5. Consider an exchange economy with 2 agents and 2 goods. a. In an Edgeworth-Bowley diagram, show and illustrate that if both agents have the same preferences, the contract curve is a straight line from the bottom left-hand corner to the top right-hand corner. Explain. b. Does it follow that if the agents do not have the same preferences, the contract curve is not a straight line? Explain. c. Suppose the two agents have the same endowments and the same preferences. Is mutually beneficial trade possible? Illustrate in an Edgeworth Bowley diagram. Explain.
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- 5. Consider an exchange economy with 2 agents and 2 goods.5. Consider an exchange economy with 2 agents and 2 goods. a) In an Edgeworth-Bowley diagram, show and illustrate that if both agents have the same preferences, the contract curve is a straight line from the bottom left-hand corner to the top right-hand corner. Explain. b) Does it follow that if the agents do not have the same preferences, the contract curve is not a straight line? Explain. c) Suppose the two agents have the same endowments and the same preferences. Is mutually beneficial trade possible? Illustrate in an Edgeworth Bowley diagram. Explain.Multiple choice question Joe and Rita each have some milk and cookies (Milk on the horizontal axis). Joe's MRS ofcookies for milk is 2. Rita's MRS of cookies for milk is 4. Which of the following statements isTRUE?a) No gains from trade are possible.b) Both Rita and Joe can be made better off if Rita gives Joe some cookies in exchange for milk.c) Rita and Joe are on the contract curve.d) Both Rita and Joe can be made better off if Joe gives Rita some cookies in exchange for milk.
- Consider a two-agent two-good barter economy. Agent 1 only cares about good 1, and agent 2only cares about good 2. There is only 1 unit of good 1, and 2 units of good 2 in the economy,which is distributed equally between the agents while agent 1 owns the only unit of good 1 inthe economy.a. Compute and explain the Pareto optimal allocations.b. Compute and explain the equilibrium prices and allocations.c. How would your answers to parts a and b change if agent 1 shared half of his good 1 withagent 2? Discuss.3. Consider an exchange environment with two consumers, Consumer 1 and Consumer 2, and two goods, a and b. Consumer 1 is initially endowed with e₁,a = 0 of good a and e₁,b = 10 of good b, while €1,6 Consumer 2 is initially endowed with e2,a = 10 of good a and €2,6 = 0 of good b. The utility of Consumer 1 from consuming x1, a ER+ of good a and 1,6 ER is u1(x1,a,x1,b) = x1,a + x1,b, while the utility of Consumer 2 from consuming x2,a Є R+ of good a and x2,6 ЄR is U2(x2,a, X2,b) = √√x2,a + x2,b. (a) Consider general equilibrium in the context of this environment in which the price of good b is normalized to 1. Compute the equilibrium price pt of good a and find the corresponding equilibrium quantities consumed by the various consumers. (b) Consider the game in which, simultaneously, Consumer 1 submits a “demand curve" and Consumer 2 submits a “supply curve” to a market mediator. In particular, the strategy space of Consumer 1 is [0,10], and the strategy d of Consumer 1 corresponds to the…16.11. Ted and Joe each consume peaches, x, and plums, y. The consumers have identical 10y7x7, MRS = 10yr^TTogether, they have 10 peaches MRSJoe utility functions, with and 10 plums. Verify whether each of the following allocations is on the contract curve: a) Ted: 8 plums and 9 peaches; Joe: 2 plums and 1 peach. b) Ted: 1 plum and 1 peach; Joe: 9 plums and 9 peaches. %3D
- 1. Hatfield and McCoy hate each other. The only good they both consume WH W2 40 Mand McCoy's is whiskey. Hatfield's utility function is UH utility function is UM = WM-W, where WHI is Hatfield's consumption 40' Η of whisky and WM is McCoy's consumption of whiskey. The sheriff has confiscated a total of 60 litres of whiskey which he could give back to them or throw in the creek. Say that the Sheriff wants them both to be as well off as possible and weighs their "happiness" equally. How much whiskey should the sheriff give to each of them? Should he throw any whiskey in the creek; if so how much? =4. a. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible theywould choose to consume some of both commodities when their income is I but would choose toconsume only x when their income is I’ > I. (Remember: if you can draw it without violating anyof the basic assumptions on preferences, it could happen.) b. Conversely, demonstrate that it is possible they would choose to consume only x when theirincome is I but would choose to consume x and y when their income is I’ > I.c. Finally, show it is possible that they would choose to consume only y when their income is I butwould choose to consume only x when their income is I’ > I.Option Baseball Bats Tennis Racquets A 20 2 19 C 4 18 6. 16 8 10 F 10 The table above shows the production possibilities frontier for a company producing only 2 goods: baseball bats and tennis racquets. Suppose the company is currently producing 4 bats and 10 racquets all of which have been ordered by customers. If customer John puts in an order for 4 bats, so that the total number of bats to produce would then be 8, what is be the opportunity cost of filling John's order? 8 racquets 10 racquets nothing 18 racquets
- Sue Tom Good A 10 4 Select one: Good B 15 5 As shown in the table above, Sue and Tom each can produce two different types of goods. For Sue, if she only produces Good A, then she can produce 10 units of Good A per day. If she only produces Good B, then she can produce 15 units of Good B per day. For Tom, if he only produces Good A, then she can produce 4 units of Good A per day. If she only produces Good B, then she can produce 5 units of Good B per day. Which of the following statement is correct about comparative advantage? O a. Tom has a comparative advantage over Sue in the production of Good A. Sue has a comparative advantage over Tom in the production of Good B O b. Tom has a comparative advantage over Sue in both tasks O c. Sue has a comparative advantage over Tom in both tasks O d. Sue has a comparative advantage over Tom in the production of Good A. Tom has a comparative advantage over Sue in the production of Good BThis problem set is about General Equilibrium, . 1. True and False. For each of the following statements, specify whether the section in bold is true, false or uncertain, and in no more than FOUR sentences, explain your answer. Note that answers that only indicate true or false without providing any further explanations Forall the following questions, consider a two-person two-good exchange econ- omy, in which preferences are well behaved. (a) Any competitive equilibrium (allocation and price ratio) must be unique. (b) The centre of the Edgeworth box must be a Pareto optimal allocation.. (c) A candidate allocation need only be within the lens formed by the two indifference curves (one for each agent) that pass through the initial al- location point, without being on the core, in order to be a competitive equilibrium). (d) Walrasian tâtonnement is the process of adjusting the relative prices of the two goods when the individually optimal allocations for each player leads to excess…1. Write down an exchange economy model with two individuals and two goods, in whichthere is no consumption externality. State and explain the key assumptions of the model.Using the model, answer the following questions:(a) Explain carefully how the concept of Pareto efficiency differs from that of socialwelfare.(b) State the Second Theorem of Welfare Economics and explain carefully why it holds.What is the importance of the assumption of convex preferences to this theorem?