Consider 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 YA²2 and UB-XB² Yв 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?
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- 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 person 1 owns 200 units of x and 100 units of y while person 2 owns 100 units of x and 200 units y. Suppose their preferences over the two goods can be represented as: U1 (x, y) = y + 50Inx U2 (x, y) = y + 150lnx 1. How much of x do they trade among each other? 2. Does the First Welfare Theorem (FWT) hold in this economy?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 2 and 1 in country B. Unit labour cost for bananas are 5 in country A and 4 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? Each country has an absolute advantage. Allowing for international trade, the production of 100 apples and 20 bananas can occur in a global market equilibrium, but not in a market equilibria under autarky. Country A will produce apples, with or without international trade. Under autarky, the relative price for apples (price for apples/price for bananas) equals 0.4 in country A and 0.25 in country B. Country B has an absolute advantage in producing bananas. Allowing for international trade, the production of 60 apples and 40 bananas is feasible, but…
- The U.S. imports lumber among other goods from Canada. The lumber has been the topic of political dialogue between the 2 countries in the past few days. So let’s take X as ‘lumber’ and Y as ‘other goods’. Suppose the Canadian lumber and other exportable goods are produced with the following production Possibilities frontier (PPF): X2 + Y2 = 900 Suppose the U.S. utility function for the Canadian lumber, X, and other exportable goods, Y, is: U = X Y a. Derive the conditions necessary to determine the ‘Optimal Product Mix’ discussed in chapter 10. b. Draw the PPF (partial just the first quadrant) with Y on the vertical axis. On the same graph, draw at least one indifference curve so as to show the “optimal product mix’. Can this graph represent the ‘pure exchange’ economy? Explain why or why not. c. Now draw in a price line that can make the ‘optimal product mix’ a competitive exchange equilibrium. Can…Consider a two-person exchange economy in which person 1 owns 200 units of x and 100 units of y while person 2 owns 100 units of x and 200 units y. Suppose their preferences over the two goods can be represented as: U1 (x, y) = y + 50Inx U2 (x, y) = y + 150lnx 1. How much of x do they trade among each other? 2. Does the First Welfare Theorem (FWT) hold in this economy? 3. Can some individuals be made better off if we are at the Pareto efficient allocation?3 Consider a pure exchange economy with 2 consumers and 2 goods. Consumer ? owns 8 units of good 1 and 1 unit of good 2, and his preference is represented by the following utility function: uA(x1, x2) = x1*x2. Consumer ? owns 2 units of good 1 and 4 units of good 2, and his preference is represented by the following utility function: uB(x1,x2)=x1+x2. Assume that the two consumers are allowed and able to trade with each other, and that good 1 is the numeraire. In this case, both consumers act as price-takers. Price takers: a market participant that is not able to dictate the prices in a market. Therefore, a price taker must accept the prevailing market price. Please find the competitive equilibrium of this pure exchange economy.
- Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation. a. always for any consumers' preferences b.only if consumers' preferences are exactly the same c. never d. non of the aboveConsider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation? a. always, for any consumers' preferences b. only if consumers' preferences are exactly the same c. Never d. None of the aboveConsider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by for Mohammed, for David and for Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. A. What are the conditions for Pareto efficiency in an exchange economy? B. Are these consumption levels economically efficient? C. Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain.
- Q. 4 Two consumers, A and B, live in a pure exchange economy with two good, x and y. Consumer A is endowed with 0 unit of x, 14 units of y; Consumer B is endowed with 4 unit of x, 6 units of y. They both have the utility function U=x1/4y3/4. What will be consumer A’s consumption of good X?State the first theorem of welfare economics of a production and exchange economy. Which conditions must be satisfied for the Pareto efficiency of an allocation of a production and exchange economy (assuming that all goods are used, produced and consumed in strictly positive quantities)? Discuss and explainConsider 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.