Presentation on theme: "Welfare measurement: individual CS, CV, EV and PS"— Presentation transcript:
1Welfare measurement: individual CS, CV, EV and PS (Cost Benefit Analysis DEC 51304)Z&D 5R. Jongeneel
2Lecture Plan Welfare function of individual Willingness to pay & willingness to acceptCompensated & Equivalent VariationConsumer & Producer Surplus measuresApproximation and accuracyBC-A in Single consumer economyInterdependent utility (social prefs)
3Welfare function of individual Understanding ‘economic man’Utility:Change:
4Welfare function of individual Conversion of utils in moneyMarginal utility of income:
5Willingness to Pay & Accept WTP: the amount one is prepared to pay in order to avoid a costWTA: the amount one would like to have to forego a goodRelated to CV & EV measures of welfare
6WTP 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€ Equivalent Utility Gains (benefit) Suppose gasoline can be bought only in lumps of one gallon.Use r1 to denote the most a single consumer would pay for a 1st gallon -- call this her reservation price for the 1st gallon.r1 is the euro equivalent of the marginal utility of the 1st gallon.
8€ Equivalent Utility Gains (benefit) Now that she has one gallon, use r2 to denote the most she would pay for a 2nd gallon -- this is her reservation price for the 2nd gallon.r2 is the euro equivalent of the marginal utility of the 2nd gallon.
9€ Equivalent Utility Gains (benefit) Generally, if she already has n-1 gallons of gasoline then rn denotes the most she will pay for an nth gallon.rn is the euro equivalent of the marginal utility of the nth gallon.
10€ Equivalent Utility Gains (benefit) r1 + … + rn will therefore be the euro equivalent of the total change to utility from acquiring n gallons of gasoline at a price of €0.So r1 + … + rn - pGn will be the euro equivalent of the total change to utility from acquiring n gallons of gasoline at a price of €pG each.
11€ Equivalent Utility Gains A plot of r1, r2, … , rn, … against n is a reservation-price curve. This is not quite the same as the consumer’s demand curve for gasoline.
13€ Equivalent Utility Gains (surplus) The euro equivalent net utility gain for the 1st gallon is €(r1 - pG)and is €(r2 - pG) for the 2nd gallon,and so on, so the euro value of the gain-to-trade is €(r1 - pG) + €(r2 - pG) + … for as long as rn - pG > 0.
14€ Equivalent Utility Gains (surplus) € value of net utility gains-to-trader1r2r3r4pGr5r6123456
15Compensating Variation and Equivalent Variation 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
16Compensating Variation Assume in a market price p1 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.
18Compensating Variation p1=p1’ p1=p1”p2 is fixed.x2u1u2x1
19Compensating Variation p1=p1’ p1=p1”p2 is fixed.x2u1u2x1
20Compensating Variation p1=p1’ p1=p1”p2 is fixed.x2u1CV = m2 - m1.u2x1
21Equivalent Variation Assume in a market price p1 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.
23Equivalent Variationp1=p1’ p1=p1”p2 is fixed.x2u1u2x1
24Equivalent Variationp1=p1’ p1=p1”p2 is fixed.x2u1u2x1
25Equivalent Variation EV = m1 - m2. p1=p1’ p1=p1” p2 is fixed. x2 u1 u2
26Relationship CV, EV and B, C Comp. Var.Equiv. VarDefinitionLeave one as well off as beforeLeave one as well off as afterWelfare gain (benefit)WTP for the changeWTA to forego the changeWelfare loss (cost)WTA as compensation for changeWTP to avert the change
27Consumer’s SurplusApproximating 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.
28Footnote on WTP curveA 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.
29Footnote on WTP & Demand 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.
30Consumer’s Surplus (€) Reservation price curve for gasoline Ordinary demand curve for gasoline$ value of net utility gains-to-tradepGGasoline
31Consumer’s Surplus (€) Reservation price curve for gasoline Ordinary demand curve for gasoline$ value of net utility gains-to-tradeConsumer’s SurpluspGGasoline
32Consumer’s SurplusThe consumer’s utility function is quasilinear in x2.Take p2 = 1. Then the consumer’s choice problem is to maximizesubject to
33Consumer’s Surplus That is, choose x1 to maximize The first-order condition isThat is,This is the equation of the consumer’s ordinary demand for commodity 1.
34Consumer’s Surplus Ordinary demand curve, p1 CS is exactly the consumer’s utility gain from consuming x1’ units of commodity 1.CS
35Consumer’s SurplusConsumer’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.
45Producer’s Surplus y Output price (p) Marginal Cost Variable Cost of producing y’ units is the sum of the marginal costsy(output units)
46Producer’s Surplus y Revenue less VC is the Producer’s Surplus. Output price (p)Marginal CostVariable Cost of producing y’ units is the sum of the marginal costsy(output units)
47CBA in Individual consumer economy & Small project
48CBA in Individual consumer economy & Small project Single individualSingle price change / income kept constantNo 2nd market price effectsFirst-best economy (no other distortions)Marshallian CS good approximationPS good approximation
49CBA in Individual consumer economy & Small project q1.0q1.1q2.1q2.0
50CBA in Individual consumer economy & Small project Change in CS : P10 a b P11Income constant : change in spending is zero!q10 c b q11 – P10 a c P11 – q21 d e q 20 = 0Change in welfare (dW)dW = P10 a b P11 = P10 a c P11 + abcdW = q10 a b q11 + q21 d e q 20
51CBA in Individual consumer economy & Small project +--q1.0q1.1q2.1q2.0
52CBA in Individual consumer economy & Small project Change in welfare: dW continued.Small project: price changes smallTotal benefits-method => income effect- method
53Interdependent Utilities & Welfare Measurement Social preferences:Altruism EnvyFormally: