Assume in the market with two consumers, Chloe and Oliver. Chloe's utility function is U(x, y) = 2x + 120¹/2 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? O 60 05 225 36
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- Two 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?Which 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.Person A has a utility function of and person B has a utility function Agent A and agent B have identical endowments of (1/2,1/2). (a) Illustrate this situation in an Edgeworth box diagram. (b) What is the equilibrium relationship between p1and p2? (c) What is the equilibrium allocation?
- Below is an edgeworth box of two individuals, Ross and Rosa, in the consumption of two goods, X and Y 1. Consider allocations b-f (meaning points a, b, and f). Which allocations(s)A. are better for Ross than “a” (ignoring Rosa)?B. are better for Rosa than “a” (ignoring Ross)?C. are worse for both Ross and Rosa than “a”?D. are better for both Ross and Rosa than “a”?E. are Pareto superior to “a”?2. Suppose that the initial allocation is point a between Ross and Rosa.A. Discuss how Ross’s condition be made better off without harming Rosa(i.e., Rosa maintains her level of utility).B. Illustrate this in a separate diagram and label point/s as necessary (also,if other point/s will have to be made or incorporated).3. Consider once again that the initial allocation is point a. A. Discuss (very briefly) how point d is reached as a Pareto efficientallocation between Ross and Rosa.B. illustrate this condition in a separate diagram.4. Consider points b, c, d, and e. Now plot the utility…Show an allocation that does not satisfy distributive efficiency and find an allocation that is Pareto superior to it.Explain the statement true or false. "It is possible to have a Pareto efficient allocation where someone is worse off than she is at an allocation that is not Pareto efficient"
- Explain the statement true or false. Give an example of a person's economic situation to explain the solution. "It is possible to have a Pareto efficient allocation where someone is worse off than she is at an allocation that is not Pareto efficient"Explain the statement true or false. Give an example of pay-off matrix to explain the solution. "It is possible to have a Pareto efficient allocation where someone is worse off than she is at an allocation that is not Pareto efficient"Come up with an example with four agents and four items in which there is only one Pareto efficient allocation
- 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…Consider two people in the market for tilapia, Reagan and Cheryl. The marginal benefit curves for both individuals are shown in the accompanying graph. a. Suppose the market price of tilapia is $2.00 per pound. Move point A to Cheryl’s quantity purchased. Move point B to Reagan’s quantity purchased. b. How many pounds of tilapia do they collectively purchase? _________ pounds c. To achieve an efficient allocation, Cheryl should purchase _______(more tilapia than, the same amount of tilapia as, less tilapia than) she is currently purchasing, and Reagan should purchase ________ (more tilapia than, the same amount of tilapia as, less tilapia than) she is currently purchasing.Grapes and bananas are perfect complements for Jane and Betty. Jane eats one grape per three bananas.; Betty eats three grapes per one banana. Once they go to sports for hours, Jane had 20 grapes and 10 bananas and Betty had 10 grapes and 20 bananas. (assume that grapes and bananas can be divided into half) 1. Dar the Edgeworth box and show all Pareto optimal allocations of grapes and bananas between Jane and Betty.