Lecture2_Question_Solution

Lecture2_Question_Solution - Lecture 2 Comprehensive...

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Unformatted text preview: Lecture 2 Comprehensive Question Solution 1. If there are no capital markets and no production, you just consume your endowment: C * = 100 , C * 1 = 0 , U = √ 100 · . 2. Like we discussed in class, there are two ways of solving it. Doing it one of either of these two ways is fine. A. Set MRS = MRT MRS =- ∂U/∂C ∂U/∂C 1 =- 1 2 · C 1 √ C √ C =- C 1 2 · C The amount you invest is your income, Y , less what you consume, C , that is, I = 100- C . So F = p 50 · (100- C ) and C 1 = 0 + p 50 · (100- C ) = p 50 · (100- C ) MRT = ∂F ∂C = ∂ ( p 50 · (100- C )) ∂C =- √ 50 2 · √ 100- C Setting MRS = MRT and substituting for C 1 gives- C 1 2 · C =- √ 50 2 · √ 100- C- p 50 · (100- C ) 2 · C =- √ 50 2 · √ 100- C Dividing both sides of the equation by- √ 50 and multiplying both sides by 2 · √ 100- C gives (100- C ) C = 1 , or 100- C = C . This can be easily solved to get C * = 50 I * = 100- C * = 50 C * 1 = p 50 · (100- 50) = 50 U = p C * · C * 1 = √ 50 · 50 = 353 . 55 B. Maximize utility directly max √ C · C 1 Substituting for C 1 gives max √ C · p 50 · (100- C ) max p 5000 C- 50 C 2 Taking the derivative with respect to C and setting it equal to zero gives...
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This note was uploaded on 10/21/2011 for the course RSM 332 taught by Professor Raymondkan during the Spring '08 term at University of Toronto.

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Lecture2_Question_Solution - Lecture 2 Comprehensive...

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