practice5b

practice5b - Practice Problems Consumption Over Time...

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Practice Problems Consumption Over Time University of California, Los Angeles 1. Courtney has an income of $50 today and $20 tomorrow. She has the following production technology: Q 2 = 20 I 1 2 1 , where I 1 is the investment today and Q 2 is the gross return of the investment. The interest rate is 100% . (a) Suppose that Courtney wants to consume $45 tomorrow. How much should she consume and invest today? (b) Find the net present value of Courtney±s maximum attainable wealth. (c) Her utility function is U ( C 1 ; C 2 ) = C 1 2 1 C 1 2 2 . Find her optimal invest- ment and consumption. 2. Sarah has $100 today. She has the following production technology: Q 2 = 110 ln ( I 1 ) , where I 1 is the investment today and Q 2 is the gross return of the investment a year from now. Sarah can borrow at a rate of 10% . Her utility function between consumption today C 1 and consumption a year from now C 2 is U ( C 1 ; C 2 ) = C 1 C 2 . (a) Find Sarah±s optimal investment choice.
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practice5b - Practice Problems Consumption Over Time...

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