Valuation 3: Welfare Measures Willingness to pay and willingness to act compensation Equivalent variation versus compensating variation Price changes versus quantity changes

WTP and WTAC Consider price fall P*  P # Willingness to pay (WTP) to secure price fall is known as equivalent variation Willingness to accept compensation (WTAC) to forego price fall is known as compensating variation WTP < WTAC, because of income effect

WTP and WTAC -2 There are gains and loss, so four measures –WTP to secure a gain –WTAC to forego a gain –WTP to prevent a loss –WTAC to tolerate a loss People view gains and losses differently Confirmed by empirical studies, but not uncontested Implies that surveys, policies need to be carefully designed

Welfare Measures Compensating variation is the quantity of income that compensates consumers for a price change, that is, returns them to their original welfare Equivalent variation is an income change that yields the same utility change as the price change

Welfare Measures -2 In case of quantity changes, compensating and equivalent variation are defined as U 0 results from (p,q 0,y). If q 0 increases to q 1, income has to be reduced by CV/p to keep the same utility

Welfare Measures -3 This need not hold for quantity changes. The reason is that the curvature of the utility function can, in principle, increase or decrease at higher levels of utility In practice, however, environmental goods are relatively scarcer than market commodities, so that one may expect the compensating variation to be smaller than the equivalent variation

Two Polar Cases An individual‘s utility u depends on the consumption of x and a fixed quantity q This yields ordinary demand functions h and an indirect utility function v An alternative way of defining compensating and equivalent variation is

Perfect Substitution The direct utility This yields indirect utility function Compensating, equivalent variation (p 1 =1) Ergo, E=C

Zero Substitutability The direct utility There are areas where q is constraining; the agent would be willing to pay a finite amount to get more q and less x However, no amount of additional x would compensate for a loss of q Here, equivalent variation is infinitely larger than compensating variation This suggests that substitution is key

A More General Case An individual‘s utility u depends on the consumption of x and a fixed quantity q The dual yields the inverse compensated demand curve And an expenditure function

A More General Case -2 Which implies Compensating, equivalent variation

WTP v WTAC Compensating, equivalent variation Thus, E>C (E<C) for a normal (inferior) good Note, Hanemann switched signs, so CV>EV

A More General Case -3 In the optimum Define a „consumper surplus“ And an income elasticity

A More General Case -4 Some trickery and approximation However, Where  is the income elasticity of ordinary demand,  is the budget share of q,  is the own-price elasticity of compensated demand, and  is the substitution elasticity of q

A More General Case -5 If  =0 (no income effect), or if  = , E=A=C If, on the other hand, income elasticity is high, or there few substitutes for q, then  can vary substantially, even over small ranges of q

Theory and Practice Horowitz and McConnell collect 208 observations of WTP and WTAC from 45 studies For all studies, the average ratio WTAC/WTP is 7.2 (0.9) However, for public or non-market goods, the ratio is 10.4 (2.5) For ordinary goods, it is 2.9 (0.3) For money, it is 2.1 (0.2) This is not inconsistent with theory

WTP v WTAC

Welfare Measures –4 (out) Compensating variation is defined as This is the same as If x is a weak compliment to q, and is the choke price, E = 0.