Consider an exchange economy with two goods, 200 agents of type A, and 100 agents of type B. The preferences of agents of type A can be represented by the utility function u4(x1,x2) = VT1, those of type B by u (x1, x2) = 2x2. Initial endowments are given by wA = (10, 20) and wB = (20, 10). Mark the correct answers: (Hint: A sketch of the Edgeworth box may be helpful.) Select one or more: a. The equilibrium allocation is Pareto efficient. b. In the Walrasian equilibrium, each consumer of type A consumes 10 units of good 1. C. The initial endowment allocation is an equilibrium allocation. d. There is no Walrasian equilibrium. e. p* = (2, 1) is a Walrasian equiliprium price. f. In the Walrasian equilibrium, each consumer of type A consumes 20 units of good 1.
Q: Consider a two-good economy, where every person has the endowment w =(0,20). For the following…
A: Solution in Step 2
Q: Assume the setting outlined in Question 1. Suppose that the social planner considers it to be…
A: Option c is correct
Q: Consider an exchange economy with two goods, 200 agents of type A, and 100 agents of type B. The…
A: For type A : Ua = ( x1)0.5 Number of agents = 200 Endowment per agent = (10 , 20 ) Budget…
Q: Show that perfect substitutes are an example of homothetic preferences
A: The goods that can be used for same purpose is known as substitute good. Consumers with different…
Q: There are two expantions for preference reversals.(In Behavior Economics) -Scale Congruence…
A: Answer - Need to find- explain for preference reversals 1. Scale Congruence:- Scale Congruence is…
Q: Now, suppose another buyer, Neha, enters the market for apartments, and her willingness to pay is…
A: The measure that depicts the difference between the price that consumers are willing to pay and the…
Q: Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A…
A: Given, The utility function of the consumer A, UA(x1A, x2A)=x1A x2A2 Here, c = 1 (power of x1A) , d…
Q: Please Answer the question by using well labelled diagrams
A: When the cost of a lower-quality item increases, two things happen: Since the inferior good's price…
Q: Person A has a utility function uA (X₁, X2)X₁X₂ and person B has a utility function 1/3 2/3 UB (X1,…
A: Hi! Thank you for the question. As per the honor code, We’ll answer the first question since the…
Q: Bert has an initial endowment consisting of 10 units of food and 1o units of clothing. ernie’s…
A: Bert Initial Endowment = 10 units of Food and 10 Units of clothing Ernie's Initial Endowment = 10…
Q: Consider an endowment setting where (@1, 2) = (1, 1). Assume that x₁, x₂ are ordinary goods. x₁ is…
A: Inferior goods refers to the type of goods which has inverse relation with income of the consumer.…
Q: Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries).…
A: The Free Trade Economics In theory, worldwide free trade is no different than trade between…
Q: Which of the follwoing theoretical results is concerned with the relationship of factor endowments…
A: Output refers to the sum of all the goods or services that a firm or producer makes within a period.…
Q: Elizabeth Swann and her husband consume wine (W) and books (B). Elizabeth's utility function is…
A: Elizabeth's Utility function : Ue = W Endowment : W , B = ( 16 , 5 ) Husband's Utility function : Uh…
Q: The next four questions are based on the following information. Consider an exchange economy with…
A: Given that, There is an exchange economy with two agents A and B and two goods X and Y A's endowment…
Q: Consider a two-person economy and both have the same utility function U(x) = x +Jx,. The ggregate…
A: Given information Both consumers have same utility function U=x1+X2 W1=200 W2=100
Q: Let Utility Function be U = min {X, Y} As given Endowment of Good 1 and Good 2 is 100 and 200…
A: Optimal bundle with price (10, 10) X=Y Budget constraint: px*X + py*Y = M px*X + py*Y = 100px +…
Q: In an exchange economy, there are two people, A and B, and two goods, z and r. Their respective…
A: Utility function for A : U(A) = min{ x1 , 2x2 } Utility function for B : U (B) = x1 + x2 Endowment…
Q: Let preferences of both individuals be given by log(ci)+ log(c). Suppose that the endowment vectors…
A: Market supply of both the goods are the sum of endowments.
Q: Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A…
A: A Walrasian equilibrium is a set of prices and a consumption bundle for each agent in which I each…
Q: Consider a two-agents, two goods economy, in which both agents, A and B, are represented by the…
A: Ua ( x1 , x2 ) = x12 x2 Ub (y1 , y2 ) = y1 y22 Set of pareto optimal allocations is called the…
Q: Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries).…
A: Production: It refers to the process of producing goods and services in the economy. The more the…
Q: An exchange economy has two goods (apples, bananas) and two types of agent (1, 2). The total…
A: Total number of apples = 7 Total number of bananas = 7 U1 = 200 + x1b + x1a U2 = -20 + 3x2b +…
Q: Consider an exchange economy with two goods, 200 agents of type A, and 100 agents of type B. The…
A: The term "equilibrium" refers to a stable condition of balance in which opposing forces cancel each…
Q: Refer to figure . At the initial price, the consumer consumers 5 units of apple. Suppose the…
A: Endowment is the consumption bundle of the 2 or more gods. In the given question 2 goods are…
Q: Rosa received a corgi pillow as a raffle prize; she would have been willing to pay $18 to buy it…
A: Given the information: The willingness to pay price for a corgi pillow = $18 Required to find the…
Q: Suppose Adam has utility function UA (X1, x2) = xy and Bob has utility function UB (X1, X2) = xx2…
A: Given Adam utility function: UA(x1,x2)=xy Bob utility function: UB(x1,x2)=x12x2 Initial endowments…
Q: Consider an general equilibrium endowment economy with two goods and two individuals. The two…
A: An indifference curve is a graph that depicts all of the product combinations that provide the same…
Q: Consider trade between two consumers (1 and 2) and two goods, X and Y. Suppose the total quantities…
A: Any kind of shock in one of the markets generally has spillover effects in the other markets in the…
Q: For Questions 5–7 below, consider the following description of a two-goods economy: Assume two…
A: For individual X : Utility function : U (x1, x2 ) = x11/3x22/3 Endowment : ( 9 , 3 ) Income = 9p1 +…
Q: Question 3 Suppose two individuals, A and B, consume two goods (x₁, x₂). A's initial endowment is…
A: i. Given below is the Edgeworth box. The Y-axis depicts the quantity of good x2. The X-axis depicts…
Q: Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 9 units…
A: Answer - Pareto efficiency:- Pareto efficiency is condition under which one individual can not be…
Q: Analyze how pareto efficiency is achieved from consumption activities in an economy
A: Human wants are unlimited but the resources to satisfy these wants are limited. Hence there is a…
Q: Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A…
A:
Q: Consider the following simple model of the Mile End Park Beautification Initiative (from the…
A: As per given information
Q: Suppose two consumers, Jack and Suzy, have identical utility functions defined for pencils (P) and…
A: The edgeworth box is a graphical diagram that shows the exchange or trade of two goods between two…
Q: Consider a pure exchange economy with two goods k = 1,2 and two households = A, B. Consider the…
A: We are going to calculate marginal rate of substitution for household A
Q: Consider an exchange economy with agents A and B and goods x and y. A's endowment is (0, 1) (i.e.,…
A: Given that, There is an exchange economy with two agents A and B and two goods X and Y A's endowment…
Q: Consider a two-people, two-goods exchange economy, where Person A and Person B have the following…
A: Utility function is described as a function which tells us about the level of satisfaction achieved…
Q: An Arrow-Debreu equilibrium occurs under the following assumption(s): (1) Consumers have a set of…
A: The answer is - B) I II, and IV That is, An Arrow-Debreu equilibrium occurs under the following…
Q: Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility…
A: Utility function of Aron : UA(xA, yA) = min{xA/3, yA} Endowment of Aron : (2 , 4 ) 2Px + 4Py =…
Q: A pure exchange economy with two consumers A(nne) and B(en) and two goods is illustrated in the…
A: Answer -
Q: Extend the model of the jungle to the case in which the number of houses is smaller than the number…
A: What is Economic Equilibrium? Economic equilibrium is a condition or state in which economic forces…
Q: Suppose that 2 agents, A and B, have preferences over goods 1 and 2: u (x4) = = ×P×3. Total…
A: Contract cirve is the locus of all Pareto optimal points where both agent's margin rate of…
Q: Consider a two-good two agent economy with the following endowments and utility functions: (ef, e) =…
A:
Q: Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initia…
A: Given There are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial…
Q: Suppose that Morris has preferences on books and wine represented by the utility function Ub, w)=b+w…
A: We need to find the contract curve here. The formula for contract curve is given by: Contract Curve…
Step by step
Solved in 2 steps
- Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. Consumer A is initially endowed with 10 units of good 1 and 10 units of good 2. Consumer B is initially endowed with 2 units of good 1 and 2 units of good 2. The consumers have the following utility functions: uA(X1A,X2A)=X1AX2A²; UB(X1B,X28)=X18+X2B- Among the prices below, which ones are Walrasian equilibrium prices? O a. P1=3, p2 =2 O b. p1=4, p2 =5 O c. None of the other answers. O d. p1=5, p2 =4 O e. p1=2, P2 =3Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, when there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is ua(XA,S)=XA.S, where xĄ is the amount of money Person A owns. Person B's utility function is ug(xg, 1s)=xB .(1-s), where xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person A has the legal right to a fill up the room with smoke and there exists a market for smoke "abatements". At the Walrasian equilibrium, how much money will person B be left with? O a. Xg=1.25 O b. Xp=2.25 O c. XB=0.25 O d. Xg=0.25 е. None of the other answers.Suppose that David and his friend Wilson derive utility from consuming two types of snacks: onion rings (9₁) and chips (9₂). The utility function for each individual is U (9₁, 92) = 9192. Their indifference curves for these two goods are assumed to have the usual (convex) shape. Suppose David has an initial endowment of 35 onion rings and 10 chips, and Wilson's initial endowment consists of 5 onion rings and 20 chips. (1) Draw an Edgeworth box and show the initial allocation of goods, to be labelled e. Indicate the initial quantities of each person's goods on the four axes.
- 4) Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2). Consumers' endowments are e1 = (4, 2) and e? = (6, 6) And their preferences are represented by utility functions: u(x, y) = x³y and u(x,y) = x³y$ (d) Set up the utility maximization problem for each consumer and solve for their Marshallian demand functions. (e) Compute the market demand for each good. () State the Walrus law for this economy and explain its economic interpretation. (g) Assume the excess demand for good x is zero, i.e., EDx = 0, and calculate the ratio of prices, i.e., p Ipy . Then, use this ratio of prices to show that the excess demand for good Yis also zero, i.e., EDy= 0. Briefly explain how this relates to the Walrus' law. (h) Given the price ratio found above, calculate the equilibrium allocations and show that feasibility, individual rationality, and Pareto efficiency holds.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 0Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3
- 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?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 %3D4. Consider a two-consumer, two-good exchange economy. Utility functions and endowments are u'(x1, x2) = (x1x2)² and e' = (18, 4),u²cx1, x2) = In(x1) + 2 In(x2) and e? = (3, 6). (a) Characterize the set of Pareto-efficient allocations as completely as possible. (b) Characterize the core of this economy. (c) Find a Walrasian equilibrium and compute the WEA. (d) Verify that the WEA you found in part (c) is in the core.
- 2. Consider an economy with two agents and two commodities. Consumers' preferences are represented by the following utility functions u₁(x,x) = (x²) ¹ (x²) ½ u₂(x², x²) = x² + x². Consumers' initial endowments are e² = (6,4). Note: You can normalize the price of one good to 1 at any point when solving this question. e¹ = (10,2) (a) Draw the Edgeworth box that represents this economy. Clearly indicate the size of the box (i.e. the maximal feasible amounts of good 1 and good 2). Show the location of the initial endowment and draw the indifference curve of each consumer that passes through the initial endowment.John 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 J B. b. C < J. c. C = J. d. C = B. e. JJohn 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. JSEE MORE QUESTIONSRecommended textbooks for youPrinciples of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSONPrinciples of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-…EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill EducationPrinciples of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSONPrinciples of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-…EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill Education