The only good in the country is mangos. They gather all the coconuts together and find that there are 400 in total. Their utility functions over mangos are: 1/2/2 Julia: Ua= xa¹/2/4 Gregor: U₁= xb¹ What would the welfare-maximizing allocation of coconuts be if the welfare function was W=UAUC?
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- 10. Consumer A and B have each been given an allocation of 2 goods x and y (assume each has positive amounts of both goods). At this allocation, consumer A has an MRS of 2, while consumer B has an MRS of 1/2. Could this allocation be Pareto efficient? Explain why or why not.1The following table shows the marginal utility per dollar of apples and pears for five consumers: Consumer Marginal Utility Per Dollar Apples Pears Darnell 8 5 Eleanor 7 8 Jacques 6 6 Kyoko 5 4.5 Musashi 4 4 Darnell, Eleanor, and Kyoko are not optimizing over their choice of fruit. In the following table, indicate which fruit each consumer should increase consumption of in order to achieve the optimal fruit consumption bundle. Consumer Apples Pears Darnell Eleanor Kyoko
- Consider an economy with 100 pieces of apple (A) and 150 pieces of banana (B) that must be completely distributed to individuals 1 and 2. The utility function of the two individuals, U, & U2, is given by U1 (A1,B1) = 2A? + B² & U2 (A2,B2) = 2A²B?, respectively. With this information, recommend an efficient allocation of the two %3D goods between the two individuals. Discuss and show the necessary solution to support your recommendationAmy and Lela have following preferences for apples, pears and bananas where > means "preferred to." Amy: apple > pear > banana Lela: banana > apple > pear Assume there is one apple, one banana and one pear to divide between Amy and Lela and that they have no other goods. For each of the following allocations, say whether it is (Pareto) efficient or inefficient. 1. Amy gets the apple and the pear and Lela gets the banana [ Select ] ["Efficient", "Inefficient"] 2. Amy gets the banana and Lela gets the apple and the pear [ Select ] ["Efficient", "Inefficient"] 3. Amy gets the pear, apple and banana and Lela gets nothing [ Select ] ["Efficient", "Inefficient"]Consider two commodities: toy cars and batteries. Each toy car takes three batteries to operate. Suppose Andy enjoys a toy car only if it moves and Andy has no other toy that needs battery. That is, one toy car and three batteries are a set of perfect complements to Andy. Task 1: Let x1 >= 0 be the quantity of toy cars and x2 >= 0 be the quantity of batteries. FindafunctionU(x1, x2)thatrepresentsthispreference. Task 2: Draw Andy's indifference curves going through bundles (2, 3), (4, 3) and (5, 5) in the commodity space in the same graph. How does Andy's preference order these 3 bundles in terms of > or ? Task 3: What mathematical expression describes the line formed by all the corners of the indifference curves?
- Only typed answeryurt23. Anita (A), Ben (B) and Carlos (C) are housemates who have moved to a new house and must decide how to allocate rooms X, Y and Z. An 'allocation' is where each housemate is assigned to exactly one room. For example, Anita → Room Z, Ben → Room X and Carlos → Room Y is allocation (Z, X, Y). Utilities for each room are given below: Room X 7 9 2 Room Y 4 3 7 Room Z 2 1 4 Utility for A Utility for B Utility for C (a) How many possible allocations are there in total? (b) Identify the two allocations which are not Pareto optimal and explain why they are not Pareto optimal. (Hint: is the allocation (Y,Z) Pareto timal?) (c) Suppose we square Carlos' utility from each room (i.e. uc (Z) becomes 16). Would the set of Pareto optimal outcomes change? Why/why not? (d) Returning to the utilities from part (a), which of the Pareto optimal allocations maximise total surplus (utility) and would all housemates weakly prefer this allocation over any other? (e) Suppose the housemates decide to allocate…
- Van brings $40 to a baseball game to spend on sodas and pizza. The following diagram shows his budget constraint: SUCES OF PIZZA 20 18 16 14 12 4 2 0 4 6 U BC 10 SODAS According to the diagram, sodas cost 5 12 14 16 18 20 each, and puzza costs $ BC ? per slice. Adjust the diagram to show how Van's budget constraint would change if he had brought more money to the ballpark (Assume the prices of sodasBucky has $20 to spend on bowling and billiards. The prices of bowling and billiards are $4 and $1 por game, respectively. Assume he has a voucher for two free games of bowling Suppose bowling is the "X" good and billiards are the "Y" good How many games of bowling can Bucky afford? How many games of billiards can Bucky afford? Where is the "link" in Bucky's budget constraint where opportunity cost of billiards in terms of bowling games changes? (This should be answered as quantity of bowling games, quantity of billiards games)Suppose Vijay has 10 onion rings and 5 sheek kababs, and his friend Tara has 5 onion rings and 10 sheek kababs. Both can benefit from trade, and after trading Vijay has 12 onion rings and 3 sheek kababs. In an Edgeworth box, label the initial allocation A and the new allocation B. Draw indifference curves that are consistent with this trade being optimal for both Vijay and Tara. Put sheek kababs on vertical axis and onion rings on horizontal axis. Put Vijay on the southwest corner and Tara on northeast corner.