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- 1. True/False: Partial equilibrium analysis only concerns supply or demand alone, whereas general equilibrium analysis concerns supply and demand simultaneously. 2. True/False: In general equilibrium analysis, an allocation is said to be as a reasonable allocation if each consumer consumes the same bundle its value is no more than the value of the consumer's income. 3. True/False: In general equilibrium analysis, an allocation is said to be as a reasonable allocation if each consumer consumes the same bundle its value is no more than the value of the consumer's income.Matthew Hamming is stranded on an island. He has decided that he will spend exactly 10 hours a day gathering food. He can either spend this time gathering coconuts or catching fish. He can catch 2 fish per hour and he can gather 3 coconuts per hour. Matthew's utility function is U(FC) = 3F0.60.3 a. How many fish should Matthew catch and how many coconuts should he gather so that his consumption maximizes his utility? Illustrate the equilibrium with a graph b. One day a native inhabitant of another island arrives on the island. The visitor offers Matthew trade of 3 fish for 1 coconut. The trade fee costs 1 fish (that must be paid prior to the exchange). Will Matthew decide to trade? What will Matthew produce and consume? Justify your answer and provide a graph.3. Jane is currently consuming 4 glasses of milk and 10 cookies, while Betty is consuming 9 glasses of milk and 3 cookies. Jane views milk and cookies as perfect substitutes (her MRS is 1), while Betty prefers cookies to milk and is willing to give up 3 glasses of milk to get 1 cookie. Is the current allocation of milk and cookies Pareto efficient? Explain with use of a diagram.
- 4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.1. a) Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by for Mohammed, for David and for Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain. b. There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A’s marginal rate of technical substitution of labour for capital is 4 while B’s marginal rate of technical…Extend the model of the jungle to the case in which the number of houses is smaller than the number of agents. In this case, an allocation is a function from the set of agents to the set H U {homeless} with the property that no two agents are assigned to the same house. Each agent has a preference ordering over H U {homeless}. Assume that this ordering is strict; assume also that every agent prefers to be allocated any house than to be homeless. Define an equilibrium for this extended model and show that it always exists.
- Find all Pareto optimal allocations, the egalitarian allocation and the competitive equilibrium with equal incomes for the following problems. 1 Ann and Bob need to divide 4 items. Their preferences are as follows: Y W Ann 25 25 25 25 Bob 10 20 30 401.2 Ann and Bob each own 10 bottles of beer and, altogether, they own 20 bags of peanuts. There are no other people and no other goods in the economy, and no production of either good is possible. Using a to denote bottles of beer and y to denote bags of peanuts, Ann's and Bob's preferences are described by the following utility functions: UA (XA, YA) = TAYA and UB (XB, YB) = 2xB+ YB. In each of the following cases, determine the market equilibrium price ratio and allocation and depict the equilibrium in an Edgeworth box diagram. (a) Bob owns 20 bags of peanuts and Ann owns no peanuts. (b) Bob owns 15 bags of peanuts and Ann owns 5 bags. (c) Ann owns 20 bags of peanuts and Bob owns no peanuts.Grapes and bananas are perfect complements for Jane and Betty. Jane eats one grape per three bananas.; Betty eats three grapes per one banana. Once they go to sports for hours, Jane had 20 grapes and 10 bananas and Betty had 10 grapes and 20 bananas. (assume that grapes and bananas can be divided into half) 1.Show all Pareto optimal allocations of grapes and bananas between Jane and Betty in the Edgeworth Box. Draw a bunch of indifference curves and look for tangencies.
- Please define and draw the utility possibilities curve. On your graph explain what is meant by pareto efficiency. Define social welfare functions. On your graph demonstrate that some efficient points need not be as good, given the social welfare function, as some inefficient points.There are only two people in the market - Amber and Zoe. Amber’s Marginal Willingness to Pay (MWTP) for the Qth bit of the good is given by MWTP=383-2*Q. Zoe’s Marginal Willingness to Pay (MWTP) for the Qth bit of the good is given by MWTP=51-3*Q. Based on this information, what is the market MWTP for the 32th bit of the good? Enter a number only.At the end of performances of his Broadway play, "Cyrano de Bergerac," Kevin Kline, who starred as Cyrano, the cavalier poet with a huge nose, auctioned his prosthetic proboscis, which he and his co-star, Jennifer Garner, autographed to benefit Broadway Cares in its fight against AIDS. An English auction was used. One night, a television producer grabbed the nose for $1,400, while the next night it fetched $1,600. On other nights it sold for $3,000 and $900. Source: (Mitchell, Dan, "This Time, Santa Has Been Too Naughty," New York Times, December 9, 2007) Why did the value fluctuate substantially from night to night? The value of the nose fluctuated from night to night because the bidders have Which bidder's bid determined the sales price? The bidder whose value determined the sales price was the How was the auction price affected by the audience's knowledge that the proceeds would go to charity? Why? Since proceeds went to the AIDS charity, private values OA. differed by each bidder's…