Consider an exchange economy with A and B. For the endowment, A has (x,y) = (10,40) and B has (x,y) (20,5). Assume that both A and B have a Cobb Douglas utility function u(x,y) = xy. Say A proposes to give B 5 units of good y. What is the most x B is willing to give to A in return? 2.5 5 10 12.5 Question 2 1 pts Consider the exchange economy in question 1 again. If the price of x is $4 and the price of y is $8, then consumer A has an income of and A's optimal basket has x* = units. 320; 40 320; 45 360; 45 360; 40
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- Consider an exchange economy with two consumers: Charlotte and Dylan, and two goods: quinoa (Q) and raspberries (R). Charlotte has an initial endowment of 83.9 units of quinoa and 99.3 raspberries. Dylan has 112.5 units of quinoa and 77.8 raspberries. Charlotte's utility function is given by Uc=Q¹/² R¹/², where Qc and Re are her consumption of Q and R, respectively. Dylan's utility function is given by Up-Q¹/³ R2/3, where Qp and Rp are his consumption of Q and R, respectively. Suppose that the market price of quinoa is po=2 and the market price of raspberries is pr=1. At these prices, how many units of Q would Dylan want to consume?2For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) c) Assume that Kim has preferences Uk (Xk, Yk) = 3Xk + 3Yk and Jung has preferences Uj (Xj, Yj) = Xj + 3Yj. Will Kim and Jung trade? Calculate the general equilibrium allocation for Kim and Jung. Compute the utility at the endowment point and at the general equilibrium allocation. Is the new allocation on the contract curve?
- For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) a) Illustrate the initial endowment in an Edgeworth box. Clearly label the axes and explain the dimensions of the box. Show the indifference curve each of them is on at the endowment point. b) Consider an allocation where Kim gets (xk, yk) = (40,40) and Jung gets the remaining Ferraris and VR headsets. Show where this point is in the Edgeworth box. Is this allocation Pareto efficient? Is it equitable? How likely is this to arise in practice?For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) d) Assume that a social planner could redistribute initial wealth (the amounts of ? and ? that Kim and Jung have). Can they reallocate resources so that Kim and Jung reach the allocation (Xk, Yk) = (20,20) and (Xj, Yj) = (20,20) as a general equilibrium (i.e. post-trade) allocation? Can the social planner redistribute resources to make the allocation where Jung owns all the resources in the economy a general equilibrium allocation?please only answer part ii
- Consider an exchange economy with two consumers (A and B) and two goods (x1 and x2). Consumer A has an endowment of 5 units of x1 and none of x2, whereas Consumer B has an endowment of 3 units of x1 and 15 units of x2. Consumer A's utility function is given by uA=xA1xA2, and Consumer B's utility function is given by uB=min{xB1,xB2}. Both goods are traded in competitive markets. Find the competitive equilibrium price for x2, assuming p1=1.D2)A and B consume only two goods, cider (C) and dumplings (D). A has an initial endowment of 10 bottles of C and 30 of D. Bob has an initial endowment of 50 bottles of cider and 50 dumplings. Alice’s utility function is uA(CA,DA) = 9ln(CA) + 10ln(DA), where CA and DA represent consumption of C and D, respectively. B’s utility function is uB(CB,DB) = CBXDB, where CB and DB denote B's consumption of C and D. a) Find the competitive equilibrium, i.e. the price ratio, of this exchange economy and the resulting equilibrium allocation. b) Find the expression of the contract curve for this economy and use your answer to check that the equilibrium allocation you found in (b) is indeed Pareto optimal.
- economicsJack Sparrow and his wife consume wine (W) and books (B). Jack Sparrow's utility function is Ujack(W, B) = W. His wife's utility function is Uwife(W, B) = B. Jack's endowment is 17 bottles of wine and 5 books and Jack's wife's endowment is 20 bottles of wine and 14 books. In the Edgeworth box, Jack's consumption is measured from the lower left corner, and his wife's from the upper right corner of the box; the wine is on the horizontal axis and books are on the vertical axis. Therefore, in an Edgeworth box for Jack and his wife, there is only one Pareto Optimal allocation that is located in the top left corner of the box. True or False? Please submit 1 if True and O if False.Elizabeth Swann and her husband consume wine (W) and books (B). Elizabeth's utility function is UE(W, B) = W. Her husband's utility function is UH(W, B) = W. Elizabeth's endowment is 16 bottles of wine and 5 books and her husband's endowment is 19 bottles of wine and 14 books. In the Edgeworth box, Elizabeth's consumption is measured from the lower left corner, and her husband's from the upper right corner of the box; the wine is on the horizontal axis and books are on the vertical axis. Therefore, in an Edgeworth box for Elizabeth and her husband, any allocation is Pareto Optimal. True or False? Please submit 1 if True and O if False.