Assume in the market with two consumers, Chloe and Oliver. Chloe's utility function is U(x, y) = 2x + 120y1/2 Oliver's utility function is U(x, y) = 2x + 10y. At a Pareto optimal allocation in which both individuals consume some of each good, how much y does Chloe consume? I O 60 05 O 225
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- Assume in the market with two consumers, Chloe and Oliver. Chloe's utility function is U(x, y) = 2x + 120y1¹/2 Oliver's utility function is U(x, y) = 2x + 10y. At a Pareto optimal allocation in which both individuals consume some of each good, how much y does Chloe consume? I O 60 05 O O 225 36Which is the correct answer ? Suppose there are 10 apples and 10 oranges in the economy. Joe is currently consuming 4 apples and 5 oranges, and Jane is consuming 6 apples and 5 oranges. At this allocation, Joe's marginal utility of apples is 3, and his marginal utility of oranges is 5. Jane's marginal utility of apples is 6, and her marginal utility of oranges is 10. The current price of apples is R4 per unit and the current price of oranges is R5 per unit. To reach a competitive equilibrium, the required price adjustment is: A. A decrease in the orange price relative to the apple price. B. A decrease in the apple price relative to the orange price. C. No change in the relative prices. D. An increase in both prices.10. Consumer A and B have each been given an allocation of 2 goods x and y (assume each has positive amounts of both goods). At this allocation, consumer A has an MRS of 2, while consumer B has an MRS of 1/2. Could this allocation be Pareto efficient? Explain why or why not.
- 5. 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 x1³x2³. If we set good 1 as the numeraire (so that p₁ = $1), what will the equilibrium price of good 2 be?Assume that the prices of good X, Y and Z are as follows R5,R1 and R4 respectively, and the Judith has an income of R37 to spend. HOW much of each good will judith consume in order to maximise her utility? What will be her total utility and marginal utility of the last rand spent on each good? Show all the calculationsKari and Hector both are interested in buying pizza slices for lunch. Kari's inverse demand for pizza slices is given by P = 250 – ()Q, where Pis the price of a pizza slice (in cents) and Q is the number of slices. Hector's inverse demand is given by P = 150 -)0. Suppose that Kari and Hector are the only two consumers in the market for pizza slices. Assuming that both Kari and Hector are consuming some pizza each, which of the following functions describes the relevant portion of the market demand curve? Choose one: O A. Q = 0 – (4 + 10)P - 400 В. Р%3D 400 + ( 4+10 C. P = – 400Q (4+10) O D. Q %3D 2,500 — (4 + 10)Р O O
- Smith 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…Question 29 Assume in the market with two consumers, Chloe and Oliver. Chloe's utility function is U(x, y) = 2x + 120y¹/2 Oliver's utility function is U(x, y) = 2x+10y. At a Pareto optimal allocation in which both individuals consume some of each good, how much y does Chloe consume? I O 60 05 O 225 O 36 Question 30 Consider the game below where the first payoff belongs to player 1 and the second payoff belongs to player 2: (1,3) (2,1) (1,0) (0,2) B D F H 2 П 2 (1,1) A C E G Use backward induction, a Nash equilibrium outcome of the game is: O (1,3) O (2, 1) O (1,0) O (1, 1)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?
- Roisin consumes only two goods, X and Y, and her utility function is given by U = XY. Her income is €50 and the price of X is €10 and the price of Y is €5. In equilibrium Roisin will choose which combination of X and Y? (Partial units are possible) X = 5; Y = 20 X = 5, Y = 10 X = 10, Y = 10 X = 2.5, Y = 5Two consumers, Budi and Marry, together have 10 apples and 4 oranges. a. Draw the Edgeworth box that shows the set of feasible allocation for the two individuals and two goods b. Suppose Budi has 5 apples and 1 orange, while Marry has 5 apples and 3 oranges. Identify this allocation in the Edgeworth box c. Suppose Budi and Marry have identical utility functions and assume that this utility function exhibits positive marginal utilities for both apples and oranges and a diminishing marginal rate of substitution of apples and oranges. Could the allocation in part (b) be economically efficient?Carol has very weird preferences. She only cares about quantity. When evaluating a bundle, Carol only looks at the highest amount of a good she can consume in each bundle, regardless of whether it is of eggs or dumplings. She is indifferent between two bundles only when the largest consumption of a good within each bundle is the same across bundles. So, for instance, if a bundle offers 5 eggs and 1 dumpling she finds that bundle indifferent to a bundle offering 4 eggs and 5 dumplings. These preferences are transitive. But are they monotone? And convex?