2 [50 points] Mr. suing If he pb 1-ps, he will lose and has initial wealth of W-

Question

2 [50 points] Mr. suing If he pb 1-ps, he will lose and has initial wealth of W-$6,000. rapper is suing his neighbor, after having slipped on the neighbor's stairs on a rainy day. al, with probability p, he will win $20,000 for his pain and suffering. But with probability th eive S0. His utility function is ue)-In(e). You may assume that Mr. Tripper the expected value of Mr. Tripper's winnings if he goes to trial, for each of the following values of P: 0.10, 0.50, and 0.90. Wealth and utility play no role in these calculations. b) Let X be smallest settlement that Mr. Tripper will accept from the defendant prior to the trial. Set up the equation that defines X. Leave ps as a variable in this equation. BE CAREFUL: think about the TOTAL amount of money that goes into Mr. Tripper's utility function under each scenario: accepts X to avoid the trial, wins the trial, and loses the trial. c) Calculate X to the nearest dollar for each of the following values of p; 0.10, 0.50, and 0.90 d) For the remainder of this problem, assume instead that Mr. Tripper has initial wealth of W - $12,000. Set up the equation that now defines X. e) Calculate X to the nearest dollar for each of the following values of p:0.10,0.50, and 0.90

Explanation / Answer

a) The expected value = $20000*ps

so there will be 3 cases as following

when ps =0.1 , expected value=$2000

when ps =0.5 , expected value=$10000

when ps =0.9 , expected value=$18000

b)Mr tripper will except that amount when his expected utility drive from the suing process is same as the utility when he has X.

so expected utility when he sue his neighbour (E(u)),

E(u)=ps*U(amount he will have after winning)+(1-ps)*U(initial wealth)

=ps*U(26000)+(1-ps)*U(6000)

=ps*ln(26000)+(1-ps)*ln(6000)

=ps*10.16585+(1-ps)*8.6995

=8.6995+ps1.466337

so,

U(X)= Expected value

ln(X)=8.6995+ps1.466337

X=exp(8.6995+ps1.466337)

c) For different values of ps

ps=0.1, X=6947.578

ps =0.5, x=12490

ps=0.9,X=22453.87

D)U(X)=ps*U(32000)+(1-ps)*U(12000)

ln(X)=ps*10.37349+(1-ps)*9.39262

X= exp(9.39262+0.98ps)

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