Question 1-4

1. (10 pts) Suppose you have the following utility function, U(I)=2I+10I1/2, where I is your income. You are considering two job opportunities. The first pays a salary of $50,000 and the other pays a base salary of $20,000 but offers a $60,000 bonus on top of the base salary. You believe there is a 50 percent probability that you will earn the bonus. a. What is the expected salary associated with each opportunity? b. Which offer gives you the highest expected utility? c. Are you risk averse, risk neutral or a risk lover? Explain. 2. (10 pts) Consider the following utility function: U(W)=lnW, where W is wealth. This function belongs to an individual who has a wealth of $90,000. He faces the possibility of a catastrophic loss of $40,000 of his wealth with probability q. a. What is the value of q, if he can purchase a fair insurance policy that fully compensates him for his loss at a premium of $8,000 ? b. Using your answer in (a), explain with math and graphically whether U[E(W)]>E[U(W)]. c. Using your answer from (a), what is the most this individual would be willing to pay for an insurance policy that fully compensates him for loss? 3. (20 pts) Consider the following game between Sony, and manufacturer of video cassette players, and Columbia picture, a movie studio. Each firm must decide whether to use the VHS or Beta formatSony to make video players and Columbia to release its movies for rental or purchase. a. Does either company have a dominant strategy? Explain. b. Does either company have a dominated strategy? Explain. c. Draw the extensive form (i.e., the game tree). d. Find the pure strategy Nash equilibrium or equilibria. e. Compute the mixed-strategy Nash equilibrium. As part of your answer, draw the best response function diagram for the mixed strategy. f. Suppose the game is played sequentially with Sony moving first and committing to this action. What are Columbia's contingent strategies? Write down the normal and extensive forms for the sequential versions of the game. g. Use backward induction to solve for the subgame-perfect equilibrium. Explain why the other Nash equilibria of the sequential game are unreasonable. 4. (8pts)K. Keith, the famous widgets producer, has the following production function: Q=L1/2K1/2, where Q represents the quantity of widgets produced for a given amount of labor (L) and capital (K)