QUESTION 1Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wf, wg) = (1,2) and Bob's endowment equals(wf, w) = (1,3). Alice's utility is given by ua(zf, x4) = 2 ln z4 + In z4, while Bob's utility is up(zf, x}) = In z? + 2 ln z}. Find thecompetitive (Walrasian) equilibrium prices in this pure exchange economy.Select one:O a.P1 = 5, P2 = 3%3DO b.P1 = 3, P2 = 7%3DO c.P1 = 7, P2 = 3O d. Pi = 1, P = 4Consider the same set up as in Question 1. Which of the following consumption bundles of consumer A belong to the contract curve?Select one:O a. rf = 1, xg = 1O b. af = 2, xg = 1O c. af = 1, xO d. af = 2, xg = 4%3D%3D3

We are going to solve this question using general equilibrium methodology which entails equality…

Answered: QUESTION 1 Alice (A) and Bob (B) have…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose that consumer I has the utility function u(x,y) = x + 2y and consumer II has the utility function u(x,y) = min{x, 2y}. Consumer I initially has 12 units of y and zero units of x, while consumer II has 12 units of x and zero units of y. It is correct to state that, in competitive equilibrium, the agents' consumption basket will be:
Problem 1. Two consumers, Alice and Bob, have utility functions given by u₁(x, y) = x¹/²y¹/4 and ug (x, y) = 4x² + y², respectively, where x and y are the number of apples and bananas respectively. Suppose that apples and bananas cost p₁ and p2 dollars each respectively and that both consumers have M dollars to spend on apples and bananas. (a) On the same axes, sketch Alice's budget set and some contours u₁(x, y) = c for positive values of c. By referring to your sketch explain why the method of Lagrange multipliers can be used to find the maximum value of u₁(x, y) subject to her budget constraint. Hence use the method of Lagrange multipliers to find Alice's optimal bundle. (b) On the same axes, sketch Bob's budget set and some contours up (x, y) = c For positive values of c. By referring to your sketch, find Bob's optimal bundle.
Consider an Edgeworth-box economy, which contains two individuals i and j, and two goods (and 2. The total endowment of good I is 8, and the total endowment of good 2 is 4. Individual i has the Leontief utility U₂C X₁, X₁z) = min (X₂₁, Xiz) for all X₁, Xiz 20, while individual j has the Linear utility U₁ (Xj₁, Xj₂)=Xj₁t Xj₂ for all X₁, Xyzzo, which allocation below this is not Patreto efficient / optimal a. (( X ²1, Xit), (X₁₁ + X₁²₂)) =((2, 2), (6,2)) 6. (( X ₂₁, Xiv), (X; ₁ ; X₁3₂)) = (C0₁0), (814)) c. (CX₁, Xt₂), (X3³₁, X₁₂)) = (( 8₁4), (0, 0)) d. ((x), X₁₂), (X₁, X3₂)) =((4,4), (4,0))
Consider an economy with 2 goods and 2 agents. The Örst agent has the utilityfunction, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is asocial planner who cares about agents equally.(a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).
(5) A has utility function u4(x4) = x4 + x and initial endowment w4 = (3,6). Consumer B has utility function uB (xB) = xf · x% and initial endowment wB = (3,6). Consider an exchange economy with two consumers and two goods. Consumer (a) Is the initial endowment a Pareto efficient allocation? Justify your answer. (b) Find a competitive equilibrium (p, xª, x³) for the economy. (c) Construct the contract curve. A picture here is not a complete answer; you need to specify analytically the set of points that are in the contract curve.
Alex's utility is U (xA, YA) = min {TA, YA}, where zA, and y, are his consumptions of %3D goods a and y respectively. Becky's utility function is U (zB, YB ) = TBYB where ap and yp are her consumptions of goods a and y. Alex's initial endowment is 20 units of x and 12 units of y. Becky's initial endowment is 12 units of x and 20 units of y. At the Walrasian equilibrium, a) Both of them consume 16 units of good y each. b) Alex consumes 8 units of good y and Becky consumes 16 units of y. c) Both of them consumes 12 units of good x each. d) Alex consumes 12 units of good x and Becky consumes 20 units of x. e) None of the above
In a two-good market, a consumer starts with an initial endowment of (x₁, x2) = (15.00, 5.00), while the market prices for these goods are given by (P1, P2) = (7.00, 3.00). The consumer has the following utility function: U 0.52 0.48 - Given this information, what will this consumer's final choice of quantity for each good be? x1 = x2 =
5.18 In a two-good, two-consumer economy, utility functions are u¹ (x₁, x₂) = x₁(x₂)², u² (x₁, x₂) = (x₁)²x₂. Total endowments are (10, 20). (a) A social planner wants to allocate goods to maximise consumer 1's utility while holding con- sumer 2's utility at u² = 8000/27. Find the assignment of goods to consumers that solves the planner's problem and show that the solution is Pareto efficient. (b) Suppose, instead, that the planner just divides the endowments so that e¹ = (10, 0) and e² = (0, 20) and then lets the consumers transact through perfectly competitive markets. Find the Walrasian equilibrium and show that the WEAs are the same as the solution in part (a).
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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.
Bob’s preferences for apples (A) and bananas (B) are represented by U(A,B)=A+2B. Apples cost £2 and bananas £1. Given that Bob’s monthly income is £30 answer the following questions:a) What type of goods are apples and bananas for Bob?b) What is the proportion to which Bob is willing to exchange apples for bananas?c) Illustrate and solve graphically Bob’s utility maximisation problem.d) If his income increases every month by £10, how will Bob’s consumption choice be affected? Illustrate graphically the income expansion path and the Engel curve for each good.e) How will an increase in the price of bananas to £6 affect Bob’s optimal consumption choice? (Bob’s income is £30)f) Graph Bob’s demand curve for each good.g) Assume that Bob wins a voucher of £20 redeemable only in apples. How would this affect Bob’s his utility? (Assume that prices and income are as described initially)h) Assume that Bob is presented with two options: an apples voucher of £20 or just £6 to spend in any good he…
Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 2 units of good X and 6 units of good Y. Consumer B is given an initial endowment of 6 units of good X and 2 units of good Y. Consumer A's utility function is given by: UAXY) = X"Y, and consumer B's utility function is given by: Ug(X,Y) - MIN (2X, Y). If the prices are Px-1 and Py- 2, if each consumer sells her initial endowment and buys back her and in the optimal bundle, then in the Market for Good X there is Select) Market for Good Y there is [Select)

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