Question 7 (a) Suppose that Johnny is an expected utility maximizer with u(x) =-

Question

Question 7 (a) Suppose that Johnny is an expected utility maximizer with u(x) =-e-0.00 1x, and has initial wealth is $75,000. Derive how Johnny feels about the following bets (i) Johnny will accept (-100, ^;X,;) if and only if X >???? (1) Johnny will accept (-200·nk) if and only if X ???? (ii) Johnny will accept -500, 3;X, 3) if and only if X >???? (iv) Johnny will accept (-750, j;X,;) if and only if X >???? (b) Like Johnny, Tommy has initial wealth $75,000. But unlike Johnny, Tommy evaluates gam bles according to prospect theory with (p) and x ifx_0 v(x) if x 0. If we observe that Tommy accepts (-100, ;X, ) if and only if X 210, what can we conclude about Tommy's ?

Explanation / Answer

U(X)=-exp(-0.001X)

Then U(75000)=-exp(-75000*0.001)=-exp(75)

To accept the offer Johnny must get utility from that offer atleast as good as -exp(75)

a)(-100+X)/2 is expected payoff and utility will be U((X-100)/2)=-exp ((X-100)/2)>=-exp (75)

(X-100)/2<=75

-50<=X<=250

B)

Similar (X-200)/2<=75

50<=X<=350

C)

(X-500)/2<=75

450<=X<=650

D)

X<=900

Ans Part B

(Lambda*(-100)+210)/2<=75

Lambda*(-100)<=-60

Lambda>=0.6

Ans Part C)

(Lambda*"(-200)+X)/2<=75

-200*Lambda<=150-X

We know Lambda =0.6

-200*(0.6)<=150-X

-120<=150-X

X<=270

Ans 2)

(Lambda*(-500)+X)/2<=75

(-300+X)/2<=75

150<=X<=450

Ans 3)

(-450+X)/2<=75

300<=X<=600

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