Meredith Delgado Owns a Small Firm That Has Developed Software

Question

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The Answer is (a)The decision is whether to go to trial (with a cost of $1 million)or settle (receive a payment of $1.5 million),represented in the decision tree by a decision node with two branches.If Meredith goes to trial,she will win (60% probability)or lose (40% probability),represented as an event node with two branches.If she loses,there is also a 50% chance that she must pay court fees,represented as an event node with two branches.If she goes to trial and wins,her net payoff is $5 million - $1 million = $4 million.If she goes to trial and loses,but doesn't pay court fees,her net payoff is -$1 million.If she goes to trial and loses and must pay court fees,her net payoff is -2 million.If she settles,she receives a net payoff of $1.5 million.The resulting solved decision tree is shown below.The decision to go to trial has a higher expected payoff of $1.8 million.

(a)The decision is whether to go to trial (with a cost of $1 million)or settle (receive a payment of $1.5 million),represented in the decision tree by a decision node with two branches.If Meredith goes to trial,she will win (60% probability)or lose (40% probability),represented as an event node with two branches.If she loses,there is also a 50% chance that she must pay court fees,represented as an event node with two branches.If she goes to trial and wins,her net payoff is $5 million - $1 million = $4 million.If she goes to trial and loses,but doesn't pay court fees,her net payoff is -$1 million.If she goes to trial and loses and must pay court fees,her net payoff is -2 million.If she settles,she receives a net payoff of $1.5 million.The resulting solved decision tree is shown below.The decision to go to trial has a higher expected payoff of $1.8 million. (b)The equivalent lottery method begins by assigning the highest possible payoff ($4 million)a utility value of 1,and the lowest possible payoff (-$2 million)a utility value of 0.What remains is to determine the appropriate utility value of the remaining two possible payoffs: -$1 million and $1.5 million.For each of these payoffs,the following question should be asked of Meredith: Given a lottery where you receive $4 million with probability p and -$2 million with probability 1-p,what would p need to be so that you would be indifferent between this lottery and a sure payoff of -$1 million (or $1.5 million)? Her answer is the appropriate utility value for -$1 million (or $1.5 million).(c)Suppose that Meredith's attitude toward risk is such that she would be indifferent between doing nothing and a gamble where she would win $1 million with 50% probability and lose $500 thousand with 50% probability.Use the exponential utility function to re-solve the decision tree from part a.The decision tree from part a is re-solved below,using an exponential utility function with R = $1 million.When accounting for Meredith's risk aversion,it turns out that settling the case and receiving the sure payoff of $1.5 million becomes the better decision.

(b)The equivalent lottery method begins by assigning the highest possible payoff ($4 million)a utility value of 1,and the lowest possible payoff (-$2 million)a utility value of 0.What remains is to determine the appropriate utility value of the remaining two possible payoffs: -$1 million and $1.5 million.For each of these payoffs,the following question should be asked of Meredith: Given a lottery where you receive $4 million with probability p and -$2 million with probability 1-p,what would p need to be so that you would be indifferent between this lottery and a sure payoff of -$1 million (or $1.5 million)? Her answer is the appropriate utility value for -$1 million (or $1.5 million).(c)Suppose that Meredith's attitude toward risk is such that she would be indifferent between doing nothing and a gamble where she would win $1 million with 50% probability and lose $500 thousand with 50% probability.Use the exponential utility function to re-solve the decision tree from part a.The decision tree from part a is re-solved below,using an exponential utility function with R = $1 million.When accounting for Meredith's risk aversion,it turns out that settling the case and receiving the sure payoff of $1.5 million becomes the better decision.

Meredith Delgado Owns a Small Firm That Has Developed Software

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