A risk-neutral plaintiff in a lawsuit is deciding whether to settle a claim or g

Question

A risk-neutral plaintiff in a lawsuit is deciding whether to settle a claim or go to trial. The defendants have offered a $100,000 settlement.
a. If the plaintiff does not settle, she believes that the probability of winning at trial is 65%. If the plaintiff wins, she is awarded X dollars. If she loses her payoff is $0. How large must X be in order for the plaintiff to turn down the settlement offer?

b. Suppose instead that the plaintiff is risk-averse, with a utility function of u(x)=SQRTofX. If the plaintiff does not settle she believes that the probability of winning at trial is 65%. If she wins she is awarded X dollars. If she loses her payoff is $0. How large must X be in order for the plaintiff to turn down the settlement offer? Is this number smaller or larger than that in part a)? Why?

Explanation / Answer

Ans A)

If Plaintiff wins then he gets X dollars and otherwise $0

then to turndown settlement order of $100,000 he should get Expected Value higher than settlement order

0.65(X)+0.35(0)=100000

X=100000/0.65=153846.2

Therefore X must be atleast as good as $153,846.2

Ans b)

U(X)=sqrt(X)

Expected Value=153846.2

EU=0.65(X^1/2)+0.35(0)=0.65sqrt(X)

Utility outo of $100000=(100000)^1/2=316.22

EU>100 to turn down the settlement

0.65sqrt(X)=316.22

sqrtX=316.22/0.65

CE=X>236674

This X is higher than previous X

Risk Premium=CE-EMV=236674-153846.2=82827

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