Valuation 3: Welfare Measures

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Valuation 3 Welfare Measures

• Willingness to pay and willingness to act
  compensation
• Equivalent variation versus compensating
  variation
• Price changes versus quantity changes

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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 lt WTAC, because of income effect

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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

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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

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Welfare Measures -2

• In case of quantity changes, compensating and
  equivalent variation are defined as
• U0 results from (p,q0,y). If q0 increases to q1,
  income has to be reduced by CV/p to keep the same
  utility

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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

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Two Polar Cases

• An individuals 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

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Perfect Substitution

• The direct utility
• This yields indirect utility function
• Compensating, equivalent variation (p11)
• Ergo, EC

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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

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A More General Case

• An individuals 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

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A More General Case -2

• Which implies
• Compensating, equivalent variation

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WTP v WTAC

• Compensating, equivalent variation
• Thus, EgtC (EltC) for a normal (inferior) good
• Note, Hanemann switched signs, so CVgtEV

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A More General Case -3

• In the optimum
• Define a consumper surplus
• And an income elasticity

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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

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A More General Case -5

• If ?0 (no income effect), or if ??, EAC
• 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

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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

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WTP v WTAC
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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.