Question

. Julia and John prefer more money to less and have transitive prefernces. Each of them faces the following decision problem. S260 $80 M T SX 30% 50% 20% S320 $80 $0 $320 S0 (a) Suppose that Julia is risk neutral. If she chooses A and then U, what can we deduce about the possible values of X and p? (b) Continue to assume that Julia is risk neutral. Suppose that X-250, p 0.9. Julia is given a choice between facing the above decision tree and playing the lottery $320 S260 $80 S60 What will she choose? If she chooses the decision tree 0.6 0.2 0. 0.1 explain what choices she makes, otherwise explain why she prefers the lottery (c) Suppose that X-100 and p 0.9 and John starts by choosing A. Then he says that he is indifferent between U and T. Is he risk neutral, risk averse or risk loving?

Answer 1

(a)The path AU gives Julia a wealth of $260 with certainty. Given that she is risk neutral, we can conclude the following:

(i) She gets less than $260 with certainty from path D

$\Rightarrow X < 260$

(ii) If she follows path AT, she gets a wealth equal to or less than $260 (with uncertainty).

Using this information, we can calculate the value of $p$ as follows:

$320 p &plus; 0(1-p) \leq 260$

$\Rightarrow 320 p \leq 260$

$\Rightarrow p \leq \frac {260}{320}$

$\Rightarrow p\leq 0.8125$

(b) Given :

$X = $250, p = 0.9$

From the decision tree, we have the following wealths from the different paths calculates as below:

Path D:

$X = $250$

Path AU gives $$260$

Path AB gives $80$

Path AM gives:

$0.3*320 &plus; 0.2*80 &plus; 0.5*0 = 112$

Path AT gives:

$p*320 &plus; (1-p)*0$

$= 0.9*320 &plus; 0.1*0$

$288$

From the lottery, Julia gets the following wealth:

$0.6*320 &plus; 0.2*260 &plus; 0.1*80 &plus; 0.1*60$

$=258$

Given the calculations, we can conclude that Julia, bein a risk neutral wealth maximizer (prefers more money to less) would choose path AT from the decision tree because that maximizes her expected wealth with $288.

(c) Given:

$X = $100, p = 0.9$

Also, John is indifferent between U and T after he chooses A. So we have:

Sure wealth from U = $$260$

Expected wealth from T

$=p*320 &plus; (1-p)*0$

$=0.9*320 &plus; 0.1*0$

$=288$

John is a wealth maximizer who prefers more money to less. Also, he is risk neutral because he is indifferent between the outcomes.