Lecture2_Question - ( C & ; C & 1 )...

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Lecture 2 Comprehensive Question You live in a two-date world, and your income is Y 0 = $100 today and Y 1 = $0 a year from now. Your utility is a function of how much you consume today, C 0 , and how much you consume in a year, C 1 as U ( C 0 ; C 1 ) = p C 0 C 1 . 1. Suppose there are no capital markets, and there are no production opportunities. What is your optimal consumption plan ( C & 0 ; C 1 ) and associated utility? 2. Suppose now that a production opportunity becomes available. You can invest some amount I today, and it will grow to amount F in a year: F = p 50 I . What is the utility-maximizing investment I ? What is your optimal consumption plan ( C & 0 ; C 1 ) and associated utility? What is the average return on your investment? available at the rate of r = 10% per year. What is your optimal consumption plan
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Unformatted text preview: ( C & ; C & 1 ) and associated utility? 4. The same investment opportunity as in part 2 exists, and borrowing and lending as in part 3 are available. What is the optimal investment I & ? What is your optimal consumption plan ( C & ; C & 1 ) and associated utility? What is the NPV of the investment? What is the average return on your investment? 5. The same investment opportunity as in part 2 exists, and borrowing and lending as in part 3 are available. Your utility function changes all of a sudden. It is now U ( C ; C 1 ) = ( C ) 1 = 3 & ( C 1 ) 2 = 3 + ( C ) 2 = 3 & ( C 1 ) 1 = 3 + p C + p C 1 : What is the optimal investment I & ? What is the NPV of the investment? Think before doing any calculations....
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