Rahim and Karim are two brothers. Rahim got 4 ice creams and 6 chocolates and Karim received 6 ice creams and 4 chocolates from heaven (the economy is assumed with no production and the amounts of goods they received as the initial endowments). The two brothers have the same Cobb-Doughlas preference structure. Draw the Edgeworth box and level the initial endowments. What is Pareto improvement? Does Pareto improvement possible here? If yes, show the Pareto improvement area in the Edgeworth box.

(a) Examine the view that it is possible to escape from the "impossibility" result of Arrow by making social preferences a function of cardinal utility rather than of individual orderings.

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.

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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.

Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3x2A; UB(X1B,X2B)=x1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (W1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (WIB,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? O a. An amount 7 of wealth should be transferred from consumer A to consumer B. O b. None of the other answers. An amount 3 of wealth should be transferred from consumer A to consumer B. O c. d. An amount 3 of wealth should be transferred from consumer B to consumer A. An amount 7 of wealth should be transferred from consumer B to consumer…

Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3X2A; UB(X1B,X2B)=X1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (w1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (w1B,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? An amount 7 of wealth should be transferred from consumer A to consumer B. O a. O b. None of the other answers. O c. An amount 3 of wealth should be transferred from consumer A to consumer B. O d. An amount 3 of wealth should be transferred from consumer B to consumer A. e. An amount 7 of wealth should be transferred from consumer B to…