Suppose that we have two individuals A and B with initial endowments (w.) for A and (,) for B. Both individuals have Cobb-Douglas prefecences over the two goods: Find the equilibrium. U^(-)-() () "(",) (()*
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- 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.1. Consider a pure exchange economy with two goods and two consumers. Let F denote food and C denote clothing. Lacy has the utility function U(F, C) = F¹/32/3. Roy has the utility function V (F, C) = F2/3¹/3. Each consumer has an initial endowment consisting of 9 units of F and 9 units of C. Normalize the price of F to one. Let P denote the price of C. (a) Is the initial endowment a Pareto efficient allocation of F and C between the two con- sumers? Explain briefly. (b) What is each consumer's demand for F and C as a function of P? [Hint: the wealth of each consumer is 9 + 9P.] (c) What is the price of C in a competitive equilibrium? (d) What is the allocation of F and C between the two consumers in a competitive equilibrium?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?
- Exercise 4 Consider an economy with two consumers, Alexia and Bart, who live two periods, t = 0 and t = 1. In each period they can consume one type of good and their preferences for consumption are given by U (co, c²) = c(c²)² _i = A, B. Alexia and Bart have the following endowment of good in each period M=1, M₁ = 1, MB = 2, MB = 2. In t = 0, Alexia and Bart can exchange a financial contract for the delivery of one unit of consumption good in t = 1 (a bond). Name p the price of the bond and b² the amount bought by agent i = =A, B. (a) Write down each agent's utility maximization and budget constraints assuming that he/she can trade the bond without restrictions. (b) Find each agent's optimal quantity b² as a function of the bond net return r. (c) Find the equilibrium value of r and the equilibrium demand/supply of each agent.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.3. Consider an economy with two individuals, Eve and Adam. There are two goods-apples(A) and figs (F). Eve has fixed-coefficient preferences {} where the superscript denotes e for Eve. Eve has an endowment of 20 apples and nothing else. Adam owns only labour, and consumes only apples, thus ua (A, F) = A. u(A, F) = min Note that Adam gets no utility from leisure, so he supplies labour inelastically. Labour (L) is needed to produce figs, using the technology F = L. Suppose initially the endowment of Adam is K units of labour. (a) Compute algebraically the competitive equilibria of this economy for both K K. Is it possible that he becomes worse off?
- 1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = X*Y UB(X,Y) = X*Y3 Therefore: • For consumer A: MUX = Y; MUY = X • For consumer B: MUX = Y3; MUY = 3XY2 The initial endowments are: A: X = 10; Y = 6 B: X = 14; Y = 19 show all work a) Suppose the price PY = 1. Calculate the price of X, PX that will lead to a competitive equilibrium. b) How much of each good does each consumer demand in equilibrium? Consumer A’s Demand for X: Consumer A’s Demand for Y: Consumer B’s demand for X: Consumer B’s demand for Y: c)What is the marginal rate of substitution for consumer A at the competitive equilibrium?There are two consumers, i = 1, 2. There are L traded goods in the economy and the consumers are price takers. Each consumer has preferences over the commodities she consumes and over some action h that is taken by consumer 1. That is, Ui (xị, ..., x, , h) Activity h is something that has no direct monetary cost for person 1. For example, it could be playing loud music. From the point of view of consumer 2, h represents an externality of consumer 1's actions if = 0 +0 0Suppose there are two consumers. A and B. The utility functions of each consumer are given by: U₁XX)-x²-y U₂XY)-x-² Therefore For consumer A: MUX-2XY: MU-X² For consumer B: MUx-Y²; MUy-2XY The initial endowments are: A:X-60; Y-150 B.X-45: Y-75 al Suppose the price of Y, Py-1. Calculate the price of X, P, that will lead to a competitive equilibrium. How much of each good does each consumer demand in equilibrium? Consumer A's demand for X: Consumer A's demand for Y Consumer B's demand for X: Consumer B's demand for Y d ts) What is the marginal rate of substitution for consumer A at the competitive equilibrium?
- Consider a pure-exchange general equilibrium model with two consumers, two goods and an initial endowment. Assuming that consumers have convex preferences, a Pareto improvement can be achieved through exchange: a. As long as indifference curves associated with the endowment are tangent to each other on the Edgeworth box. b. As long as indifference curves associated with the endowment are not tangent to each other on the Edgeworth box. с. Only when one of the consumers has no endowment of one of the goods. d. Only when the initial endowment is on the contract curve.Please answer all parts it would mean alot. For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) a) Illustrate the initial endowment in an Edgeworth box. Clearly label the axes and explain the dimensions of the box. Show the indifference curve each of them is on at the endowment point. b) Consider an allocation where Kim gets (xk, yk) = (40,40) and Jung gets the remaining Ferraris and VR headsets. Show where this point is in the Edgeworth box. Is this allocation Pareto efficient? Is it equitable? How likely is this to arise in practice? c) Assume that Kim has preferences Uk (Xk, Yk) = 3Xk + 3Yk and Jung has…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 %D