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Welfare measurement: individual CS, CV, EV and PS (Cost Benefit Analysis DEC 51304) Z&D 5 R. Jongeneel.

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Presentation on theme: "Welfare measurement: individual CS, CV, EV and PS (Cost Benefit Analysis DEC 51304) Z&D 5 R. Jongeneel."— Presentation transcript:

1 Welfare measurement: individual CS, CV, EV and PS (Cost Benefit Analysis DEC 51304) Z&D 5 R. Jongeneel

2 Lecture Plan  Welfare function of individual  Willingness to pay & willingness to accept  Compensated & Equivalent Variation  Consumer & Producer Surplus measures  Approximation and accuracy  BC-A in Single consumer economy  Interdependent utility (social prefs)

3 Welfare function of individual  Understanding ‘economic man’  Utility:  Change:

4 Welfare function of individual  Conversion of utils in money  Marginal utility of income: 

5 Willingness to Pay & Accept  WTP: the amount one is prepared to pay in order to avoid a cost  WTA: the amount one would like to have to forego a good  Related to CV & EV measures of welfare

6 WTP and Gains-to-Trade  You can buy as much gasoline as you wish at €1 per gallon once you enter the gasoline market.  Q: What is the most you would pay to enter the market?

7  Suppose gasoline can be bought only in lumps of one gallon.  Use r 1 to denote the most a single consumer would pay for a 1st gallon -- call this her reservation price for the 1st gallon.  r 1 is the euro equivalent of the marginal utility of the 1st gallon. € Equivalent Utility Gains (benefit)

8  Now that she has one gallon, use r 2 to denote the most she would pay for a 2nd gallon -- this is her reservation price for the 2nd gallon.  r 2 is the euro equivalent of the marginal utility of the 2nd gallon. € Equivalent Utility Gains (benefit)

9  Generally, if she already has n-1 gallons of gasoline then r n denotes the most she will pay for an nth gallon.  r n is the euro equivalent of the marginal utility of the nth gallon. € Equivalent Utility Gains (benefit)

10  r 1 + … + r n will therefore be the euro equivalent of the total change to utility from acquiring n gallons of gasoline at a price of €0.  So r 1 + … + r n - p G n will be the euro equivalent of the total change to utility from acquiring n gallons of gasoline at a price of €p G each. € Equivalent Utility Gains (benefit)

11  A plot of r 1, r 2, …, r n, … against n is a reservation-price curve. This is not quite the same as the consumer’s demand curve for gasoline. € Equivalent Utility Gains

12 r1r1 r2r2 r3r3 r4r4 r5r5 r6r6

13  The euro equivalent net utility gain for the 1st gallon is €(r 1 - p G )  and is €(r 2 - p G ) for the 2nd gallon,  and so on, so the euro value of the gain-to-trade is €(r 1 - p G ) + €(r 2 - p G ) + … for as long as r n - p G > 0. € Equivalent Utility Gains (surplus)

14 r1r1 r2r2 r3r3 r4r4 r5r5 r6r6 pGpG € value of net utility gains-to-trade

15  Two ‘true’ monetary measures of the total utility change caused by a price change and/or income change are Compensating Variation and Equivalent Variation.  Principle: measure difference between utility indifference curves Compensating Variation and Equivalent Variation

16  Assume in a market price p 1 rises.  Q: What is the least extra income that, at the new prices, just restores the consumer’s original utility level?  A: The Compensating Variation. Compensating Variation

17 x2x2 x1x1 u1u1 p1=p1’p1=p1’p 2 is fixed.

18 Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

19 Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

20 Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. CV = m 2 - m 1.

21  Assume in a market price p 1 rises.  Q: What is the least extra income that, at the original prices, just restores the consumer’s original utility level?  A: The Equivalent Variation. Equivalent Variation

22 x2x2 x1x1 u1u1 p1=p1’p1=p1’p 2 is fixed.

23 Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

24 Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

25 Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. EV = m 1 - m 2.

26 Relationship CV, EV and B, C Comp. Var.Equiv. Var DefinitionLeave one as well off as before Leave one as well off as after Welfare gain (benefit) WTP for the change WTA to forego the change Welfare loss (cost) WTA as compensation for change WTP to avert the change

27  Approximating the net utility gain area under the reservation-price curve by the corresponding area under the ordinary demand curve gives the Consumer’s Surplus measure of net utility gain. Consumer’s Surplus

28  A consumer’s reservation-price curve is not quite the same as her ordinary demand curve. Why not?  A reservation-price curve describes sequentially the values of successive single units of a commodity.  An ordinary demand curve describes the most that would be paid for q units of a commodity purchased simultaneously. Footnote on WTP curve

29  The difference between the consumer’s reservation-price and ordinary demand curves is due to income effects.  But, if the consumer’s utility function is quasilinear in income then there are no income effects and Consumer’s Surplus is an exact € measure of gains-to-trade. Footnote on WTP & Demand

30 Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pGpG $ value of net utility gains-to-trade (€)

31 Consumer’s Surplus Gasoline Reservation price curve for gasoline Ordinary demand curve for gasoline pGpG $ value of net utility gains-to-trade Consumer’s Surplus (€)

32 Consumer’s Surplus The consumer’s utility function is quasilinear in x 2. Take p 2 = 1. Then the consumer’s choice problem is to maximize subject to

33 Consumer’s Surplus That is, choose x 1 to maximize The first-order condition is That is, This is the equation of the consumer’s ordinary demand for commodity 1.

34 Consumer’s Surplus Ordinary demand curve, p1p1 CS is exactly the consumer’s utility gain from consuming x 1 ’ units of commodity 1.

35  Consumer’s Surplus is an exact euro measure of utility gained from consuming commodity 1 when the consumer’s utility function is quasilinear in commodity 2.  Otherwise Consumer’s Surplus is an approximation. Consumer’s Surplus

36 Consumer’s Surplus and P-change p1p1 CS before p 1 (x 1 )

37 Consumer’s Surplus and P change p1p1 CS after p 1 (x 1 )

38 Consumer’s Surplus and P change p1p1 Lost CS p 1 (x 1 ), inverse ordinary demand curve for commodity 1.

39  Relationship 1: When the consumer’s preferences are quasilinear, all three measures are the same. Consumer’s Surplus, Compensating Variation and Equivalent Variation

40 So when the consumer has quasilinear utility, CV = EV =  CS. But, otherwise, we have: Relationship 2: In size, EV <  CS < CV.

41 CV, EV and CS and price decline p1p1 M(p,m) A B C H(p,U 1 ) H(p,U 11 ) CS = A + B CV = A EV = A + B + C 1 2

42  Changes in a firm’s welfare can be measured in dollars much as for a consumer.  Producer surplus is quasi-rent and not ‘real surplus’.  Amount for remunerating quasi-fixed factors Producer’s Surplus

43 y (output units) Output price (p) Marginal Cost

44 Producer’s Surplus y (output units) Output price (p) Marginal Cost Revenue =

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

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

47 CBA in Individual consumer economy & Small project

48  Single individual  Single price change / income kept constant  No 2 nd market price effects  First-best economy (no other distortions)  Marshallian CS good approximation  PS good approximation

49 CBA in Individual consumer economy & Small project P 1.0 P 1.1 P 2.0 q 1.0 q 1.1 q 2.1 q 2.0 d e a b c

50 CBA in Individual consumer economy & Small project  Change in CS : P 10 a b P 11  Income constant : change in spending is zero!  q 10 c b q 11 – P 10 a c P 11 – q 21 d e q 20 = 0  Change in welfare (dW)  dW = P 10 a b P 11 = P 10 a c P 11 + abc  dW = q 10 a b q 11 + q 21 d e q 20

51 CBA in Individual consumer economy & Small project P 1.0 P 1.1 P 2.0 q 1.0 q 1.1 q 2.1 q 2.0 d e a b c + --

52 CBA in Individual consumer economy & Small project  Change in welfare: dW continued .  Small project: price changes small . Total benefits- method => income effect- method

53 Interdependent Utilities & Welfare Measurement  Social preferences:  Altruism Envy  Formally:

54 Interdependence & Welfare  Household h’s utility change:

55 Double Interdependence & Welfare  h cares about k and k cares about h  Int.dep. multiplier: 


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