Q. An economy with two consumers whose preferences are represented by utility functionsU1 = min (x1,2y1) and U2 = 2x2 +2y2And the aggregate endowment of 4 units of x and 3 units of y(a) Find a Pareto efficiency allocation and depict it in the Edge-worth box.(b)ls there a Pareto efficient allocation in which one consumer has all of the goods? Explain.

Answered: . An economy with two consumers whose…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Explain how the consumer decides how many units of a good to consume by explaining the assumptions of the cardinal approach.
1. Use the budget constraint P_X + P_Y = M, thinking of good X as a food item and good Y x as other goods. Present an analysis where an increase in price of the food item causes the consumer to buy less food, demonstrating the "law of demand." b. Then, present a second analysis where an increase in the price of the food item causes the consumer to buy more of the food item, which is the Giffen Good case. Finally, identify two food items, one which you think fits the first case and one which you think fits the second case.
1. True/False: Partial equilibrium analysis only concerns supply or demand alone, whereas general equilibrium analysis concerns supply and demand simultaneously. 2. True/False: In general equilibrium analysis, an allocation is said to be as a reasonable allocation if each consumer consumes the same bundle its value is no more than the value of the consumer's income. 3. True/False: In general equilibrium analysis, an allocation is said to be as a reasonable allocation if each consumer consumes the same bundle its value is no more than the value of the consumer's income.
3. [In class, we noted that the consumer will spend all their money if they have in- creasing preferences. Here, we give a calculus-based condition for the consumer to spend all their money, that doesn't assume more is always better. The con- dition is a stronger version of what is sometimes called "local non-satiation".] Let E X, and let MU, denote the marginal utility for good i € {1,2} at r. (a) Suppose some good i has MU, #0 (it could be positive or negative), and suppose the consumer is not spending all her money at bundle x (that is pr 0 if MU; <0. Argue that the consumer would not optimally choose r. x (b) Suppose MU₁(x) = MU₂(x) = 0, the good is affordable (p ≤ m), and u is concave. Explain why r is optimal.
3. Jane is currently consuming 4 glasses of milk and 10 cookies, while Betty is consuming 9 glasses of milk and 3 cookies. Jane views milk and cookies as perfect substitutes (her MRS is 1), while Betty prefers cookies to milk and is willing to give up 3 glasses of milk to get 1 cookie. Is the current allocation of milk and cookies Pareto efficient? Explain with use of a diagram.
plz explain the solution in detail. Part a-d
7. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution, and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo). (b) Suppose MRSa = Ya/Xa, MRSB = Yb/Xb, Xa = 10, Ya, = 100, Xb = 50, Yb = 20, and let good Y be the numeraire (Py =1). Verify that the competitive…
A date with Alex costs you $100 and gives you an additional 1000 units of utility. A date with Kelly costs you $200 and an additional 4,000 units of utility. Based only on the information you have, using the theory of rational choice, you most likely would: O be indifferent between the two dates O go on a date with Alex because the marginal utility per dollar is the greater of the two O go on a date with Kelly O go on a date with Alex
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.Show all Pareto optimal allocations of grapes and bananas between Jane and Betty in the Edgeworth Box. Draw a bunch of indifference curves and look for tangencies.
Bucky has $20 to spend on bowling and billiards. The prices of bowling and billiards are $4 and $1 por game, respectively. Assume he has a voucher for two free games of bowling Suppose bowling is the "X" good and billiards are the "Y" good How many games of bowling can Bucky afford? How many games of billiards can Bucky afford? Where is the "link" in Bucky's budget constraint where opportunity cost of billiards in terms of bowling games changes? (This should be answered as quantity of bowling games, quantity of billiards games)
7
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?

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