2.3 Specifying Empirical Functions.pdf - Specifying Empirical Func2ons for Welfare Measurement Welfare measurement in cost-bene\ufb01t analysis Welfare

2.3 Specifying Empirical Functions.pdf - Specifying...

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Specifying Empirical Func2ons for Welfare Measurement Welfare measurement in cost-benefit analysis Welfare Measurement in Cost-Benefit Analysis
Suppose we don’t know this en=re demand curve. We observe the equilibrium price and quan=ty of P* and X* and want to es=mate a change in consumer surplus. With an elas=city we can es=mate the change in CS for any change in price. Change in Consumer Surplus (CS) Welfare Measurement in Cost-Benefit Analysis
Change in CS as func2on of elas2city Price elas=city of demand ε d = (% Δ X d )/(% Δ P) = ( Δ X d / X d )/( Δ P/P) = ( Δ X d / X d ) (P/ Δ P) = ( Δ X d / Δ P) (P/X d ) This implies: Δ X d = ε d ( Δ P X d )/P So the change in consumer surplus (for linear demand) is Δ CS = [(- Δ P) X*] + [½ ⋅Δ X (- Δ P)] SeRng X d =X* and P=P*, this can be wriTen as Δ CS = [(- Δ P) X*] + [½ [ ε d ( Δ P X*)/P*] (- Δ P)] [(- Δ P) X*] [1+(½ ⋅ε d ⋅Δ P/P*)] Welfare Measurement in Cost-Benefit Analysis
Es2ma2ng Changes in Consumer Surplus using Elas2city An empirical example Assume X* = 15.3 P* = $30 and P 1 = $28

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