Question 2: Consider a competitive exchange economy with two individuals (A and B) and two goods (F and W). The total endowments of F and W are 10 each. Consumer A has the following utility function: UA = FW while consumer B has preferences such that she must have one unit of F for every unit of W. (a) Derive an expression for the contract curve and illustrate in an Edgeworth box dia- gram. (b) What is the relative price of F, PF/Pw, in a competitive equilibrium? (c) Now suppose that consumer B's utility function is UB = F +2W Let consumer A's utility function remain unchanged. Derive an expression for the con- tract curve now and illustrate in a new Edgeworth box diagram. (d) What is the relative price of F, Pr/Pw, in a competitive equilibrium?
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- Sarah and Andrew are two traders in a pure exchange economic with two goods, Bikes (B) and Computers (C). Sarah's preferences are described by the Cobb-Douglas Utility function: U, = B!³ C?3 1/3 S. Andrew's preferences are given by: UA = B}{²C}2 ´A Assume the price of Bikes is 1 and the price of computers is p. The initial endowments are BA = 10, Bs = 20, CA = 20 and Cs= 10. What is the equilibrium price of computers relative to bikes (p)? %3D %DJohn 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. JI 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?Please answer every part. 4. Consider an economy consisting of two individuals, Ann and Bob, and two goods, scotch and wine. Aun has 5 bottles of scoteh and 2 bottles of wine as her endowment, while Bob has 3 bottles of each. Suppose their preferences are described by the following utility functions uA(s, w) = sw and up(s, w) = s'u. Assume also that the prices of goods scotch and wine are represented by P,= 1 (scotch is the mumeraire), and P>0. a. Sketch the Edgeworth box of the economy with Ann at the lower left corner and Bob at the upper right corner; scotch on the horizontal axis, and wine on the vertical axis. Indicate the endowment point e in the box. b. Write the budget lines for Ann and Bob. e. Solve Ann's utility maximization problem. Expross Ann's optimal consumption bundle in terms of P. d. Solve Bob's utility maximization problem. Express Bob's optimal consumption bundle in terms of P. e. Define competitive equilibrium. Compute and plot the CE for this problem.9. Consider an Edgeworth box economy with two consumers, whose utility func- tions and endowments are e' = (5,5) 2 = (5,5) In the following, use the normalization p2 = 1. (a) Find the competitive equilibrium price. (b) State the first fundamental theorem of welfare and verify that it holds in this economy. (e) Consider the allocation ã = (x',) = (2,3), (8, 7). Show whether this allo- cation can supported as an equilibrium with transfers. (d) State the second fundamental theorem of welfare, and briefly discuss whether the result in part (c) conform with or violate this theorem.D7) In a two good two consumer economy, utility functions are U1(x1,x2) =x1(x2)2 and U2(x1,x2) = (x1)2 x2 The endowments of the consumers are e1 =(10,0) and e2=(0,20). Find the allocation of goods in Walrasian equilibrium.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.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.Suppose that 2 agents, A and B, have preferences over goods 1 and 2: u+(x4) 2x + x5 and u (x³) = xFx. Total endowments are ej = B B Total endowments are e¡ = e2 = 4, (a) Find the contract curve. (b) If initial endowments are e4 = A (4,0) and eB (0, 4), what is the core?Q. Consider two rational behaving consumers, A and B, in a two-good exchange economy. Their utility functions are defined as follows: 1A 2A X1/2X¹/3 X1/3 X2B 1B Their initial endowments are given by w₁ = (8,5) and wB = (4,3). a. Describe the initial condition that will lead to an exchange. After the exchange, how many units of Good 2 will Individual B end up receiving/offering in the final allocation? Elaborate in detail on the steps towards the solution and round up the final answer to two decimal places. UA UB - = b. Sketch an Edgeworth Box precisely showing the initial allocation and the final allocation on the vertical axis. You do not have to sketch the budget constraint and the indifference curves.Consider a two-person endowment economy characterized by the Edgeworth Box below: a. b. C. X2. OA A E B OB X1 Are the allocations depicted at points A and B Pareto efficient? Explain your reasoning. Add bowed indifference curves that reflect the utility that the two consumers get from the endowment depicted at point E (assume that they value both goods). What is meant by the term "Pareto improvement." In your diagram highlight the set of Pareto improving allocations given the endowment.5. Devin and Giannis consume books and videos. Devin has the endowment (30, 8) while Giannis has (50, 12). Each has the utility function u(b, v) = 4vb + 4vv. (i) Sketch the Edgeworth Box. (ii) Find the equation for the contract curve. (iii) If pv = 1, what is the equilibrium value of pB? (iv) Now suppose that Devin and Giannis both have the utility function u(b, v) = min{½b, v} instead. If pv = 1, what is the equilibrium value of pB?SEE MORE QUESTIONS