( ) = CS x t dt Welfare change involved in moving from ( p 0 , - PDF document

Contents of the presentation • Consumers’ surplus • Equivalent and compensating variations Measuring Welfare Change • Measuring welfare • Welfare change for quasilinear utility Mari Lymysalo & Miikka Taponen • Aggregate consumers’ surplus • Nonparametric bounds • Consumers’ surplus and cigarette industry S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 1 Seminar on Microeconomics - Fall 1998 / 2 What is consumers’ surplus? An ideal measure ′ p ∫ ( ) = CS x t dt • Welfare change involved in moving from ( p 0 , m 0 ) to ( p ´ , m ´ ) is the difference in indirect 0 p utility: • Consumers’ surplus (CS) is a classical ( ) ( ) ′ ′ − 0 0 v p , m v p , m . measure of welfare change • It is an exact measure only in special • The utility theory is purely ordinal in nature, circumstances and therefore; a monetary measure to quantify these utility changes would be convenient => More general measures are needed S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 3 Seminar on Microeconomics - Fall 1998 / 4 Compensating and equivalent variations A monetary measure for welfare change ( ) ( ) ( ) = µ ′ − µ = µ ′ − ′ ′ 0 0 0 0 0 0 EV p p ; , m p p ; , m p p ; , m m • If we adopt the indirect money metric utility ( ) ( ) ( ) = µ ′ ′ ′ − µ ′ = ′− µ ′ ′ function as the measure of utility, the utility 0 0 0 CV p p ; , m p p ; , m m p p ; , m difference becomes: ( ) ( ) µ ′ ′ − µ q p 0 m 0 q p ; , m ; , EV: “What income change at the current prices would be equivalent to the proposed change?” • Choosing the base prices q equal to p 0 or to CV: “What income change would be necessary p´ leads to the following two measures: to compensate for the occurred price change?” S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 5 Seminar on Microeconomics - Fall 1998 / 6 1

Equivalent and compensating variations Measuring Welfare • EV and CV are not generally equal because • Paper by Ebert suggests axiomatic approach the value of money depends on what the • 4 properties required from welfare measure prices are – indicates welfare increase reliably • The sign of EV and CV is the always the – ranks different situations appropriately same because they measure the same utility – evaluates changes in money differences – can be derived from observable data • Which is the most suitable measure? • Let’s examine a measure of the change in welfare, W S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 7 Seminar on Microeconomics - Fall 1998 / 8 Property I (exactness) Property II (correct ranking) • If the individual is better off facing prices p 2 • Sign of W must reflect the type of welfare change correctly than prices p 1 then welfare change with respect to a common status quo should ( ) ( ) ( ) > ⇒ < register this fact 0 1 0 1 W p , p 0 v p , m v p , m ( ) ( ) ( ) ( ) ( ) ( ) ( ) = ⇒ = 0 1 0 1 ≤ ⇔ ≤ W p , p 0 v p , m v p , m 0 1 0 2 1 2 W p , p W p , p v p , m v p , m ( ) ( ) ( ) < ⇒ > 0 1 0 1 W p , p 0 v p , m v p , m S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 9 Seminar on Microeconomics - Fall 1998 / 10 Property III (normalisation) A measure fulfilling I-III • W should be measured in money • There is only one measure that fulfils all the properties I-III, namely Hicksian equivalent • One possible measure could be variation ( ) ( ) ( ) ( ) ( ) ( )   = = − ( ) 0 1 0 1 0 1 0 0 1 W p p , EV p p , e p v p m , , e p v p m , , , α =  −  0 0 W p p 1 m   α • Proved in the paper • This W exists for all v, it is well-defined, and it is computable S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 11 Seminar on Microeconomics - Fall 1998 / 12 2

Other welfare measures Quasilinear utility ( ) ( ) = + v p m , v p m • In some cases the compensating variation (CV) is better measure than EV • Quasilinear utility is independent of income – CV does not fulfil property II, but there is a (if the income is not too small) similar property that CV does fulfil • Example: toilet paper • Consumer’s surplus CS is a popular welfare • Consumers’ surplus is an exact measure of measure welfare change if and only if the utility is – It is an acceptable approximation of EV quasilinear – CS is easy to compute, it can be derived from • Then: EV = CV = CS. Why? market demand S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 13 Seminar on Microeconomics - Fall 1998 / 14 Consumers’ surplus as an Integral of Hicksian demand approximation? • Equivalent and compensating variations can be written as: (derived in Varian’s book) • Hicksian demand is not directly observable 0 p since it depends on utility ( ) ( ) ( ) ∫ = ′ − ′ ′ = ′ 0 EV e p u , e p u , h p u dp , • Could consumers’ surplus be used as a good ′ p approximation for welfare change? p 0 ( ) ( ) ( ) ∫ = − ′ = 0 0 0 0 CV e p u , e p u , h p u dp , • It can be shown that CS lies between ′ p equivalent and compensating variations • The integral of Hicksian demand curve is the correct measure of welfare S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 15 Seminar on Microeconomics - Fall 1998 / 16 Aggregate consumers’ surplus Nonparametric bounds ∞ ∞ ( ) n ( ) n n ∑ ∑ ∑ ∫ ( ) ∫ ( ) = = = • Nonparametric bounds on the money metric V p v p x t dt x t dt i i i = = = i 1 i 1 i 1 p p utility function can be derived without having to specify a single parametric form • Aggregate consumers’ surplus is an appropriate measure if utility functions of all consumers are • The bounds can be tightened by increasing quasilinear the amount of observed choices (see 8.11) • In general it is not an exact measure for welfare, • The overcompensation function and the however; it is often used as one undercompensation function bound the true • This issue is discussed in next week’s compensation function m ( p , x 0 ) presentation S ystems S ystems Analysis Laboratory Analysis Laboratory Session 8 - M. Lymysalo & M. Taponen Session 8 - M. Lymysalo & M. Taponen Helsinki University of Technology Helsinki University of Technology Seminar on Microeconomics - Fall 1998 / 17 Seminar on Microeconomics - Fall 1998 / 18 3