University Econ 101 Spring

2 Inverse Demand Functions Taking quantity demanded as given and then asking what the price must be describes the inverse demand function of a commodity. Usually we ask Given p 1 what is the quantity demanded of? But we could also ask the inverse question Given that the quantity demanded is, what must p 1 be? 2

3 Inverse Demand Functions p 1 Given p 1, what quantity is demanded of commodity 1? Answer: units. p 1 * 3

4 Inverse Demand Functions p 1 p 1 Given p 1, what quantity is demanded of commodity 1? Answer: units. The inverse question is: Given units are demanded, what is the price of x * commodity 1? 1 Answer: p 1 4

5 Consumer s Surplus p 1 p 1 CS Consumer s surplus is the consumer s utility gain from consuming units of commodity 1. * 5

6 Change in Consumer s Surplus The change to a consumer s total utility due to a change to p 1 is approximately the change in her Consumer s Surplus. 6

7 Change in Consumer s Surplus p 1 p 1 ( ), the inverse ordinary demand curve for commodity 1 p 1 * 7

8 Change in Consumer s Surplus p 1 p 1 ( ) p 1 CS before * 8

9 Change in Consumer s Surplus p 1 p 1 ( ) p 1 " CS after p 1 " * 9

10 Change in Consumer s Surplus p 1 p 1 ( ) p 1 " p 1 Lost CS " * 10

11 In Class: Calculating Consumer Surplus 11

12 Producer s Surplus Changes in a firm s welfare can be measured in dollars much as for a consumer. 12

13 Producer s Surplus Output price (p) S = Marginal Cost y (output units) 13

14 Producer s Surplus Output price (p) S = Marginal Cost p y y (output units) 14

15 Producer s Surplus Output price (p) S = Marginal Cost p Revenue = py y y (output units) 15

16 Producer s Surplus Output price (p) p y S = Marginal Cost Variable Cost of producing y units is the sum of the marginal costs y (output units) 16

17 Producer s Surplus Output price (p) Revenue less VC is the Producer s Surplus. S = Marginal Cost p Variable Cost of producing y units is the sum of the marginal costs y y (output units) 17

18 Cost-Benefit Analysis Can we measure in money units the net gain, or loss, caused by a market intervention; e.g., the imposition or the removal of a market regulation? Yes, by using measures such as the Consumer s Surplus and the Producer s Surplus. 18

19 Cost-Benefit Analysis Price The free-market equilibrium Supply p 0 Demand q 0 Q D, Q S 19

20 Cost-Benefit Analysis Price The free-market equilibrium and the gains from trade generated by it. Supply CS p 0 PS Demand q 0 Q D, Q S 20

21 Cost-Benefit Analysis Price CS The gain from freely trading the q 1 th unit. Consumer s gain Supply p 0 PS Producer s gain Demand q 1 q 0 Q D, Q S 21

22 Cost-Benefit Analysis Price The gains from freely trading the units from q 1 to q 0. Consumer s gains CS Supply p 0 PS Producer s gains Demand q 1 q 0 Q D, Q S 22

23 Cost-Benefit Analysis Price The gains from freely trading the units from q 1 to q 0. Consumer s gains CS Supply p 0 PS Producer s gains Demand q 1 q 0 Q D, Q S 23

24 Cost-Benefit Analysis Price p 0 CS PS Consumer s gains Producer s gains Any regulation that causes the units from q 1 to q 0 to be not traded destroys these gains. This loss is the net cost of the regulation. q 1 q 0 Q D, Q S 24

25 Cost-Benefit Analysis t Price p b CS Tax Revenue An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss p s PS q 1 q 0 Q D, Q S 25

26 Cost-Benefit Analysis Price p f CS An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss So does a floor price set at p f PS q 1 q 0 Q D, Q S 26

27 Cost-Benefit Analysis Price CS An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss So does a floor price set at p f, a ceiling price set at p c p c PS q 1 q 0 Q D, Q S 27

28 Cost-Benefit Analysis Price p e p c CS PS An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss So does a floor price set at p f, a ceiling price set at p c, and a ration scheme that allows only q 1 units to be traded. q 1 q 0 Q D, Q S Revenue received by holders of ration coupons. 28

29 Compensating Variation and Equivalent Variation Two additional dollar measures of the total utility change caused by a price change are Compensating Variation and Equivalent Variation. 29

30 Compensating Variation p 1 rises. Q: What is the extra income that, at the new prices, just restores the consumer s original utility level? Or, after the policy has been implemented, how much must you be compensated to reach the same utility as before the policy? A: The Compensating Variation. 30

31 Compensating Variation p 1 =p 1 p 2 is fixed m = p x + p x u 1 31

32 Compensating Variation " p 1 =p 1 p 1 =p 1 u 1 p 2 is fixed = px " 1 " 1 + p " 2 m = p x + p x " u 2 32

33 Compensating Variation " " p 1 =p 1 p 1 =p 1 p 2 is fixed = px " 1 " 1 + p " 2 m = p x + p x " " 2 = p1x1 p2x u 1 m + " 2 u 2 " " 33

34 Compensating Variation " " p 1 =p 1 p 1 =p 1 p 2 is fixed = px " 1 " 1 + p " 2 m = p x + p x " " 2 = p1x1 p2x u 1 m + " 2 u 2 CV = m 2 -m 1. " " 34

35 Equivalent Variation p 1 rises. Q: What is the extra income that, at the original prices, just restores the consumer s original utility level? Or, how much would you pay to avoid moving to the new policy? A: The Equivalent Variation. 35

36 Equivalent Variation p 1 =p 1 p 2 is fixed m = p x + p x u 1 36

37 Equivalent Variation " p 1 =p 1 p 1 =p 1 u 1 p 2 is fixed = px " 1 " 1 + p " 2 m = p x + p x " u 2 37

38 Equivalent Variation " " p 1 =p 1 p 1 =p 1 u 1 p 2 is fixed = px " 1 " 1 + p " 2 " " 2 = m = p x + p x m p x p x u 2 " " 38

39 Equivalent Variation " p 1 =p 1 p 1 =p 1 p 2 is fixed = px " 1 " 1 + p " 2 " " 2 = m = p x + p x m p x p x " u 2 u 1 EV = m 1 -m 2. " " 39

40 Consumer s Surplus, Compensating Variation and Equivalent Variation When the consumer has quasilinear utility, CV = EV = CS. Why? There are no income effects with quasilinear utility. Otherwise, EV < CS < CV. 40