Consider a two-people, two-goods exchange economy, where Person A and Person B have the following utility functions. In which case, the Pareto optimal allocation can be on the boundary of the Edgeworth box? Note: Do not consider the origins as the boundary points. (Boundary points are the edges of the Edgeworth box except for the origins.) ) UA = min (XA1, XA2) and ug = Xạ.Xg2 (1) UA = log(xA1) + log(XA2) and ug = 3Xg1 + X8z Gii) UA - (KA1X2) and ug = 3log(xe1) + X82 (iv) UA = (XA1)2 + XA2 and ug = log(xe1) + Xp2
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- Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 8 units of X and a TOTAL of 8 units of Y. The consumers' utility functions are given by: UA(X,Y) = 2X + Y UB(X,Y) = X*Y2 Which of the following allocations is Pareto Efficient? None of the other answers are Pareto Efficient. Consumer A gets 3 units of X and 8 units of Y, and Consumer B gets 5 units of X and O units of Y. Consumer A gets 4 units of X and 4 units of Y, and Consumer B gets 4 units of X and 4 units of Y. Consumer A gets 1 units of X and 4 units of Y, and Consumer B gets 7 units of X and 4 units of Y. Consumer A gets 8 units of X and 8 units of Y, and Consumer B gets 0 units of X and O units of Y.Carol and Bob both consume the same goods in an economy of pure exchange. Carol is initially endowed with 9 units of good 1 and 6 units of good 2. Bob is initially endowed with 18 units of good 1 and 3 units of good 2. They both have the utility function U(x₁, x₂) = 1/3 2/3 x1³x2³. If we set good 1 as the numeraire (so that p. = $1), what will the equilibrium price of good 2 be?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…
- Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by UA, UB: R30 →R where UA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: (If you wish to change your response, please untick your selected answer before selecting another answer.) There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient. For all price vectors PER²0, we have p₁z₁ + P2z2 = 0 where z; is the excess demand of good i € {1, 2}. 0 Preferences of both players satisfy strict convexity. At initial endowment eд = (5, 5), eg = (5, 5), there is a…Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. Consumer A is initially endowed with 10 units of good 1 and 10 units of good 2. Consumer B is initially endowed with 2 units of good 1 and 2 units of good 2. The consumers have the following utility functions: uA(X1A,X2A)=X1AX2A²; UB(X1B,X28)=X18+X2B- Among the prices below, which ones are Walrasian equilibrium prices? O a. P1=3, p2 =2 O b. p1=4, p2 =5 O c. None of the other answers. O d. p1=5, p2 =4 O e. p1=2, P2 =3Consider a two-agents, two goods economy, in which both agents, A and B, are represented by the following utility function: UA(1, 22) = rr2 UB(y1, Y2) = Y1y% There are w units of each good in the economy. 1. Characterize the set of Pareto optimal allocations and represent it in the Edgeworth box. The 3 units of each goods are initially share as follows: A has w units of good 1 and zero unit of good 2; B has zero unit of good 1 and w units of good 2. 2. Determine the Walrasian equilibrium 3. Represent the economy in the Edgeworth box.
- Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U = 4P + 3C . In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of PepsiConsider 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…Remy and Emile consume only blueberries (x,) and raspberries (x,). Remy has utility function UR = x (x5)² and Emile has utility function UE = (xf)²x. Remy is endowed with 5 blueberries and 5 raspberries and Emile is endowed with 10 blueberries and 10 raspberries. (a) Derive the equation of the contract curve, i.e., find x%(xf). (b) Set x2 as the numeraire, i.e., assume p, = p and p2 = 1. Find the competitive equilibrium – the equilibrium price ratio, P1/P2, and the equilibrium allocation, ((xf, x5), (xf,x£ )).
- The utility possibility frontier is defined as the set of maximum utility levels for all consumers that is feasible in the economy, given resource constraints and preferences. For a two-consumer economy, it is defined formally as the solution to: u (ūB) = max u A (xA) subject to ug(xB) > ūg and (xA, XB)feasible. For each of the economies above, find an equation for the utility possibilities frontier, and graph it.John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where J B. b. C < J. c. C = J. d. C = B. e. JJohn and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where ] B. b. C < J. c. C = J. d. C = B. e. JSEE MORE QUESTIONSRecommended textbooks for youPrinciples of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSONPrinciples of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-…EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill EducationPrinciples of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSONPrinciples of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-…EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill Education