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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- 3. 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: Utility for A Utility for B Utility for C Room X 7 9 2 Room Y 4 3 7 Room Z 2 1 4 (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,X) Pareto optimal?) (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…The 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 KyokoSuppose Zaharah (Z) and Quah (Q) are now at an allocation bundle where their marginal rates of substitution (MRS) are given by MRS₂ = 10 and MRSQ = 5, respectively. In general equilibrium analysis, this suggests that Andaikan Zaharah (Z) dan Quah (Q) kini berada pada sesuatu longgok alokasi di mana kadar penggantian marginal (MRS) masing-masing adalah MRS₂ = 10 dan MRSQ = 5. Dalam analisis keseimbangan am, ini menunjukkan bahawa a. both individuals have already engaged in voluntary exchange of resources kedua-dua individu telah pun terlibat dalam pertukaran sumber secara sukarela b. Zaharah's situation is better off than Quah situasi Zaharah adalah lebih baik daripada Quah there exists a basis for voluntary exchange for resources between both terdapat asas untuk pertukaran sumber secara sukarela antara kedua-duanya d. both of them are in equilibrium C.
- 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 recommendationWhich is the correct answer ? Suppose there are 10 apples and 10 oranges in the economy. Joe is currently consuming 4 apples and 5 oranges, and Jane is consuming 6 apples and 5 oranges. At this allocation, Joe's marginal utility of apples is 3, and his marginal utility of oranges is 5. Jane's marginal utility of apples is 6, and her marginal utility of oranges is 10. The current price of apples is R4 per unit and the current price of oranges is R5 per unit. To reach a competitive equilibrium, the required price adjustment is: A. A decrease in the orange price relative to the apple price. B. A decrease in the apple price relative to the orange price. C. No change in the relative prices. D. An increase in both prices.| Two people trade two goods that they cannot produce. Suppose that one Mary's indifference curves are bowed away from the origin-the usual type of curves-but Joe's are concave to the origin. In an Edgeworth box, show that a point of tangency between the two consumers' indifference curves is not a Pareto efficient bundle. (Identify another allocation that Pareto dominates.) Put Mary on the southwest corner and Joe on northeast corner.
- 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?23. 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…Bucky 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)
- 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 sodasA date with Alex costs you $100 and gives you an additional 1000 units of utility. A date with Kelly costs you $200 and an additional 4,000 units of utility. Based only on the information you have, using the theory of rational choice, you most likely would: O be indifferent between the two dates O go on a date with Alex because the marginal utility per dollar is the greater of the two O go on a date with Kelly O go on a date with AlexSuppose 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.