Putting it all together: Jim has mean variance utility with A=2. He has paid $40

Question

Putting it all together: Jim has mean variance utility with A=2. He has paid $40 to play a coin toss game where, if heads is flipped, Jim receives $100, if tails Jim receives 0.

a. How happy is Jim in utiles?

b. Brian is risk neutral (e.g. A=0) how much would he be willing to pay for the same coin toss gamble if not doing anything makes Brian 0 happy?

c. How happy is Jim if he can sell his gamble to Brian for cash (assuming that Jim has all of the bargaining power so will be able to get the price from (b))?

Explanation / Answer

a) In order to happy Jim, there is a need to maximize the utility of Jim by using a Lagrange function. It can be explained as:-

L = U(X,Y) - ( Px + Py - my)

L = 2X - ( 40 + Py - 100)

change in L/change in X = 2

change in L/ change in Y = 0

change in L/change in = 60-Py=0

2)

L = U(X,Y) - ( Px + Py - my)

L = 2X - ( 40 + Py - 0)

change in L/Change in Y=0

change in L/change in X=2

change in L/change in = -40-Py=0

3) L = U(X,Y) - ( Px + Py - my)

L = 2X +Y - ( 40 + Py - 100)

change in L/Change in Y=1

change in L/Change in X=2

change in L/Change in =60-Py=0

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.