6. In an Edgeworth box for two consumers, A and B, with endowments of = commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution. and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo).

6. In an Edgeworth box for two consumers, A and B, with endowments of = commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution. and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo).

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 8PA

See similar textbooks

Similar questions

7. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution, and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo). (b) Suppose MRSa = Ya/Xa, MRSB = Yb/Xb, Xa = 10, Ya, = 100, Xb = 50, Yb = 20, and let good Y be the numeraire (Py =1). Verify that the competitive…
6. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (b) Suppose MRSa = Ya/Xa, MRSb = Yb/Xb, Xa = 10, Ya, = 100, Xb= 50, Yb = 20, and let good Y be the numeraire (Py = 1). Verify that the competitive equilibrium price is Px = 2.
2. Consider a two person pure exchange economy with two divisible goods: : a consumer can consume any positive amount of any good The goods are; x1 and x2. The utility function are u' (x1, x2) = x1+Vx2, and u?(x1, x2) = x1 + x2, and the initial endowments are el Pi = 1, compute the competitive equilibrium for this economy. It is to say that you need to find the vector of prices, and allocations that sustain the Walrasian equilibrium. (25, 75) and e? = (75, 25). Assuming
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?
3. Consider an exchange environment with two consumers, Consumer 1 and Consumer 2, and two goods, a and b. Consumer 1 is initially endowed with e₁,a = 0 of good a and e₁,b = 10 of good b, while €1,6 Consumer 2 is initially endowed with e2,a = 10 of good a and €2,6 = 0 of good b. The utility of Consumer 1 from consuming x1, a ER+ of good a and 1,6 ER is u1(x1,a,x1,b) = x1,a + x1,b, while the utility of Consumer 2 from consuming x2,a Є R+ of good a and x2,6 ЄR is U2(x2,a, X2,b) = √√x2,a + x2,b. (a) Consider general equilibrium in the context of this environment in which the price of good b is normalized to 1. Compute the equilibrium price pt of good a and find the corresponding equilibrium quantities consumed by the various consumers. (b) Consider the game in which, simultaneously, Consumer 1 submits a “demand curve" and Consumer 2 submits a “supply curve” to a market mediator. In particular, the strategy space of Consumer 1 is [0,10], and the strategy d of Consumer 1 corresponds to the…
3. Anita (A), Ben (B) and Carlos (C) are housemates who have moved to a new house and must decide how to allocate rooms X, Y and Z. An 'allocation' is where each housemate is assigned to exactly one room. For example, Anita → Room Z, Ben → Room X and Carlos → Room Y is allocation (Z, X, Y). Utilities for each room are given below: Utility for A Utility for B Utility for C Room X 7 9 2 Room Y 4 3 7 Room Z 2 1 4 (a) How many possible allocations are there in total? (b) Identify the two allocations which are not Pareto optimal and explain why they are not Pareto optimal. (Hint: is the allocation (Y,Z,X) Pareto optimal?) (c) Suppose we square Carlos' utility from each room (i.e. uc (Z) becomes 16). Would the set of Pareto optimal outcomes change? Why/why not? (d) Returning to the utilities from part (a), which of the Pareto optimal allocations maximise total surplus (utility) and would all housemates weakly prefer this allocation over any other? (e) Suppose the housemates decide to…
5. 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 x1³x2³. If we set good 1 as the numeraire (so that p₁ = $1), what will the equilibrium price of good 2 be?
Q. An economy with two consumers whose preferences are represented by utility functions U1 = min (x1,2y1) and U2 = 2x2 +2y2 And the aggregate endowment of 4 units of x and 3 units of y (a) Find a Pareto efficiency allocation and depict it in the Edge-worth box. (b)ls there a Pareto efficient allocation in which one consumer has all of the goods? Explain.
d) An exchange economy has two goods (apples, bananas) and two types of agents (1, 2). Endowment of agent 1 is (3 bananas, 3 apples), and endowment of agent 2 is (4 bananas, 2 apples). Both goods are divisible goods, so that it is possible to consume frac- tions of each good (e.g. 4.92 bananas and apples). Each type 1 agent's preferences are represented by the utility function U(x,x) = min{x, x}, where x and x denote the agent's consumption of bananas and apples, respectively. Each type 2 agent's preferences are represented by the utility function U(x3, x²) = 7min{x3, x4} where x and r² denote the agent's consumption of bananas and apples, respectively. Use an Edgeworth's Box to depict the set of Pareto efficient allocations in this economy. Please capture consumption of bananas on the horizontal axis.
1. Hatfield and McCoy hate each other. The only good they both consume WH W2 40 Mand McCoy's is whiskey. Hatfield's utility function is UH utility function is UM = WM-W, where WHI is Hatfield's consumption 40' Η of whisky and WM is McCoy's consumption of whiskey. The sheriff has confiscated a total of 60 litres of whiskey which he could give back to them or throw in the creek. Say that the Sheriff wants them both to be as well off as possible and weighs their "happiness" equally. How much whiskey should the sheriff give to each of them? Should he throw any whiskey in the creek; if so how much? =
7) Jane has 3 liters of soft drinks and 9 sandwiches. Bob, on the other hand, has 8 liters of soft drinks and 4 sandwiches. With these endowments, Jane's marginal rate of substitution ( MRS) of soft drinks for sandwiches is 4 and Bob's MRS is equal to 2. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is, explain why. If it is not, what exchanges will make both parties better off?
3. Anita (A), Ben (B) and Carlos (C) are housemates who have moved to a new house and must decide how to allocate rooms X, Y and Z. An 'allocation' is where each housemate is assigned to exactly one room. For example, Anita → Room Z, Ben → Room X and Carlos → Room Y is allocation (Z, X, Y). Utilities for each room are given below: Room X Utility for A 7 Utility for B 9 Utility for C 2 Room Y 4 3 7 Room Z 2 1 4