Question

Kascade is a DJ and has a large collection of records worth $10,000. He has a cat called

Jazz whom he loves dearly. Kascade knows that with probability 0.2 Jazz will scratch his records and will damage his collection. If this occurs the value of his collection will be reduced to $2,500.

Kascade’s attitude toward risk is characterized by u(M )= M , where M is hisr wealth level as represented by the value of the collection.

a) Compute Kascade’s expected utility and show it on the carefully labelled diagram.

b) Suppose that Kascade can buy a record storage box that fully protects his collection from Jazz. What is the maximum amount he is willing to pay for the box?

Suppose instead that Megan offers Kascade the following arrangement: if Kascade pays her $P, then in the event that Jazz damages his collection, she will pay him for the damage; and if Jazz does not damage his collection, she will pay him nothing. Megan’s utility function is with respect to wealth is givenbyu(M)=M .

c) Will both Kascade and Megan benefit from this arrangement? Explain your answer.

Answer 1

ans a) expected utility = utilty if jazz does not damage* probability of jazz not damaging records+  utilty if jazz does damage* probability of jazz damaging records

= 10000 *0.8 + 2500*0.2

= 8000+ 500 = 8500b) if box is purchased records will safe and value of records as well utility = $1000 or 1000 utils

Utility laorol - - 2500 voo M-Wealth level

so net gain will be 1500 utils wih certainity

so jazz will pay max $1500 for box

Suppose instead that Megan offers Kascade the following arrangement: if Kascade pays her $P, then in the event that Jazz damages his collection, she will pay him for the damage; and if Jazz does not damage his collection, she will pay him nothing. Megan’s utility function is with respect to wealth is givenbyu(M)=M

c) in that case kascade will for sure get utility of 10000 always after paying $P

and Megan will get utility of P utils

so both will gain but kascade will be willing to pay maximum of 1500 $ or less than $1500 then only he will be benefitted