Consider a two-person (1 and 2) two good (X and Y) exchange economy. The utility function of person 1 is given by U1 = A1 x1 - b1 x1^2 + y1 and the utility function of person 2 is given by U2 = A2 x2 - b2 x 2^2 + y2 where xi and yi denote respectively person i's the consumption amount of good X and good Y, i = 1, 2. Let A1 = 231, b1 = 1/2, A2 = 231 and b 2 = 1/8 be the values of the parameters above. Suppose the economy has a total of 108 units of good X and 85060 units of good Y What is the value of the marginal rate of substitution of person 1 when each person has the efficient amount of good X ?
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- Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U = 4P + 3C . In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of PepsiConsider a pure-exchange economy of two individuals (A and B) and two goods (X and Y). Individual A is endowed with 5 units of good X and 3 units of good Y, while individual B with 3 and 4 units of goods X and Y, respectively. Assuming utility functions of individuals A and B to be UA=XA YA² and UB-XB² YB where Xi and Yi for i= {A, B} represent individual i's consumption of good X and Y respectively, what will be the set of Pareto optimal allocation in this economy?Assume the setting outlined in Question 1. Suppose that the social planner considers it to be imperative that agent B consumes exactly one unit of good 1l and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforce transfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 would guarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2? Select one: O a. One half unit of good 1 has to be transferred from agent A to agent B. O b. There is no endowment for which agent B would consume x = in the corresponding competitive equilibrium. Therefore, no such transfers exist. 1 and æ = 4 O c. One unit of good 1 has to be transferred from agent A to agent B. O d. Transferring good 1 is not sufficient. It is necessary to transfer one unit of good 2 from agent A to agent B.
- Give typing answer with explanation and conclusion Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2. Person A is initially endowed with ωA = (0,10) and person B is initially endowed with ωB = (11,0). They have identical preferences, which are given by U^A(x1,x2) = U^B(x1,x2) = x1^2*x2. Suppose that p2 =1. Under the competitive equilibrium, what is p1? Round answers to two decimal places.Suppose that Abel and Eden spend their incomes on two goods, food (F) and clothing (C).Abel’s preferences are represented by the utility function U(F,C)=10FC, while Eden’spreferences are represented by the utility function U(F,C)= 0.20F2C2A) With food on the horizontal axis and clothing on the vertical axis, identify on a graph theset of points that give Abel the same level of utility as the bundle (10, 5). Do the same forEden on a separate graph.B) On the same two graphs, identify the set of bundles that give Abel and Eden the samelevel of utility as the bundle (15, 8).C) Do you think Abel and Eden have the same preferences or different preferences? ExplainThere 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 0
- A pure exchange economy with two consumers A(nne) and B(en) and two goods is illustrated in the following Edgeworth box. Both agents' preferences are representable by an increasing linear utility function. The dashed lines (blue) display three indifference curves for Anne, the solid lines (red) represent three indifference curves of Ben's preferences. The points a to f mark different allocations. Mark the correct answers. B A d Good 1 Select one or more: a. Allocation f is located on the contract curve. b. Allocation b is located in the core of the economy. C. Allocation f is a Walrasian equilibrium allocation. d. Allocation c is a Walrasian equilibrium allocation. e. Allocation a is a Walrasian equilibrium allocation. f. Allocation d is a Walrasian equilibrium allocation. g. Allocation e is located in the core of the economy. h. There is no Walrasian equilibrium. Good 2Suppose Lan's utility function is U₁(x,y) =x_y_¹0 and Dan's utility function is U₁(x,y) =xD³y5, where x; and y₁ denote respectively the amount of good X and of good Y consumed by person i, i=L, D. A total of 44 of each good is available and it is to be divided efficiently between Lan and Dan. How many units of good Y should Lan get if we give Dan 14 units of good Y such that the allocation is efficient?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 2/3 x1³x2³. If we set good 1 as the numeraire (so that p. = $1), what will the equilibrium price of good 2 be?
- 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.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?