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Michael Rothschild UCLA Economics 145a October 14, 2009 1 Problem 1. The &rst homework problem asks you to do comparative statics in a prob- lem where an individual picks how much of life to spend on schooling. Let±s write equation (4) of the handout for April 21²which gives the ex- pected present discounted value of earning ²correctly. With s years of schooling you earn at a rate W ( s ) = e bs while you are working. If you start school at age 6 and work until age T and discount earnings at rate r the present discounted value of your earnings are V ( s ) = W ( s ) e 6 r Z T 6+ s exp( rt ) dt .Start out by simplifying the above expression by mutliplying by the pos- itive constant e 6 r : We further simplify the notation somewhat letting ~ T = T 6 years. Then our problem is to choose s to maximize ~ V ( s ) = W ( s ) Z ~ T s exp( rt ) dt: We can now drop the tildes and just choose s to maximize V ( s ) = W ( s ) Z T s exp( rt ) dt The &rst term is the wage that you earn; the second term is just the discounted amount of time that you work. Integrating we see that

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