6. (b) Consider an exchange economy with two agents Á and B, and two goods i and y. Consumption of the two goods is given by: „(1-a) U^(Xa»Ya) = xfyt-a) U°(Xp,Y») = x$y{t-b) Where xA is agent A's consumption of good x etc. Let the agents' initial endowments be: Good Agent A 1 B 1 (%)- i) Find competitive equilibrium price ratio |for this economy. ii) Why is it sufficient to compute the market clearing price ratio for just one ma (say) to answer (i).
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- 5 Three Goods Consider a pure exchange economy with three goods: x1, x2 and x3. Consumer A’s utility function is U A = min {x1, x2}. He starts with one unit of x1 and none of the other goods. Consumer B’s utility function is U B = min {x2, x3}. He starts with one unit of x2 and none of the other goods. Consumer C’s utility function is U C = min {x1, x3}. He starts with one unit of x3 and none of the other goods. Find the general equilibrium prices and allocationProblem 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.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
- 5. Consider an exchange economy with 2 agents and 2 goods. a) 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. Explain. b) Does it follow that if the agents do not have the same preferences, the contract curve is not a straight line? Explain. c) Suppose the two agents have the same endowments and the same preferences. Is mutually beneficial trade possible? Illustrate in an Edgeworth Bowley diagram. Explain.7. Assume a two-good production economy characterized by the production functions: Q1 = K1 1/2L1 1/2 and Q2 = K2 + L2 With fixed total endowments of 100 for both K and L. Derive the production possibilities frontier for this economy and provide a graphGive 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 countries A and B produce and consume (assuming convex preferences) apples and bananas using only labour. Unit labour cost for apples in country A are 1 and 2 in country B. Unit labour cost for bananas are 2 in country A and 5 in country B. The labour force is the same in both countries, and given by 100 in each country. Which three of the following statements are true? A Country B has a comparative advantage in producing bananas. B Allowing for international trade, the production of 50 apples and 50 bananas can occur in a global market equilibrium feasible, but not in market equilibria under autarky. C Each country has an absolute advantage. D Allowing for international trade, the production of 50 apples and 50 bananas is feasible, but not under autarky. E Under autarky, the relative price for apples (price for apples/price for banans) equals 0.5 in country A and 0.4 in country B. F Country A will produce bananas, with or…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.Q1: Match each diagram in Figure 1 with its description here.Assume that the economy is producing or attempting to produce at point A and that most members of society like meat and not fish. Some descriptions apply to more than one diagram, and some diagrams have more than one description. Inefficient production of meat and fish Productive efficiency An inefficient mix of output Technological advances in the production of meat and fish The law of increasing opportunity cost An impossible combination of meat and fish
- 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.Consider a two-good exchange economy with two types of consumers. Type A have the utility function And an endowment of 3 units of good 1 and k units of good 2. Type B has the utility function And an endowment of 6 units of good 1 and 21 - k units of good 2. a. Find the competitive equilibrium outcome and show that the equilibrium price p* = p1/p2 of good 1 in terms of good 2 is p* = 21+k/15. b. Find the income levels (MA; MB) of both types in equilibrium as a function of k. c. Suppose that the government can make a lump-sum transfer of good 2, but it is impossible to transfer good 1. Use your answer to part b to describe the set of income distributions attainable through such transfers. Draw this in a diagram. d. Suppose that the government can affect the initial distribution of resources by varying k. Find the optimal distribution of income if (i) the SWF is W = log(MA) + log(MB) and (ii) W = MA + MB.Assume that Cliff and Paul were both producing wheat and corn, and each was dividing their time equally between the two. Then they decide to specialize in the product they have a comparative advantage in and trade 3 bushels of wheat for 3 bushels of corn. What would Cliff now be able to consume? Question 10 options: 3 bushels of wheat and 3 bushels of corn 3 bushels of wheat and 4 bushels of corn 4 bushels of wheat and 3 bushels of corn 2 bushels of wheat and 3 bushels of corn