The question is attached in the image below. Note that that options for Q5 is attached in the second image. Please provide a 'mathematical' as well figurative proof for your answers (please solve for price equilibriums). The question is a past year entrance test question provided by the university for practice purposes for their entrance exam. Please do not reject it. The next four questions are based on the following information.Consider an exchange economy with agents A and B and goods r and y. A's endowmentis (0, 1) (i.e., no good r and 1 unit of y) and B's endowment is (2,0) (i.e., 2 units ofgood x and no good y. The agents can consume only nonnegative amounts of x and y.4. Suppose A lexicographically prefers r to y and B considers r and y to be perfect sub-stitutes, i.e., between bundles (x, y) and (x', y'), she strictly prefers (x, y) if and only ifx + y > x' + y'. The competitive equilibrium allocation for this economy isA. A gets (0, 1) and B gets (2,0).B. A gets (2,0) and B gets (0, 1).C. A gets (3/2, 0) and B gets (1/2, 1).D. A gets (1,0) and B gets (1, 1).5. Refer to the previous question. The set of all possible competitive equilibrium pricesconsists of all pr > 0 and Py > 0 such that A. Pz/Py = 1В. р-/Ру — 1C. Pe/Py < 1D. Pa/Py > 06. Now suppose A lexicographically prefers y to x and B considers r and y to be perfectsubstitutes. The set of all possible competitive equilibrium prices consists of all Pa > 0and p, >0 such thatA. Pa/Py = 1B. Pa/Py > 1C. Pz/Py < 1D. Pz/Py > 0

Given that, There is an exchange economy with two agents A and B and two goods X and Y A's endowment…

The next four questions are based on the following information. Consider an exchange economy with agents A and B and goods x and y. A's endowment is (0, 1) (i.e., no good r and 1 unit of y) and B's endowment is (2,0) (i.e., 2 units of good x and no good y. The agents can consume only nonnegative amounts of x and y. 4. Suppose A lexicographically prefers x to y and B considers r and y to be perfect sub- stitutes, i.e., between bundles (x, y) and (x', y'), she strictly prefers (x, y) if and only if x + y > x' + y'. The competitive equilibrium allocation for this economy is A. A gets (0, 1) and B gets (2, 0). B. A gets (2,0) and B gets (0, 1). C. A gets (3/2, 0) and B gets (1/2, 1). D. A gets (1,0) and B gets (1, 1).

The next four questions are based on the following information. Consider an exchange economy with agents A and B and goods x and y. A's endowment is (0, 1) (i.e., no good r and 1 unit of y) and B's endowment is (2,0) (i.e., 2 units of good x and no good y. The agents can consume only nonnegative amounts of x and y. 4. Suppose A lexicographically prefers x to y and B considers r and y to be perfect sub- stitutes, i.e., between bundles (x, y) and (x', y'), she strictly prefers (x, y) if and only if x + y > x' + y'. The competitive equilibrium allocation for this economy is A. A gets (0, 1) and B gets (2, 0). B. A gets (2,0) and B gets (0, 1). C. A gets (3/2, 0) and B gets (1/2, 1). D. A gets (1,0) and B gets (1, 1).

Economics For Today

10th Edition

ISBN:9781337613040

Author:Tucker

Publisher:Tucker

Chapter1: Introducing The Economic Way Of Thinking

Section: Chapter Questions

Problem 7SQ

See similar textbooks

Similar questions

Problem 5 Consider an exchange economy with two people: Will and Bob; and two goods: apples and bananas. Will's initial endowment is 10 apples and 5 bananas. Bob's initial endowment is 5 apples and 10 bananas. Will likes apples and hates bananas. Bob likes both apples and bananas. The preferences of both Will and Bob are strictly convex. (a) Draw an Edgeworth Box with apples on the horizontal axes. Put Will at the bottom left corner and Bob at the top right corner. Show the initial endowment and label it with W.
Bluth’s preferences for paper and houses can be expressed as Ub(p, h) = 2pb + hb, while Scott’s preferences can be expressed as Us(p, h) = ps + 2bs. Bluth begins with no paper and 10 houses, whereas Scott begins with 10 units of paper and no houses. 1. Is the starting endowment Pareto efficient? Justify your answer using an Edgeworth box? Determine whether each of the following price pairs is consistent with a competitive equilibrium. If yes, determine the resulting allocation of goods, sketching that equi- librium in your Edgeworth box. If not, explain why not (for what good is there a shortage, for what good is there a surplus?) pp =$3 and ph =$1 along with pp =$1 and ph =$1 Assume that the price of houses is $1. Given that price, determine the highest price pp that is consistent with a competitive equilibrium.
####### Consider the following pure exchange, Edgeworth box economy. There are 2 consumers and 2 goods. Consumer 1 has an endowment of 3 units of good Y, while consumer 2 has an endowment of 3 units of good X. For both consumers the utility function is given by: U (x, v) = x^2y, where x and y denote the respective quantities of goods X and Y. Find the Walrasian equilibrium price ratio P/Pr and the Walrasian allocations. Does trade take place in equilibrium? i want answer in 1 hour. if you provide solution within time, i will upvote. thanks in advance
An exchange economy consists of two individuals and two goods. The two individuals have the following Leontief utility functions: Person 1: U1(x1, y1) = 3x1 + y1 Person 2: U2(x2, y2) = x2 + 2y2 Person 1 has an endowment of e1 = (3, 2). Person 2’s endowment is e1 = (3, 4). In an Edgeworth Box diagram, show which allocations are in the core. Describe the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). What price ratio(s) P* will support a competitive equilibrium allocation for this economy?
Chris and Dana live in an exchange economy with two goods: good Q and good R. Chris starts off with an endowment of 6 units of Q and 10 units of R. Dana starts off with an endowment of 8 units of Q and 8 units of R. Suppose that the price of good R is pR=1 and the price of good Q is pQ=2. a )At these prices, does the market clear? Yes or no? Explain your answer. b) What relationship must hold between the consumption of each agent and the price of the two goods at the market clearing equilibrium? Write the equation
Consider the following simplified bargaining game. Players 1 and 2 have preferences over two goods, x and y. Player 1 is endowed with one unit of good x and none of good y, while Player 2 is endowed with one unit of y and none of good x. Player i has utility function: min{xi, yi} where xi is i's consumption of x and yi his consumption of y. The "bargaining" works as follows. Each player simultaneously hands any (nonnegative) quantity of the good he possesses (up to his entire endowment) to the other player. (a) Write this as a game in normal form. (b) Find all pure strategy equilibria of this game. (c) Does this game have a dominant strategy equilibrium? If so, what is it? If not, why not? Please show all work. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
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 2 agents and 2 goods. In an Edgeworth-Bowley diagram, show and illustrate that if both agents have the same preferences, the contract curve is a straight line from the bottom left-hand corner to the top right-hand corner. Does it follow that if the agents do not have the same preferences, the contract curve is not a straight line? Suppose the two agents have the same endowments and the same preferences. Is mutually beneficial trade possible? Illustrate in an Edgeworth Bowley diagram. State and explain Walras Law. What are the implications of Walras’s Law? Illustrate Walras Law in an Edgeworth-Bowley diagram.
Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They both consume good X, a private good, and the protection of the fort, P. One unit of good X costs 1 unit of currency, and one unit of P costs 2 units of currency. Both Jon and David have an income of 100 and a utility function of the form: U = log(Xi) + 2 × log(PJ + PD)The budget constraint for each is given by:Xi + 2 × Pi = 100 (a) Find the amount of protection Jon will provide as a function of how much David provides, and explain why the relationship is the way it is.
Andy, Brad, and Carly are playing a new online video game: Zombie Civil War. Each has an army of 100 zombies and must decide how to allocate them to battle each of the other two players’ armies. Three simultaneous battles are occurring: one between Andy and Brad, one between Andy and Carly, and one between Brad and Carly. Let Ab denote how many zombie soldiers Andy allocates to his battle with Brad, with the remaining 100 - Ab soldiers in Andy’s zombie army assigned to the battle with Carly. Bc denotes the number of zombie soldiers that Brad allocates to his battle with Carly, and 100 - Bc zombies go to his battle with Andy. Ca is the the number of zombie soldiers that Carly allocates to the battle with Andy, and 100 - Ca in her battle with Brad. To see how payoffs are determined, consider Andy. If Ab > 100 - Bc, so that Andy has more zombies than Brad in the Andy-Brad battle, then Andy wins the battle and receives w points where w > 2. If Ab = 100 - Bc, so that Andy and Brad…
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) c) Assume that Kim has preferences Uk (Xk, Yk) = 3Xk + 3Yk and Jung has preferences Uj (Xj, Yj) = Xj + 3Yj. Will Kim and Jung trade? Calculate the general equilibrium allocation for Kim and Jung. Compute the utility at the endowment point and at the general equilibrium allocation. Is the new allocation on the contract curve?
If A has TIOLI power in an exchange, which of the following are true? a. Person A will capture most or all of the gains from trade. b. Person B will lose utility compared to their initial endowment. c. A Pareto-efficient outcome is assured. d. Person B could gain utility if they agree to A's offer.