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? O a. An amount 7 of wealth should be transferred from consumer A to consumer B. O b. None of the other answers. ○ 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.
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- Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, when there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is ua(XA,S)=XA.S, where xĄ is the amount of money Person A owns. Person B's utility function is ug(xg, 1s)=xB .(1-s), where xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person A has the legal right to a fill up the room with smoke and there exists a market for smoke "abatements". At the Walrasian equilibrium, how much money will person B be left with? O a. Xg=1.25 O b. Xp=2.25 O c. XB=0.25 O d. Xg=0.25 е. None of the other answers.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. Consumer A is initially endowed with 10 units of good 1 and 10 units of good 2. Consumer B is initially endowed with 2 units of good 1 and 2 units of good 2. The consumers have the following utility functions: ua(X1a,X2a)=X1AX2A²; uB(x1B,X2B)=X1B+X2g. Among the prices below, which ones are Walrasian equilibrium prices? O a. p1=3, p2 =2 O b. p1=4, P2 =5 O C. None of the other answers. O d. p1=5, p2 =4 O e. P1=2, p2 =3
- 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?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.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?
- Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U = 4P + 3C . In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of PepsiSmith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…Suppose that there are two goods (X and Y ). The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers (A and B). The utility functions for the consumers are UA (X, Y): = X0.5y-0.5 UB (X,Y)= X0.8y-0.2 Consumer A has an income of $100, and Consumer B has an income of $300. PAGE 2 (a) Use Lagrangians to solve the constrained utility-maximization problems for Consumer A and Consumer B. (b) Calculate the marginal rate of substitution for each consumer at his or her optimal consumption bundles. (c) Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at her optimal consumption bundle? Why?
- Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y IS SI per unit. There are two consumers (A and B). The utility functions for the consumers are U A(X,Y) = X0.5 yo.5 UB (X,Y) = X 0.8 yo.2 %3D Consumer A has an income of $100, and Consumer B has an income of $300. a. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer A. b. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer B. C. Calculate the marginal rate of substitution of Y for X (X is increasing and Y is decreasing; MRSXY) for consumer A at his or her optimal consumption bundles. d. Calculate the marginal rate of substitution of Y for X for consumer B at his or her optimal consumption bundles. e. Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at…Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3