101A_lec11

101A_lec11 - Economics 101A(Lecture 11 Stefano DellaVigna...

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Economics 101A (Lecture 11) Stefano DellaVigna February 24, 2009

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Outline 1. Application 2: Intertemporal choice II 2. Application 3: Altruism and charitable donations 3. Introduction to probability 4. Expected Utility
1 Intertemporal choice II Nicholson Ch. 17, pp. 597-601 (502—506, 9th) Comparative statics with respect to income M 0 Rewrite ratio of f.o.c.s as U 0 ( c 0 ) 1 + r 1 + δ U 0 ( c 1 ) = 0 Substitute c 1 in using c 1 = M 1 +( M 0 c 0 ) (1 + r ) to get U 0 ( c 0 ) 1 + r 1 + δ U 0 ( M 1 + ( M 0 c 0 ) (1 + r )) = 0

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Apply implicit function theorem: ∂c 0 ( r, M ) ∂M 0 = 1+ r 1+ δ U 00 ( c 1 ) (1 + r ) U 00 ( c 0 ) 1+ r 1+ δ U 00 ( c 1 ) ( (1 + r ))
Denominator is always negative Numerator is positive ∂c 0 ( r, M ) /∂M 0 > 0 – consumption at time 0 is a normal good. Can also show ∂c 0 ( r, M ) /∂M 1 > 0

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Comparative statics with respect to interest rate r Apply implicit function theorem: ∂c 0 ( r, M ) ∂r = 1 1+ δ U 0 ( c 1 ) U 00 ( c 0 ) 1+ r 1+ δ U 00 ( c 1 ) ( (1 + r )) 1+ r 1+ δ U 00 ( c 1 ) ( M 0 c 0 ) U 00 ( c 0 ) 1+ r 1+ δ U 00 ( c 1 ) ( (1 + r )) Denominator is always negative Numerator: First term negative (substitution e ff .) Numerator: Second term (income e ff ect:) positive if M 0 > c 0 negative if M 0 < c 0 .
2 Altruism and Charitable Dona- tions Maximize utility = satisfy self-interest?

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