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
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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
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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 ):
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This note was uploaded on 09/02/2010 for the course ECON 101a taught by Professor Staff during the Fall '08 term at University of California, Berkeley.

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

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