Alex and Jennifer are roommates. Alex values listening to loud music at $800, and Jennifer values peace and quiet at $650. If Jennifer has the property rights to the apartment, who's preferences prevail according to the Coase Theorem?
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- 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 AnswerProblem 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.Consider two consumers (1; 2), each with income M to allocate between two goods. Good 1 provides 1 unit of consumption to its purchaser and units of consumption to the other consumer. Each consumer i, i = 1; 2, has the utility function is consumption of good 1 and is consumption of good 2. a. Provide an interpretation of α. b. Suppose that good 2 is a private good. Find the Nash equilibrium levels of consumption when both goods have a price of 1. c. By maximizing the sum of utilities, show that the equilibrium is Pareto-ancient if α = 0 but incident for all other values of α. d. Now suppose that good 2 also provides 1 unit of consumption to its purchaser and a, 0 ≤ α ≤ 1, units of consumption to the other consumer. For the same preferences, find the Nash equilibrium and show that it is ancient for all values of α. e. Explain the conclusion in part d.
- Bleecker Street runs from A to B, as shown in the diagram. The lone convenience store currently in operation along this street is at A. An entrepreneur who wants to open another store in the neighborhood is weighing a choice between the only two available locations, C and D. If customers, who are uniformly distributed along Bleecker Street, always shop at the store nearest to where they live, which of the locations C or D would be optimal from the perspective of customers and why? A C D B O Location D because that would minimize the average travel time for customers. O Location D because that would mean each store would get an equal share of the market. O Location C because that would give the new entrepreneur higher profits. O Locations C and D would be equally attractive because consumers have no reason to care about the relative profitability of different entrepreneurs.Jia is considering whether to go out to dinner at a restaurant with her friend. The meal is expected to cost $40, Jia typically leaves a 20% tip, and an Uber will cost $5 each way. Jia values the restaurant meal at $25. Jia enjoys her friend s company and is willing to pay $30 just to spend an evening with her.7
- 5.18 In a two-good, two-consumer economy, utility functions are u¹ (x₁, x₂) = x₁(x₂)², u² (x₁, x₂) = (x₁)²x₂. Total endowments are (10, 20). (a) A social planner wants to allocate goods to maximise consumer 1's utility while holding con- sumer 2's utility at u² = 8000/27. Find the assignment of goods to consumers that solves the planner's problem and show that the solution is Pareto efficient. (b) Suppose, instead, that the planner just divides the endowments so that e¹ = (10, 0) and e² = (0, 20) and then lets the consumers transact through perfectly competitive markets. Find the Walrasian equilibrium and show that the WEAs are the same as the solution in part (a).Angela works on farmland owned by Bruno. The diagram illustrates their joint feasible frontier. Angela's indifference curves are all assumed to have an identical slope, for any given amount of free time. This means that they are all parallel. Angela and Bruno can bargain costlessly. Bushels of grain 8 12 Angela's reservation indifference curve, IC₁ IC₂ D 0 0 16 Angela's hours of free time 20 24 Feasible frontier: Angela and Bruno combined a) Assume that Angela's reservation option is at point F. Explain the meaning of "Pareto efficient" and give two ways that we know that point F is not Pareto-efficient. Explain why moving between point F and point E would not improve efficiency. (4 marks) b) How might Angela and Bruno achieve a Pareto-efficient outcome? Explain how the negotiation might work. Use indifference curves to show where this outcome will be on the diagram. (3 marks) c) Explain why it would not be Pareto-efficient to simply aim to produce the maximum total amount of grain,…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…
- Consider the golfing question from above. Suppose that Ken values golfing for the afternoon at $65. That is, he puts a price on his happiness from golfing for the afternoon at $65. Should he go golfing? Why or why not? Yes, he should go golfing because his enjoyment ($65) is greater than the $30 price. No, he should not go golfing because the fees ($30) are greater than his lost income. Yes, he should go golfing because his enjoyment ($65) is greater than his lost income from not working ($60). No, he should not go golfing because his enjoyment ($65) is less than the cost ($90). Yes, he should go golfing. You should always go golfing when you get the chance!John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where J B. b. C < J. c. C = J. d. C = B. e. JThe non-satiation assumption we make about people's's preferences entails that the indifference curves never cross. True or False