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- a) (3) Consider two investments X and Y, where X pays $0 and $10 with equal probability and Y pays 0 with probability 0.75 and $20 with probability 0.25. What investment would an investor choose if her utility function is u(x) = x? u(x) = x u(x) = 1-e 10 () (i) (ii)Two events, A and B, are such that P(A∪B) = 0.86, P(B) = 0.72 and P(A) = 64. Determine P (A U B)'M2
- Exercise 3.1 List all the reduced pure strategies, then reduce the tree to strategic form. START b ㅍ 9 e d e I (2, 0) (3, 0) h h J k k (1, 1) (0, 2) 1 (0, 2) (1, 1) (2,0) (1, 1) (1, 1) (2,0)There are two firms, A and B, located on a mile stretch. Firm A has a marginal cost=$4, and Firm B has a marginal cost=$6. For both: N=potential clients in the area=4,000 V=max willingness to pay=$40 travel cost=$8/1mile Please find the best response functions for both firms and graph them.which is the nash equilibrium? small pig does press large pig does press (20, 130), small pig doesn't press large pig does press (140, 10), small pig does press large pig doesn't press (-5, 150), small pig does not press large pig doesn't press (0,0).
- k : ces As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 50 percent chance of low demand and a 50 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P= 300,000-400Q and P= 500,000 -225Q, respectively. Your cost function is CQ) = 165,000+ 243,750Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $1A local insurance company offers both home and auto insurance to four types of customers with the reservation prices listed in the figure below. Assume for simplicity that there is only one consumer of each type. Home Auto Bundle Customer A $90 $67 $157 Customer B Customer C Customer D $117 $87 $204 $103 $77 $180 $83 $52 $135 If the firm were to sell home and auto insurance separately, it would charge $83 for home insurance, $52 for auto insurance, and earn a combined revenue of $540. Determine the revenue the firm would receive if it used a pure bundle. Comparing the revenue of the pure bundle to the revenue of selling home and auto insurance separately, we can conclude that the reservation prices of the consumers must: O A. have no correlation B. be positively correlated C. be negatively correlated D. be serially correlatedSuppose 2 players play the following game infinite times in the future. What should be the minimum value of the time discount so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (10, 10) Defect (2, 12) (4,4) (12, 2)
- 7) Manager B Effort Level Chance of success Cost of effort High Effort 0.6 100,000 Routine Effort 0.5 60,000 What is the minimum bonus that will entice high effort? 1. 40,000 2. 260,000 3. 300,000 4. 400,000 5. 520,000 6. 60,000 7. 100,000 8. 0 6) Manager A Effort Level Chance of success Cost of effort High Effort 0.6 300,000 Routine Effort 0.5 260,000 What is the minimum bonus that will entice high effort? 1. 40,000 2. 260,000 3. 300,000 4. 400,000 5. 520,000 6. 60,000 7. 100,000 8. 0 5) ABC Instrument, a manufacturer of precise scientific instruments, relies heavily on the efforts of its local salespeople. Selling an instrument requires either luck, high effort, or some combination of the two. A salesperson who chooses to work hard has a 40 percent chance of selling an instrument in a given year while a salesperson who chooses…The decision tree below describes the game faced by firm H and firm T. The payoffs are profits in million of US$. The SPNE is(are): (Build large, Build large) (Build Small, Build Small) (Build Small, Build Large) (No build, Build Large) (Build Large, No Build)