Dracula - Econ 210A Problem Set 6 Answer Key Jehle and Reny...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 210A Problem Set 6 Answer Key Jehle and Reny Exercise averse over gambles involving nonnegative wealth levels if and only if her VNM utility funciton is strictly concave on R + . Suppose that an individual is risk averse, which implies that u ( E ( g )) > u ( g ) : u ( E ( g )) > u ( g ) ) u p i w i ) > p i u ( w i ) u ( p 1 w 1 + ::: + p n w n ) > p 1 u ( w 1 ) + ::: + p n u ( w n ) This holds for all p 0 s that are between 0 and 1 and sum to one and u ( p 1 w 1 + ::: + p n w n ) u ( w t ) and p 1 u ( w 1 ) + ::: + p n u ( w n ) T 1 u ( w 1 ) + ::: + T n u ( w n ) Hence, u ( w t ) > T 1 u ( w 1 ) + ::: + T n u ( w n ) which implies u is strictly concave. , Suppose that a consumer has a concave utility function over all wealth levels that are positive. This implies that u ( E ( g )) = u n i p i w i ) > n i p i w i = u ( g ) . Therefore the consumer is risk averse. 2.23 Consider the quadratic VNM utility function U ( w ) = a + bw + cw 2 . a) What restrictions if any must be placed on parameters a;b and c for this function to display risk aversion? Risk aversion is characterized by the utility function when U 0 ( w ) > 0 and U 00 ( w ) < 0 . U 0 ( w ) = b + 2 cw > 0 U 00 ( w ) = 2 c < 0 ) c < 0 b) U 0 ( w ) > 0 ) b + 2 cw > 0 or w < ± b 2 c c) Given the gamble g = ((1 = 2) ( w + h ) ; (1 = 2) ( w ± h )) show that CE < E ( g ) and P > 0 . U ( CE ) = 1 2 U ( w + h ) + 1 2 U ( w ± h ) ) a + bCE + cCE 2 = 1 2 a + b ( w + h ) + c ( w + h ) 2 ± + 1 2 a + b ( w ± h ) + c ( w ± h ) 2 ± ) u ( CE ) = a + b ( CE ) + c ( CE ) 2 = a + bw + cw 2 + ch 2 > u ( w ) = u ( E ( g )) Because utility is strictly increasing, CE < E ( g ) . P = E ( g ) ± CE is then greater than 0. d) Show that this function, satisfying the restrictions in part (a), cannot represent preferences that display decreasing absolute risk aversion. 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
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/01/2011 for the course ECONOMY 6 taught by Professor Fallahi during the Spring '10 term at Cambridge.

Page1 / 4

Dracula - Econ 210A Problem Set 6 Answer Key Jehle and Reny...

This preview shows document pages 1 - 2. Sign up to view the full document.

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