1. B is offering to buy an object from S. S values the good at $4 (type "H"), or $3 (type "M") or $2 (type "L"). But S's exact valuation is unknown to B, who simply attaches equal probabilities to all three possibilities, a fact known commonly to both players. B values the good at $5. B makes a take-it-or-leave-it offer to S. (a) Analyze the perfect Bayesian equilibrium of this game. (b) What if S's valuation is distributed uniformly over [2, 4]? Repeat the same exercise as in (a).
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- Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ Losses Losses i-600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "10o0", not "$1000"Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10.a. Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summerare players in this Game. Rick designed the game and is not a player. b. Find all Nash equilibria of this game. c. Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. Hint: draw three matrices, with Morty choosing the…
- Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10. a.Draw the normal (matrix) form of this game, with Morty choosing the row and Summer choosing the column. Does either Morty or Summer have a dominant strategy? Explain your answer. Note: only Morty and Summer are players in this Game. Rick designed the game and is not a player. b.Find all Nash equilibria of this game. c.Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. d.Find all Nash equilibria of the three-player…Rick thinks either Morty or Summer broke his TV. Morty and Summer each have to decide simultaneously whether to take the blame or blame the other person. If they both blame the same person (both blame Morty or both blame Summer), the person they blame gets a small punishment and utility of -2, while the blameless person gets a utility of 0. Otherwise (if they both blame the other or both blame themselves), they both get a more severe punishment and a utility of -10. Suppose instead there are three suspects: Morty, Summer, and Jerry. Otherwise, the rules are the same as before. Draw the normal (matrix) form of the game. Hint: draw three matrices, with Morty choosing the row, Summer choosing the column, and Jerry choosing between the three matricesSelect the correct option : When the expected utility of offer A is larger than offer B, a rational individual would always prefer offer A to offer B. 1. True 2.False
- 2. Two consumers, Owen and Sylvan have preferences over two goods, X (on the horizontal axis) and Y. Owen's utility function is Uo (X, Y) = 12X + 3Y, while Sylvan's utility function is Us (X,Y) = 6X +8Y, where X, Y > 0. Owen has £120 to spend, while Sylvan has £168 to spend. The market demand and supply functions for good X are: Qax = 500 - 7P; Qsx 180 +9P. The market demand and supply functions for good Y are: Qay = 600 - 12P; Qsy = 120 + 8P. Which of the following is correct? = (a) Owen will purchase 6 units of good X and 0 units of good Y, while Sylvan will purchase 0 units of good X and 7 units of good Y. (b) Owen will purchase 0 units of good X and 5 units of good Y, while Sylvan will purchase 8.4 units of good X and 0 units of good Y.Suppose that Abe and his brother Moe are lost in the desert and are in need of guidance to find an oasis. They can seek such guidance from either a burning bush or a golden calf. Abe has the following preferences: • If Moe chooses to talk to the golden calf, Abe prefers the outcome where he to chooses to talk to the golden calf than talk to the burning bush. • If Moe chooses to talk to the burning bush, Abe is indifferent between the outcome where he choose to talk to the burning bush and the outcome where he chooses to talk to the golden calf. • Regardless of his own decision, Abe prefers all outcomes where Moe talks to the burning bush than if he chose to talk to the golden calf. Moe has the following preferences: • If Abe chooses to talk to the golden calf, Moe prefers the outcome where he chooses to talk to the golden calf than talking to the burning bush. • If Abe chooses to talk to the burning bush, Moe prefers the outcome where he chooses to talk to the golden calf than talking…Eric, Kenji, and Paolo are roommates who are trying to decide how much money each should contribute to a party they are throwing. • Paolo does not care about the party and is on a tight budget. Therefore, he prefers to contribute no money to the party, and his utility declines at a constant rate as the roommates increase the amount of money they spend. • Kenji would ideally contribute $15 because he only wants to buy pizza. However, he would prefer contributing $55 to contributing $0 and not having a party at all. • Eric wants to buy a $120 keg of beer and $45 worth of pizza. Therefore, he would ideally like each to contribute $55 to the party, but if the others are unwilling to contribute that much, he would settle for buying just the pizza (and contributing $15 each) and asking guests to bring beer. Suppose the three roommates vote on spending either $0, $15, or $55 on the party using the Borda count system of voting. That is, each roommate awards three points to his first choice,…
- 4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain.4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…