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 given by u(M ) = M .

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

Answer 1

Collection of record worth = 10,000 Value reduces to if scratched by Jazz = 2500 U(M) = M Ma wealth level , prob. (p) of schatching! 1 - 0 0 0 La) |_ Elu) : = = P x U(M') + (1-P)* VLM) 0.2 x U/ 2500) + 0.8 x 0(10000) 0.2x 2500 +0.88 10000 8500 -U(M) toooo 8500 2500 2500 8500 10000 b) We chave to find containity equivalent Elu(m)): ULCE) Elu(M)) : C.E. 3500 : C.E. ei Risk premium = E(M) - C.E. ) 0.2 x 25000.8x10000 - 3500 in R.P.: 8500 - 8500 . He is willing to pay o amount for - the box Stanned with GamScanner

the and and te neutral willingneity in crude Megan their weich As noted aboue Kascade's risk premium is zero ie he is not willing to pay anything to avoid the gamble , chis Gie. its equal to expected nealth and the in vist neutral Kascade and Megan would be willing to unter the contract is their expected utility increases by entering into it which is not the case There Hence , there exist no such premium where Rascade will be willing to enter into a contact with Megan Seanned with CamScanner