332mid08a - UNIVERSITY OF TORONTO Joseph L Rotman School of...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Oct. 21, 2008 Ezer/Kan/Florence RSM332 MID-TERM EXAMINATION Pomorski/Zhou SOLUTIONS 1. (a) For Mr. Oh, his consumption at time 0 and time 1 are given by C = 1000- I and C 1 = 30 I 1 2 . Therefore, we can write his utility as U O = C 1 2 C 1 2 1 = (1000- I ) 1 2 (30 I 1 2 ) 1 2 = √ 30(1000- I ) 1 2 I 1 4 = √ 30(1000 I 1 2- I 3 2 ) 1 2 . Differentiating U O with respect to I , we obtain d U O d I = 1 2 √ 30(1000 I 1 2- I 3 2 )- 1 2 1000 2 I- 1 2- 3 2 I 1 2 . Setting the derivative equal to zero, we have 1000 2 I- 1 2- 3 2 I 1 2 = 0 ⇒ I = 333 . 33 . Therefore, the optimal investment by Mr. Oh is I * = 333 . 33. (b) If Mrs. Ner follows the investment decision of Mr. Oh, her consumption at time 0 and time 1 will be C = 1000- 333 . 33 = 666 . 67 and C 1 = 30 √ 333 . 33 = 547 . 72. It follows that her utility will be U N ( C ,C 1 ) = C 1 4 C 3 4 1 = (666 . 67) 1 4 (547 . 72) 3 4 = 575 . 30 . (c) The utility of Mrs. Ner is given by U N = C 1 4 C 3 4 1 = (1000- I ) 1 4 (30 I 1 2 ) 3 4 = 30 3 4 (1000- I ) 1 4 I 3 8 = 30 3 4 (1000 I 3 2- I 5 2 ) 1 4 . Differentiating U N with respect to I , we obtain d U N d I = 1 4 30 3 4 (1000 I 3 2- I 5 2 )- 3 4 3000 2 I 1 2- 5 2 I 3 2 . Setting the derivative equal to zero, we have 3000 2 I 1 2- 5 2 I 3 2 = 0 ⇒ I = 600 . 1 Therefore, the optimal investment by Mrs. Ner is I * = 600. At the optimal level of investment, the utility of Mrs. Neh is given by U N = (1000- I * ) 1 4 (30 I * 1 2 ) 3 4 = 631 . 19 . (d) When Mrs. Ner invests 333.33, her consumption at time 0 and 1 are given by C = 666 . 67 and C 1 = 547 . 72. In order for Mrs. Ner to have a utility of 631.19, she needs a consumption at time 0 to satisfy C 1 4 (547 . 72) 3 4 = 631 . 19 ⇒ C = 965 . 98 . This means that she needs an additional consumption of 965 . 98- 666 . 67 = 299 . 31 at time 0 for her to be indifferent....
View Full Document

This note was uploaded on 01/10/2011 for the course RSM RSM332 taught by Professor Booth during the Spring '10 term at University of Toronto.

Page1 / 6

332mid08a - UNIVERSITY OF TORONTO Joseph L Rotman School of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online