Suppose Adam has utility function UA (X1, x2) = xy and Bob has utility function UB (X1, X2) = xx2 Total endowments are E = 8 and E2 = 12. %3D If the current allocation is Pareto efficient and Adam has 4 units of good 1, how many units of good 2 mus be have?
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- Two individuals, Fred and Helen, are in an economy with no production, and each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Find the general equilibrium prices and allocation, then show that the G.E. allocation is Pareto efficient.I need help with this homework problem. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = (X^1/2)*(Y^1/2) UB(X,Y) = X + Y The initial endowments are: A: X = 8; Y = 3 B: X = 4; Y = 5 What is the marginal rate of substitution for consumer A at the initial allocation? What is the marginal rate of substitution for consumer B at the initial allocation? Is the initial allocation Pareto Efficient?Can you help me with this question. Im finding it quite difficult. In a two-good economy there are two equal-sized groups of people: type a have preferences given by 2 log(xa1) + log(xa2) and type b have preferenceslog(xb1)+2log(xb2) where xhi means consumption by a type h person of good i. The division of property is as follows: each a-person has an endowment of (30, k) units of the two goods; each b-person has an endowment of (60, 210−k) units, where k is some given number between 0 and 210. Assume that there is no production and that people can freely exchange goods to maximise their utility. If there is a competitive equilibrium, what are the individuals’ incomes (ya, yb) in equilibrium as a function of k?
- Consider a market with M= 2 consumers and L = 2 goods. The preferences of each consumer are u₁(x₁) = min (x₁, x2} (6) U₂(x2) = X1X2 (7) Draw the Edgeworth box for this economy, where endowments are ₁ = (0,1) and ₂ = (1,0). Be sure to label the budget constraint, endowment point, equilibrium price ratio, equilibrium allocation, and the indifference curves of each consumer. Please do fast ASAP fastConsider an economy with 2 goods and 30 agents. There are 10 agentseach with the utility function u (x1; x2) = ln x1 + 2 ln x2 and endowments e = (3; 1).Also, the other 20 agents each have the utility function u (z1; z2) = 2 ln z1 + ln z2 andendowments e = (1; 2). Normalize p2 = 1. Calculate the Walrasian equilibrium pricep1*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.
- Two consumers, Budi and Marry, together have 10 apples and 4 oranges. a. Draw the Edgeworth box that shows the set of feasible allocation for the two individuals and two goods b. Suppose Budi has 5 apples and 1 orange, while Marry has 5 apples and 3 oranges. Identify this allocation in the Edgeworth box c. Suppose Budi and Marry have identical utility functions and assume that this utility function exhibits positive marginal utilities for both apples and oranges and a diminishing marginal rate of substitution of apples and oranges. Could the allocation in part (b) be economically efficient?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).Persons 1 and 2 have the following utility functions over goods x and y: Person 1: U1(x1, y1) = min{2x1, y1} Person 2: U2(x2, y2) = x2 + y2 Person 1 has an endowment of e1 = (2, 1). Betty’s endowment is e2 = (1, 2). Graph the Edgeworth Box for this economy. Draw each person’s indifference curve through the endowment point. Are there allocations that Pareto dominate the endowment? If so, show them on the diagram. Also, identify which allocations are Pareto optimal relative to the endowment point. Solve for the contact curve for this economy. Illustrate it in the Edgeworth Box.
- Explain the statement true or false. Give an example of a person's economic situation to explain the solution. "It is possible to have a Pareto efficient allocation where someone is worse off than she is at an allocation that is not Pareto efficient"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…Kindly help on these two question... The result that every competitive equilibrium is pareto efficient. a) the second fundamental theorem of welfare economics. b) Edgeworth's condition c) The first fundamental theorem of welfare economics d) Waras's law 2) Assume that there are two consumers ( A and B) in an economy that have preferences that can can be represented as cobb-douglas utility functions. Also assume that there are two firms that have concave production possibility frontiers over goods x and y . Which of the following conditions must be true for an allocation to be distributivity efficient? Select all that apply. a) all goods in the economy are consumed. b) producers must be operating on their production possibilities frontier. c) all consumers must have marginal rates of substitution that are equal. d) all producers must have marginal rates of transformation that are equal . e) consumers must value goods at the margin at the same rate it costs society to produce them