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Willig_approximation_AEM_630_2009

# Willig_approximation_AEM_630_2009 - How inaccurate is S...

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1 Δp q o q 1 P o P 1 a b c H(u 1 ) H(u 0 ) D(m 0 ) Income effect Substitution effect How inaccurate is S? Willig’s Approximation Δq ΔS = a + b CV = a EV = a + b + c a and b triangles: height 1 P 0 – P 1 Substitution effect: hold U constant and vary p and m Income effect = Δq (hold p constant) can estimate areas b and c (may be small?) (1) q m Δm Δq η =

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2 ∆m = the income effect of price ∆ (real income ∆ caused by price ∆ that leads to ∆q, when p is held constant) Income ∆ that leads to ∆q ≈ ∆S (area a + b; exact ∆ really = area a) Substitute ∆S for ∆m in equation (1) and solve: (for small ∆p or linear demand) Assume ∆S ≈ q(∆p) (4) (approx. if linear demand curve and at midpoint) We know ∆S = a + b (5) Therefore, CV (area a) ≈ ∆S (= area a + b) – area b After substituting LHS of (4) into (3), get: (2) m ΔS ηq Δq 2245 ) 3 ( m Δp q ΔS η 2 1 b area get (2), from and Δp Δq 2 1 b area figure, From = 2245
3 This simplifies to: ∆S overestimates CV and error = income elasticity over 2 times the ratio of income ∆ to total income ∆S okay as long as: (1) low income elasticity, and/or

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Willig_approximation_AEM_630_2009 - How inaccurate is S...

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