2010_lecture_11_ho

2010_lecture_11_ho - Economics 101Lecture 11 Time and...

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Economics 101—Lecture 11 Time and Valuing Life George J. Mailath February 22, 2011
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In our last episode 1 Insurance is actuarially fair if the expected value of the insurance is 0. If the probability of the bad state (accident) is π b , actuarially fair insurance is priced at p = π b , where p is ex ante price of $ 1 in the bad state. 2 A risk averse consumer always fully insures if actuarially fair insurance is available. 3 A risk averse consumer with a riskless endowment, will always invest in a risky asset with positive expected return. A tax on investments will increase the amount invested.
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Intertemporal Decision Making Suppose a bank offers an interest rate of r per period (such as a year). Give $ x to the bank today, and the bank gives you $ x ( 1 + r ) next period. So, a promise $ y next period is worth y 1 + r now. This is the discounted value of the promise. The present value of a bond that pays $ y in perpetuity is PV = y 1 + r + y ( 1 + r ) 2 + y ( 1 + r ) 3 + ∙∙∙ = t = 1 y ( 1 + r ) t = y 1 + r ± 1 1 ( 1 1 + r ) ² = y r .
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The budget constraint I Suppose there are two periods (0 and 1). Consumer has income I in period 0 and no income in period 1. Consumer can save at rate r . Consumption bundle ( c 0 , c 1 ) , where c t is consumption in period t , t = 0 , 1. Consumption in period 1 is c 1 = ( I c 0 )( 1 + r ) , so budget constraint is c 0 ( 1 + r ) + c 1 = I ( 1 + r ) = c 0 + 1 ( 1 + r ) c 1 = I . The price of period-1 consumption in terms of period-0 consumption is p 1 = 1 / ( 1 + r ) .
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The budget constraint II Now consumer has no income in period 0 and income I in period 1. Consumer can borrow at rate r . Consumption in period 1 is
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This note was uploaded on 03/02/2011 for the course ECON 101 taught by Professor Dannicatambay during the Spring '08 term at UPenn.

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2010_lecture_11_ho - Economics 101Lecture 11 Time and...

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