Fall 2007 - Newhouse's Class - Exam 2

Fall 2007 - Newhouse's Class - Exam 2 - Economics 171:...

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

View Full Document Right Arrow Icon
Economics 171: Decisions Under Uncertainty Midterm 2 (November 15, 2007) – Solutions 1. (25 pts) Beth’s utility function is 1 ln 2 ux = . Matthew’s utility function is ln vx x =+ . a. Calculate Beth’s coefficient of absolute risk aversion. 2 2 11 ', ' ' 22 1 '' 1 2 1 ' 2 uu xx u x x λ == =− = b. Show whether Beth is nonincreasingly, nondecreasingly or constantly risk averse. 2 1 0 < Beth is nonincreasingly risk averse. c. Find Beth’s certainty equivalent for lottery p = {$e, 0.5; $e 3 , 0.5}. () 33 2 1 3 ln ; ln 2 2 $,0 .5 ;$ ,0 11 13 1 22 22 1 ln 1 2 ln 2 ue e e e u e u e x x xe = = =+= = = d. Calculate Matthew’s coefficient of absolute risk aversion.
Background image of page 1

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

View Full DocumentRight Arrow Icon
() 2 22 11 '1 ;' ' '' 1 '1 1 vv xx v x vx x η =+ =− −− = + + + e. Without calculating it explicitly, what’s the most that can be said about Matthew’s certainty equivalent for lottery p = {$e, 0.5; $e 3 , 0.5}? Briefly explain. First note that Beth is at least as risk averse as Matthew. 1 1 1 This must hold since 0. x λη => = + +> > Therefore Matthew’s certainty equivalent must be at least as big as Beth’s. 2 Matt CE e 2. (24 pts) Bill is a risk averse, von Meumann-Morgenstern utility maximizer. Determine his preferences between each of the following pairs of lotteries. Explain why. a. a = {$10, 0.2; $20, 0.3; $40, 0.5}, b = {$10, 0.4; $40, 0.6} [ ] ( ) ( ) [] () () 0.2 10 0.3 20 0.5 40 $28 0.4 10 0.6 40 $28 is a mean preserving spread of . Ea Eb ba ab =++= =+= ; b. c = {$50, 0.4; $90, 0.6}, d = {$40, 0.2; $60, 0.2; $70, 0.2; $100, 0.4} [ ] ( ) [] () () () ( ) 0.4 50 0.6 90 $74 0.2 40 0.2 60 0.2 70 0.4 100 $74 is equivalent to zero conditional-mean noise.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/23/2008 for the course ECON 171 taught by Professor Newhouse during the Fall '07 term at UCSD.

Page1 / 5

Fall 2007 - Newhouse's Class - Exam 2 - Economics 171:...

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