Joe is contemplating either opening another store or expanding its existing loca

Question

Joe is contemplating either opening another store or expanding its existing location. The payoff table for these two decisions is: Paul has calculated the indifference probability for the lottery having a payoff of $160,000 with probability p and -$80,000 with probability (1-p) as follows: a. Is Joe a risk avoider, a risk taker, or risk neutral? b. Suppose Joe has defined the utility of -$80,000 to be 0 and the utility of $160,000 to be 80. What would be the utility values for -$40,000, $20,000, and $100,000 based on the indifference probabilities? c. Suppose P(s1) =.4, P(s2) = -3, and P(s3) =.3. Which decision should Joe make? Why? Compare with the decision using the expected value approach.

Explanation / Answer

Payoff of $160,000 with probability of p and payoff of -$80,000 with probability (1-p)

Therefore expected payoff ( when p=.4, .7, .9) is p*160000 + (-80000*(1-p))

a. Based on the above comparison of Amount and expected payoff, we can say that Joe is risk avoider

b. Utility of -$80,000 to be 0 and the utility of $160,000 to be 80

Therefore utility value of -$40,000 is {(80-0)/(160000-(-80000))} * (-40000-(-80000)) =.0003333*40000=13.33

Similarly utility value of $20,000 is .0003333*100000=33.33

Utility value of $100,000 is .0003333*180000=60

c. In case P(s1)=.4, P(s2)=.3 and P(s3)=.3

Expected value is Sigma pi*xi,

As the expected value is more in case of New Store, therefore Joe may make the decision in favour of New Store on the basis of maximization of expected value.

Amount Indifference Probability Expected payoff -40000 0.4 16000 20000 0.7 88000 100000 0.9 136000

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