1. Consider a pure exchange economy with two goods, 1 and 2, and two consumers, A and B, who have utilities and u¹(x₁, x₂) = min{1, 2} u³(x₁, x2) = x³x2. Recall that the Marshallian demands corresponding to these utility functions are, respectively, x^(p, w): W W
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- 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.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 allocationConsider a simple economy consisting of two countries, England and France. England has 25 workers and France has 75 workers. England can produce 4 units of grain and 2 units of cloth with each unit of labor. France can produce 1 unit of grain and 1 unit of cloth with each unit of labor. Wages per unit of labor are the same in both countries. c. Assume that consumers have utility ?=?????^(1/2) ⋅????ℎ^(1/2). How much does each country produce and consume of each good in autarky? Show the consumption graphically by drawing the indifference curves into your two diagrams. d. Now allow for trade. How much does each country produce and consume of each good in this case? Draw the new production possibilities frontier, indifference curves, and equilibrium point into your two diagrams, and indicate exports and imports. e. What is the utility of consumers in each country under free trade? How much does utility change relative to autarky?
- 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?Options: 1. A) Yes, you can still afford the bundle at your previous consumer equilibrium B) No, you now cannot afford the bundle at your previous consumer equilibrium C) It is uncertain whether or not you can still afford the bundle at your previous consumer equilibrium 2. A) For each peck of apples, you will buy 1/3 pounds of oranges B)For each peck of apples, you will buy 1 pounds of oranges C)For each peck of apples, you will buy 3 pounds of oranges D) For each peck of apples, you will buy 6 pounds of orangesConsider the utility functions below of two individuals, A and B, and bundles of goods Q and R. UA=X0.5Y0.5; UB=X+2Y; Bundle Q (10, 10); Bundle R (10, 15). Suppose the total X and total Y available in the economy are both equal to 20. a. If initially both individuals are consuming bundle Q, then a pareto-improvement is possible through reallocation of goods, i.e. individual A gives B some of his good X in exchange for some of individual B’s good Y. (True or False? Explain through mathematical examples).b. Pareto-optimality is achieved if we give individual B Bundle R and the remaining goods X and Y available in the economy is given to individual A. (True or false? Explain through a graphical example)
- 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?Consider an economy composed of 16 consumers. Of these, 5 consumers each own one right shoe and 11 consumers each own one left shoe. Shoes are indivisible. Everyone has the same utility function, which is Min(2R, L}, where R and L are, respectively, the quantities of right and left shoes con sumed. A) (10%) Is the status quo (where each individual has his own shoe) Pareto efficient? If so, briefly explain why. If not, provide a Pareto improvement b) (10%) Characterize all Pareto efficient allocationsSuppose 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…
- I need help with this question in my homework. Suppose a consumer’s utility function is given by U(X,Y) = MIN (5X, Y). Also, the consumer has $60 to spend, and the price of good X is P(x) = $5. Let good Y be a composite good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. What is the Indirect Utility Function? What is the Expenditure Function?Tia and Lia consume bread (R) and clothes (B) with the following utility functions: Tia : UT = 30 R0.25 B0.75Lia : UL = 50 R0.5 B0.5 It is known that the price of bread (Pbread) is Rp. 100,000 while the price of clothes (Pclothes) is Rp. 300,000 If Tia currently consumes 5 pieces of bread and 10 clothes, while Lia consumes 12 pieces of bread and 18 clothes, specify: a. Have Tia and Lia reached an efficient allocation level? Use calculations and the Edgeworth Box to help your explanation. b. If it turns out that the level of consumption is not efficient, what is the consumption of each to reach the Paretto Optimum? Use calculations and the Edgeworth Box to help your explanation.Consider a two-city (A and B) regional economy where each city operates on the negatively sloped portion of its utility curve. In the initial equilibrium, the two cities are identical. Then air pollution (lead emissions) in city B decreases the brain power and productivity of workers in the city by 20 percent. Illustrate the effects of lead emissions on the regional equilibrium, indicating the direction of changes in city size (the number of workers) and regional utility.
