We have n agents with identical strictly concave utility functions. There is some initial bundle of goods w. Show that equal division is a Pareto efficient allocation.
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A: * SOLUTION :-
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A: X = LX0.25KX0.25 Y = 2LY0.25KY0.25 L=100, K=100
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A: We are going to find the Pareto efficient allocation bundle first to answer this question.
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A: Hi! As per Bartleby's guidelines, I am providing you with the answers to the first three subparts.…
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A: The option is(D).
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A: Yes. Point E is Pareto efficient allocation.
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Q: Consider a two-agents, two goods economy, in which both agents, A and B, are represented by the…
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- Show an allocation that does not satisfy distributive efficiency and find an allocation that is Pareto superior to it.Q. It is possible to have a Pareto efficient allocation where everyone is worse off than they are at an allocation that is not Pareto efficient?Below is an Edgeworth box of two individuals, Ross and Rosa, in the consumption of two goods, X and Y. Rosa Contract Curve IRos Ress 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 efficient allocation between Ross and Rosa. B. illustrate this condition in a separate diagram. 4. Consider points b,…
- 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.Suppose one of the consumers has Leontief preferences (i.e., views the two goods as perfect complements) and the other has a Cobb-Douglas utility function. If an allocation is Pareto optimal, then the two consumers who consume both goods_ while the budget line touches both consumers' indifference curves a. will not necessarily have the same MRS; at infinitely many points b. will not necessarily have the same MRS; at exactly one point c. will necessarily have the same MRS; at infinitely many points d. will necessarily have the same MRS; at exactly one point a. will not necessarily have the same MRS; at infinitely many pointsQ.2 (a) (i)Define "weakly Pareto efficient" and "strongly Pareto efficient" allocations. (ii) show that an allocation that is 'strongly Pareto efficient' is also 'weakly Pareto efficient. But in general the reverse is not true. (ii) If preferences are continuous and monotonic prove that an allocation is 'weakly Pareto efficient' if and only if it is 'strongly Pareto efficient'.
- If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then (Select all that applies) Group of answer choices a. two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios. b. two consumers with the same income who consume both goods must have the same MRS, but if their incomes differ, their MRSs may differ. c. any two consumers who consume both goods must consume them in the same ratio. d. for any two consumers who consume both goods, neither will prefer the other consumer’s bundle to his own. e. all consumers receive the bundle that they prefer to any other bundle the economy could produce for them.For an individual the Marginal Rate of Substitution is constant and equal to 1/2 for allcombinations of goods X and Y in his consumption set. The price of good X is $12 per unitand the price of good Y is $8 per unit. The individual has a total budget of $400. Determinethe bundle of goods X and Y that maximize his utility.Throughout this problem set, we will look at exchange economies with two goods and two agents. Let X = R², let u denote agent i's utility, and let wie X denote agent i's endowment. 1. Suppose u¹(x¹) = min{ri, 2} and wi = (4,8) for both agents i. (a) Argue that every Pareto optimal allocation has r≥r for both agents i. (b) Argue that every allocation z with r≥r for both agents i is Pareto optimal. (c) Draw an Edgeworth box, with a picture depicting every Pareto-optimal allocation. In this picture, also draw the endowment allocation, and draw each agent's indifference curve through the endowment. (d) Argue that, in any competitive equilibrium, the price of good 2 must be zero. (e) Find all competitive equilibria.
- 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"The First Theorem of Welfare Economics can be expressed asA) the competitive equilibrium results only when no transactions costs exist.B) the competitive equilibrium does not involve reallocation of endowments.C) any efficient allocations can be achieved by competition.D) the competitive equilibrium is efficient.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?
