In an exchange economy, there are two agents, A and B, and there are 560.00 total units of x and 560.00 total units of y. The twoconsumers have utility functions u(x, y) = x²y and u³ (x, y) = xy, respectively.Assume the initial endowments are wд = (504.00, 56.00) and wB = (56.00, 504.00).Let p be the price of good y, and let the price of good x be 1. The competitive equilibrium value of p isanswer to the nearest two decimals if needed.)(Round your

The question is solved below:Here CE denotes competitive equilibriumIn the given scenario, the…

Answered: In an exchange economy, there are two…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider an exchange economy with two agents (i = a, b) and two goods (j = 1, 2) with the following characteristics. Agent a: Initial endowment (ea,1, Ca,2) = (1,0) and utility function Ua(Ca,1, Ca,2) = - exp(-ca,1) – exp(-ca.2) Agent b: Initial endowment (e,1, C,2) = (0, 3) and utility function U(ch1, Ch,2) = – exp(-c1) – exp(-c,2) Assume that there exists a competitive market for each good. Let p, denote the price of good j = 1,2. a) What is the competitive equilibrium of this economy? b) Illustrate the competitive equilibrium in the Edgeworth box. Draw at least the agents' indifference curves, the budget line, and the contract curve (i.e., the set of all Pareto optimal allocations). Clearly indicate which curves represent what.
Consider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions: V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py Where Mi is the income level of person i and Px and Py are the prices for goods x and goods y, respectively. a) Calculate the market clearing prices.
Consider an exchange economy with two agents, A and B, and two commodities, X and Y. Assume their endowments are (w,w%) = (3,8) and (w,w%) U (xA, YA) = XAYA and U(xB, YB) = xB + YB• (2, 2). Also assume their utility functions are (a) Draw an Edgeworth box and show their endowments. (b) Find Pareto Efficient Allocations and show them on your Edgeworth box. Show the core of this exchange economy. (c) Is there a competitive equilibrium? If there is, find competitive equilibrium price ratio and allocation. If there exists no competitive equilibrium, tell which condition(s) of the first theorem of welfare economics is violated and show what goes wrong when price ratio is 1.
A small exchange economy is comprised of two of individuals, A and B, and two types of goods, x, ,x,. The individuals' preferences over two goods are can be represented by the following utility functions: U*(x;,.x; ) = min (2.x,x; ) and U* (x;,x;) = min(x;.2x, ). Initial endowments are 10 x, (individual A), and 10 x, (individual B). Calculate the price ratio which yields an equilibrium in the exchange market.
In an exchange economy, there are two people, A and B, and two goods,X1 and X2. Their respective utility functions and endowments are u (x, x) = min {xf, 2x ) u (xf, x) = xf + x? %3D @A = (4, 9), w = (4, 0). Note: The As and Bs in the equations above are not powers but rather superscripts to indicate each agent. The minimum and maximum possible amounts of x*2 on the contract curve are Minimum x: %3D Maximum x %3D O 0; 4 O 4; 8 O4; 4
In an exchange economy, there are two people (Shadi and Nino) and two goods (x1 and x2). Their initial endowments are ωS = (2, 4) and ωN = (3, 6). Their utility is given by the following functions: US(x1,x2) = x12x23 and UN(x1,x2) = x1x24. Which of the following is the equation for the contract curve? Group of answer choices a. x2N = 96x1N / (15 + 4x1N) b. x2N = 47x1N / (8 + 4x1N) c. x2N = 91x1N / 5 d. x2N = 16x1N / (3 + x1N) e. x2N = 41x1N / (9 + x1N)
In an exchange economy, two agents have utility functions u^(x, y) = x2 y and u"(x, y) = x · y, respectively, from x units of Good 1 and y units of Good 2. Assume the initial endowments are w A = (@A.1,2) and oB = (32,40), respectively. Suppose that an equilibrium is found in which the prices of the good are equal (that is, Pi = P2, i.e., the relative price is 1). If WA.1 = 60, then wA.2 %3D
Consider an exchange economy with two consumers (A and B) and two goods (x1 and x2). Consumer A has an endowment of 5 units of x1 and none of x2, whereas Consumer B has an endowment of 3 units of x1 and 15 units of x2. Consumer A's utility function is given by uA=xA1xA2, and Consumer B's utility function is given by uB=min{xB1,xB2}. Both goods are traded in competitive markets. Find the competitive equilibrium price for x2, assuming p1=1.
Consider an exchange economy with two consumers: Charlotte and Dylan, and two goods: quinoa (Q) and raspberries (R). Charlotte has an initial endowment of 83.9 units of quinoa and 99.3 raspberries. Dylan has 112.5 units of quinoa and 77.8 raspberries. Charlotte's utility function is given by Uc=Q¹/² R¹/², where Qc and Re are her consumption of Q and R, respectively. Dylan's utility function is given by Up-Q¹/³ R2/3, where Qp and Rp are his consumption of Q and R, respectively. Suppose that the market price of quinoa is po=2 and the market price of raspberries is pr=1. At these prices, how many units of Q would Dylan want to consume?
(1) Consider a small exchange economy with two consumers, A and B, and two commodities, ₁ and 2. Consumer A's initial endowment is 3 units of ₁ and 2 unit of 2. Consumer B's initial endowment has 5 units of 2₁ and 4 units of r2. Consumer A's utility function is given by U(₁, ₁) = x^x^. Consumer B's utility function is given by U(x,x) = 2x² + x2. Note that and are the amounts of the two goods for Consumer A, and rf and are amounts of the two goods for Consumer B. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Consumer A's consumption from the lower left and Consumer B's from the upper right. Also measure the number of ₁ on the horizontal axis and the number of r2 on the vertical axis. (b) Draw Consumer A's indifference curve (ICA) going through E. (c) Draw Consumer B's indifference curve (ICB) going through E.
Tom and Jerry are room mates. They spend a total of 80 hours a week together in their room. Tom likes loud music, even when he sleeps. His utility function is UT(CT, M) = CT + M, where CT is the number of cookies he eats per week and M is the number of hours of loud music per week that is played while he is in their room. Jerry hates all kinds of music. His utility function is M² 12 UJ = CJ Every week, Tom and Jerry each get 12 chocolate chip cookies sent from home. They have no other source of cookies. We can describe this situation with a box that looks like an Edgeworth box. The box has cookies on the horizontal axis and hours of music on the vertical axis. Let the bottom-left corner be the origin for Tom, and the bottom-right corner be the origin for Jerry. Suppose the dorm's policy is "rock-n-roll is good for the soul." Thus, M=80 in the initial endowment. Consider a trade between Tom and Jerry: Jerry gives Tom one cookie for reducing one hour of music. Then the change in Jerry's…
Suppose that 2 roommates, Andy and Bob, are trying to pick an apartment in Chicago. Locations can be chosen from set of alternatives A={ x: x exists [0,1]}. Andy and Bob both want to minimize their daily commute but they work at different locations: Andy at xA=0.3, while Bob at xB=0.6. Specifically, their utility functions are: ui(x)= -(x-xi)2. Question: What is the set of all Pareto Efficient outcomes in A, assuming no money can be exchanged.

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