Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally. Q3 Sam has another idea: They buy two tickets (that have independent outcomes) and share the costs and proceeds equally.
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Q2
Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally.
Q3
Sam has another idea: They buy two tickets (that have independent outcomes) and share the costs and proceeds equally.
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- QUESTION 1 Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wt, w) = (1,2) and Bob's endowment equals (wf , w) = (1,3). Alice's utility is given by u4 (xf, xf) = 2 ln xf + In æ£ , while Bob's utility is uB(xf, x}) = ln xf + 2 ln x? . Suppose that the social planner considers it to be imperative that agent B consumes exactly one uni of good 1 and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforce transfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 would guarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2? Answer this please Select one: O a. One half unit of good 1 has to be transferred from agent A to agent B. O b. There is no endowment for which agent B would consume x = 1 and x = 4 in the corresponding competitive…(3) Willig is willing to pay as much as $130 to buy the last ticket to a music concert at Canada's Wonderland, while Norman is willing to pay as much as $200 for a ticket. Willig is first in line and buys a ticket for $110. He then resells his ticket to Norman for $170. Assume that both took rational decisions given their options. Willig by reselling his ticket rather than going to the concert himself, caused the total surplus, (a) to increase by $70 (b) to remain unchanged. (c) to increase by $90- to decrease by $20 (d) to increase by $30 none of the options are correctTwo individuals (A and B) live on an island where they consume coconuts (good x) and bananas (good y) for survival. A owns the coconut producing part of the island and B owns the banana part. Their utility functions and endowments are given by UA (TA,YA) = A+YA +min {A, YA}, UB (TB, YB) = TB +YB + min {ïß, YB}, (ww) = (0, 12) B B Assume that the price of coconuts is p and that of bananas is 1, so relative prices are denoted by p. (ww) = (10,0) A 1. What are their respective budget constraints? 2. What are their individual demand functions? (Hint: you have to consider multiple cases for the value of p) 3. The individuals trade their endowments with each other. What is the competitive equilibrium price in the market? What are their respective utilities at equilibrium?
- Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure: First, Max eliminates one of three choices. Then, Sally decides among the two remaining choices. Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining). a.Write down the extensive form (game tree) to represent this game. b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be? c.What is the subgame-perfect equilibrium of the above game? d. Does your answer in b. differ from your answer in c.? Explain why or why not. Only typed AnswerFrank and Nancy met at a sorority sock hop. They agreed to meet for a date at a local bar the next week. Regrettably, they were so fraught with passion that they forgot to agree on which bar would be the site of their rendezvous. Luckily, the town has only two bars, Rizotti's and the Oasis. Having discussed their tastes in bars at the sock hop, both are aware that Frank prefers Rizotti's to the Oasis and Nancy prefer the Oasis to Rizotti's. In fact, the payoffs are as follows. If both go to the Oasis, Nancy's utility is 3 and Frank's utility is 2. If both go to Rizotti's, Frank's utility is 3 and Nancy's utility is 2. If they don't both go to the same bar, both have a utility of 0. There are two Nash equilibrium in pure strategies and a Nash equilibrium in mixed strategies where the probability that Frank and Nancy go to the same bar is 12/25. This game has two Nash equilibria in pure strategies and a Nash equilibrium in mixed strategies where each person has a probability of 1/2 of…Problem 1. Two consumers, Alice and Bob, have utility functions given by u₁(x, y) = x¹/²y¹/4 and ug (x, y) = 4x² + y², respectively, where x and y are the number of apples and bananas respectively. Suppose that apples and bananas cost p₁ and p2 dollars each respectively and that both consumers have M dollars to spend on apples and bananas. (a) On the same axes, sketch Alice's budget set and some contours u₁(x, y) = c for positive values of c. By referring to your sketch explain why the method of Lagrange multipliers can be used to find the maximum value of u₁(x, y) subject to her budget constraint. Hence use the method of Lagrange multipliers to find Alice's optimal bundle. (b) On the same axes, sketch Bob's budget set and some contours up (x, y) = c For positive values of c. By referring to your sketch, find Bob's optimal bundle.
- d) Another classmate cares more about good grades: She gets 50 units of happiness for a B and 80 units of happiness for an A. If this classmate were your partner (but your preferences remained the same), how would your answers to parts (a) and (b) change? Which of the two classmates would you prefer as a partner? Would she also want you as a partner?Consider an agent who want to maximize her utility function, u (C₁, C₂) = C₁ C₂ subject to the budget constraint, c₁ + pc₂ = w with C₁, C₂ > 0 indicating consumption of commodity 1 and 2, respectively, while p>0 and w>0 are exogenously given parameters, indicating the relative price of good 2 and the relative wealth in term of good 1's price. Decide whether the following claims are true or false. W • The value of the Lagrange multiplier is λ = 2p False True w² • The value function u(w) is equal to u(w) = 4p True False • λ(w) measures the approximate change in utility that can be obtained from an increase/decrease in wealth w. True FalseTwo officers are working in a police department. During a working day Officer One can either catch 20 criminals or she can write 60 reports. During a working day Officer Two can either catch 2 criminals of she can write 21 reports. The boss of the officers has the following utility function U=min(criminals; reports}. Officers want to make their boss as happy as possible. Find how many criminals will be optimally caught during the day.
- Apply the various principles of choice (dominance, Laplace, Minimax, Hurwicz, and Minimax Regret) to the following matrix. The numbers in the matrix are costs.An old lady is looking for help crossing the street. Only one person is needed to help her; if more people help her, this is no better. You and I are the two people in the vicinity who can help; we have to choose simultaneously whether to do so. Each of us will get pleasure worth a 3 from her success (no matter who helps her), But each one who goes to help will bear a cost of 1, this being the value of our time taken up in helping. If neither player helps, the payoff for each player is zero. Set up this game in strategic form.Suppose an insurance company wants to charge a very healthy individual a premium of $1,200 a year for health coverage. It also wants to charge a less healthy individual a premium of $3,600 a year for health coverage. It is seeking to ascertain from any given customer information regarding his/her health by asking for several pieces of health-related information, such as doctor assessments of the person’s health, history of health-related problems, etc. The opportunity cost of a very healthy person securing a health report is $250 and the opportunity cost of a less healthy person securing a health report is $650. Of the choices below, how many reports should the company request to best ensure its paying the right premium to the right person? Reconsider the previous health insurance question. Of the choices below, which one is closest to the spread between the minimum possible number of reports and the maximum possible reports to achieve the company’s desired outcome? Reconsider again…