An economy has two types of people. The utility function of Type 1 is U(x, y) = x+ y, and that of Type 2 is U(x, y)= Min (2x, y). Type 1 initially has 8 units of good X only (no good Y), and Type 2 has 2 units of good X and 10 units of good Y. a) Show this economy in an Edgeworth box, and draw the contract curve (i.e the set of Pareto efficient allocations). b) Find the competitive equilibrium prices and consumptions for each type of person. c) Is the competitive equilibrium allocation you found in b) Pareto efficient? Why or why not?
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- Carol and Bob both consume the same goods in an economy of pure exchange. Carol is initially endowed with 9 units of good 1 and 6 units of good 2. Bob is initially endowed with 18 units of good 1 and 3 units of good 2. They both have the utility function U(x₁, x₂) = 1/3 2/3 x1³x2³. If we set good 1 as the numeraire (so that p. = $1), what will the equilibrium price of good 2 be?Carol and Bob both consume the same goods in an economy of pure exchange. Carol is initially endowed with 9 units of good 1 and 6 units of good 2. Bob is initially endowed with 18 units of good 1 and 3 units of good 2. They both have the utility function U(x₁, x₂) = = $1), what will the equilibrium price of x1/³x/3. If we set good 1 as the numeraire (so that p₁ good 2 be?Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 8 units of X and a TOTAL of 8 units of Y. The consumers' utility functions are given by: UA(X,Y) = 2X + Y UB(X,Y) = X*Y2 Which of the following allocations is Pareto Efficient? None of the other answers are Pareto Efficient. Consumer A gets 3 units of X and 8 units of Y, and Consumer B gets 5 units of X and O units of Y. Consumer A gets 4 units of X and 4 units of Y, and Consumer B gets 4 units of X and 4 units of Y. Consumer A gets 1 units of X and 4 units of Y, and Consumer B gets 7 units of X and 4 units of Y. Consumer A gets 8 units of X and 8 units of Y, and Consumer B gets 0 units of X and O units of Y.
- a) Consider 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 Susan. Mohammed and David are bothProblem 1: Suppose that in an economy there are two goods, food, F, and clothing, C, and two consumers, Anne and Bob. Anne and Bob both have the same utility function U(F,C) = FC. The marginal rate of substitution of food for clothing associated with this utility function is MRSF.C = Firms in this economy have produced 10 units of food and 10 units of clothing. Explain why an allocation where Anne gets all the food and Bob gets all the clothing does not satisfy exchange efficiency. Explain why this allocation would never happen if Anne and Bob both have to pay the market prices for food and clothing and both make optimal choices. Hints: 1: Use the definition of exchange efficiency from the class slides or textbook. 2: Optimal choices must solve MRS=price ratio.Consider 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.
- Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3x2A; UB(X1B,X2B)=x1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (W1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (WIB,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? O a. An amount 7 of wealth should be transferred from consumer A to consumer B. O b. None of the other answers. An amount 3 of wealth should be transferred from consumer A to consumer B. O c. d. An amount 3 of wealth should be transferred from consumer B to consumer A. An amount 7 of wealth should be transferred from consumer B to consumer…Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3X2A; UB(X1B,X2B)=X1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (w1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (w1B,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? An amount 7 of wealth should be transferred from consumer A to consumer B. O a. O b. None of the other answers. O c. An amount 3 of wealth should be transferred from consumer A to consumer B. O d. An amount 3 of wealth should be transferred from consumer B to consumer A. e. An amount 7 of wealth should be transferred from consumer B to…Consider 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 〖MRS〗_xy^M = 〖2y〗_M/x_M for Mohammed, 〖MRS〗_xy^D = 〖2y〗_D/x_D for David and 〖MRS〗_xy^S = y_S/x_S 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. What are the conditions for Pareto efficiency in an exchange economy?
- Pedro, a retired economics professor, grows lemons and oranges in his back- yard. He consumes some of these fruits, and sells some in a local farmer's market. Pedro's preferences are represented by the following utility function U(x, y) = min{x,y}. In one season he can harvest 20 pounds of lemons and 60 pounds of oranges. In the local market, price of lemons is $4 per pounds and price of oranges is $2 per pound. Pedro receives $300 income from his retirement plan per season. Question 1 Part a Find Pedro's optimal consumption bundle. Make sure to draw his budget con- straint and indifference curves to show his optimal choice. Question 1 Part b Suppose that the price of lemons rises to $5 per pound. What is Pedro's optimal consumption bundle now? Decompose the total change in demand due to a price change into a substitution effect, ordinary income effect and endowment income effect and graphically demonstrate it.4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for 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). Solve for the Walrasian competitive equilibrium allocation and price ratio.(In this question we denote income by Y, not by W as in the lecture notes). The following figure shows the consumption of x and y for two market situations. We can conclude that: x is a normal good for all market situations. py is greater than px. It is not conclusive. x is an inferior good for some market situation. y is an inferior good for some market situation.