In an exchange economy, there are two people (A and B), and two goods (X and Y). The utility functions of A and B are given by UA(X,Y) = 3X4YA and UB(X,Y) XBYB. Person A starts with 15 units of X and 5 units of Y. Person B starts with 15 units of X and 10 units of Y. Which expression below gives you the equation for the contract curve in terms of person A's consumption? a. XA = 3YA b. XA = 2YA c. YA = 30XA d. XA = 20YA
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- 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?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 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?
- 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?Q/ Country X and Country Y are neighbours. Both Country X and Country Y can produce two goods: food and clothing. In one week, Country X can produce 4,400 clothing units or 2,200 food units, or a mix of the two. In one week, Country Y can produce 5,000 clothing units or 2,000 food units, or a mix of the two.For both Country X and Country Y, their individual trade-offs between clothing units and food units are constant, regardless of how they allocate their time. Currently, Country X produces 2,400 clothing units and 1,000 food units per week while Country Y produces 2,500 clothing units and 1,000 food units per week. c. Which country has a comparative advantage in food production? Which country has acomparative advantage in clothing production? Illustrate your answer using the PPC and showall the calculations. d. Should Country X and Country Y specialize and trade with one another? Why?In an exchange economy there are two people (A and B), and two goods (x and y). Their respective utility functions and endowments are: UA(xA,yA) =5xA+yA , UB(xB,yB)=xB+5yB; wA=wB=(10,10). What is the minimum possible amounts of xA in the core? Round your answer to 2 decimal points. The answer is 12, please explain.
- 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 simple exchange economy with two people: Bob and Jake. Bob and Jake both have ten hoursof time available. The can use their time to do one of two things: make pancakes or make hamburgers.Bob can make two hamburgers in an hour or one pancake in an hour. Jake can make three pancakes in anhour or two hamburgers in an hour. Use this information to answer the following questions:a.) Draw Jake and Bob’s PPFs, with hamburgers on the x-axis.b.) Give equations for Jake and Bob’s PPFs in y = mx+b form, still treating hamburgers as the xvariable.c.) Who has absolute advantage in the production of hamburgers? Who has absolute advantage inthe production of pancakes?d.) Who has comparative advantage in the production of hamburgers? Who has comparativeadvantage in the production of pancakes?e.) Can Bob and Jake both benefit from trade if the terms of trade are one pancake per hambruger?WhySuppose 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…
- Alice and Bob are both capable of producing goods X and Y. In one hour, Alice can produce one unit of each good. In the same amount of time, Bob can produce two units of each good. If Alice and Bob have access to the same amount of time, calculate the difference between the slope of Alice's PPF and the slope of Bob's PPF. (round to two decimal places if necessary)Consider the barter exchange model owith 5 agents (A, B, C, D, and E) and 5 goods (a, b, c, d, and e), where agent A initially owns good a, agent B initially owns good b, agent C initially owns good c, agent D initially owns good d, and agent E initially owns good e. The preferences of the agents are given below. Find the allocation that is obtained by using the top trading cycles (TTC) procedure. Show your work in how you obtained your answer. Agent A: b> c> d > e>a Agent B: d > c> e> a > b Agent C: e > a > b> d>c Agent D: 6 > a > c> e>d Agent E: d > b > c> a > eConsider 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 allocations