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Lecture 11

# Lecture 11 - Economics 101A(Lecture 11 Stefano DellaVigna...

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Economics 101A (Lecture 11) Stefano DellaVigna October 6, 2009

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Outline 1. Application 3: Altruism and charitable donations II 2. Introduction to probability 3. Expected Utility 4. Insurance
1 Altruism and Charitable Dona- tions II Wendy maximizes max c M ,D u ( c W ) + αu ( M M + D ) s.t. c W M W D Rewrite as: max D u ( M W D ) + αu ( M M + D ) First order condition: u 0 ( M W D ) + αu 0 ( M M + D ) = 0 Second order conditions: u 00 ( M W D ) + αu 00 ( M M + D ) < 0

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Assume α = 1 . Solution? u 0 ( M W D ) = u 0 ( M M + D ) M W D = M M + D or D = ( M W M M ) / 2 Transfer money so as to equate incomes! Careful: D < 0 (negative donation!) if M M > M W Corrected maximization: max D u ( M W D ) + αu ( M M + D ) s.t.D 0 Solution ( α = 1 ) : D = ( ( M W M M ) / 2 if M W M M > 0 0 otherwise
Assume interior solution . ( D > 0 ) Comparative statics 1 (altruism): ∂D ∂α = u 0 ( M M + D ) u 00 ( M W D ) + αu 00 ( M M + D ) > 0 Comparative statics 2 (income of donor): ∂D ∂M W = u 00 ( M W + D ) u 00 ( M W D ) + αu 00 ( M M + D ) > 0 Comparative statics 3 (income of recipient ): ∂D ∂M M = αu 00 ( M M + D ) u 00 ( M W D ) + αu 00 ( M M + D ) < 0

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A quick look at the evidence From Andreoni (2002)
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Lecture 11 - Economics 101A(Lecture 11 Stefano DellaVigna...

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