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Q: Answer the attached question
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- If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then (Select all that applies) Group of answer choices a. two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios. b. two consumers with the same income who consume both goods must have the same MRS, but if their incomes differ, their MRSs may differ. c. any two consumers who consume both goods must consume them in the same ratio. d. for any two consumers who consume both goods, neither will prefer the other consumer’s bundle to his own. e. all consumers receive the bundle that they prefer to any other bundle the economy could produce for them.Use the Fundamental Theorem of Exchange and draw Edgeworth Box diagrams to show the conditions necessary for an 'efficient' allocation of two goods between two individuals. Use this model o evaluate the statement: "If two individuals have identical endowments of both goods there are no possible gains from trade". Hint: you need to develop your explanation of the theory and the efficiency conditions step-by-step. You need to draw several diagrams showing Edgeworth Box (rather than drawing one complicated crowded diagram).1.Suppose that Chris's utility function is given by UC=QC1/2 RC1/2 , where QC and RC are his consumption of Q and R, respectively. Dana's utility function is given by UD=QD1/3 RD2/3, where QD and RD are her consumption of Q and R, respectively. Write an equation for the marginal rate of substitution (MRS) between Q and R for each of the two agents. 2.Suppose that the price of good R is pR=1 and the price of good Q is pQ=2. How much is Chris's and Dana's initial income, given his endowments and given these prices? 3. At these prices, how many units of Q would Chris and Dana want to consume? 4. At these prices, how many units of R would Chris and Dana want to consume?
- Person A has a utility function of and person B has a utility function Agent A and agent B have identical endowments of (1/2,1/2). (a) Illustrate this situation in an Edgeworth box diagram. (b) What is the equilibrium relationship between p1and p2? (c) What is the equilibrium allocation?6. Person 1 with preferences u(x, y) = y1 – 2x1 is endowed with x̂1 = 2 and ŷ1 = 40. Person 2 with preferences u(x, y) = x2– 2y2 is endowed with x̂2 = 20 and ŷ2 = 60. Be prepared to upload an Edgeworth Box Diagram that illustrates the Pareto Preferred Region, the Contract Curve and the Equilibrium. Calculate the Edgeworth Box equilibrium price level.Which 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.
- Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…Suppose the household’s preferences are given the following forms: u(c)=log(c), v(l)=log(l), that ß=2/3, and that the production functions are given by: F1(L)=L1/2 and F2(K)=K1/2. a) What are the equilibrium conditions? Derive them. b) What are the quilibrium quantities?Suppose Coke and Pepsi are perfect substitutes for me, and right and left shoes are perfect complements. A. Suppose my income allocated to Coke/Pepsi consumption is $100 per month, and my income allocated to right/left shoe consumption is similarly $100 per month. a. Suppose Coke currently costs $0.50 per can and Pepsi costs $0.75 per can. Then the price of Coke goes up to $1 per can. Illustrate my original and my new optimal bundle with "Coke" on the horizontal and "Pepsi" on the vertical axis. b. Suppose right and left shoes are sold separately. If right and left shoes are originally both priced at $1, illustrate (on a graph with "right shoes" on the horizontal and "left shoes" on the vertical) my original and my new optimal bundle when the price of left shoes increases to $2. c. True or False: Perfect complements represent a unique special case of homothetic tastes in the following sense: Whether income goes up or whether the price of one of the goods falls, the optimal bundle…
- In an exchange economy, there are two people (Shadi and Nino) and two goods (x1 and x2). Their initial endowments are ωS = (2, 4) and ωN = (3, 6). Their utility is given by the following functions: US(x1,x2) = x12x23 and UN(x1,x2) = x1x24. Which of the following is the equation for the contract curve? Group of answer choices a. x2N = 96x1N / (15 + 4x1N) b. x2N = 47x1N / (8 + 4x1N) c. x2N = 91x1N / 5 d. x2N = 16x1N / (3 + x1N) e. x2N = 41x1N / (9 + x1N)Explain why an economy in which airlines charge different passengers different prices for the same flight will not have exchange efficiency. b. Going back to our two good (Apples, Oranges), two person (Ed, Mary) economy, suppose that at a given allocation, Ed’s MRSAO is 3 and Mary’s MRSAO is 1. Use proof by contradiction to show that this allocation is not exchange efficient. Identify a trade that will increase the utility of Ed and Mary. Explain. Show this graphically (with indifference curves). Going back to our two good (Apples, Oranges), two person (Ed, Mary) economy, suppose that at a given allocation, Ed’s MRSAO is 3 and Mary’s MRSAO is 1. Use proof by contradiction to show that this allocation is not exchange efficient. Identify a trade that will increase the utility of Ed and Mary. Explain. Show this graphically (with indifference curves).Below is an edgeworth box of two individuals, Ross and Rosa, in the consumption of two goods, X and Y 1. Consider allocations b-f (meaning points a, b, and f). Which allocations(s)A. are better for Ross than “a” (ignoring Rosa)?B. are better for Rosa than “a” (ignoring Ross)?C. are worse for both Ross and Rosa than “a”?D. are better for both Ross and Rosa than “a”?E. are Pareto superior to “a”?2. Suppose that the initial allocation is point a between Ross and Rosa.A. Discuss how Ross’s condition be made better off without harming Rosa(i.e., Rosa maintains her level of utility).B. Illustrate this in a separate diagram and label point/s as necessary (also,if other point/s will have to be made or incorporated).3. Consider once again that the initial allocation is point a. A. Discuss (very briefly) how point d is reached as a Pareto efficientallocation between Ross and Rosa.B. illustrate this condition in a separate diagram.4. Consider points b, c, d, and e. Now plot the utility…