Rubinstein2005-page130

Rubinstein2005-page130 - Problem 3. ( Standard ) Consider a...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
October 21, 2005 12:18 master Sheet number 128 Page number 112 Problem Set 9 Problem 1. ( Standard. Based on Rothschild and Stiglitz 1970. ) We say that p second-order stochastically dominates q and denote it by pD 2 q if p % q for all preferences % satisfying the vNM assumptions, monotonicity and risk aversion. a. Explain why pD 1 q implies pD 2 q . b. Let p and ε be lotteries. DeFne p + ε to be the lottery that yields the prize t with the probability 6 α + β = t p (α)ε(β) . Interpret p + ε . Show that if ε is a lottery with expectation 0, then for all p , pD 2 ( p + ε) . c. (More difFcult) Show that pD 2 q if and only if for all t < K , 6 t k = 0 [ G ( p , x k + 1 ) G ( q , x k + 1 ) ][ x k + 1 x k ]≥ 0 where x 0 < ... < x K are all the prizes in the support of either p or q and G ( p , x ) = 6 z x p ( z ) . Problem 2. ( Standard. Based on Slovic and Lichtenstein 1968. ) Consider a phenomenon called preference reversal . Let L 1 = 8 / 9 [ $4 ]⊕ 1 / 9 [ $0 ] and L 2 = 1 / 9 [ $40 ]⊕ 8 / 9 [ $0 ] . a. What is the maximal amount you are willing to pay for L 1 ? ±or L 2 ? b. What lottery do you prefer? c. Discuss the “typical” answer that ranks L 1 as superior to L 2 but attaches a lower value to L 1 (see Slovic, Tversky and Kahneman 1990).
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem 3. ( Standard ) Consider a consumers preference over K-tuples of K uncertain assets. De-note the random return on the k th asset by Z k . Assume that the random variables ( Z 1 , . . . , Z K ) are independent and take positive values with proba-bility 1. If the consumer buys the combination of assets ( x 1 , . . . , x K ) and if the vector of realized returns is ( z 1 , . . . , z K ) , then the consumers total wealth is K k = 1 z k x k . Assume that the consumer satisFes vNM assumptions, that is, there is a function v (over the sum of his returns) so that he maximizes the expected value of v . Assume that v is increasing and concave. The con-sumer preferences over the space of the lotteries induce preferences on the space of investments. Show that the induced preferences are monotonic and convex....
View Full Document

This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

Ask a homework question - tutors are online