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 10units 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,X28)=X18+X2B-Among the prices below, which ones are Walrasian equilibrium prices?O a. P1=3, p2 =2O b. p1=4, p2 =5O c. None of the other answers.O d. p1=5, p2 =4O e. p1=2, P2 =3

A Walrasian equilibrium is a set of prices and a consumption bundle for each agent in which I each…

Answered: Consider the pure exchange economy with…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1
D2)
Consider a pure exchange economy with two goods k = 1,2 and two households i = A, B. The total available amount of good 1 and 2 is 9 and 12 units, respectively. Utility functions for households A and B are UA (TA1, A2) = TA1TA2 and UB(B1, B2) = XB1T32. (a) Find an expression for the Pareto optimal set. (b) Assume e A = (4,4) and eg (5,8) are A and B endowments, respectively. Find the competitive equilibrium. (c) Is the competitive equilibrium allocation in the Pareto Optimal set? Why this result should not surprise us?
3
D2)
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
Amy and Barbara share an office. They put a scent diffuser in the middle of the room, and they need to buy essence oil (G) to make the office smell good. They each can also buy cookies (x) as their own snacks. Each of them has $15 to spend on essence oil and cookies. Amy and Barbara's utility functions are UA (TA, GA, GB) = x²(G₁+G³)² and uB (TB, GA, GB) = x³ (GA+GB)³, where A and B are Amy's and Barbara's individual cookie consumption, and GA and GB are respectively Amy's and Barbara's contributions in dollars for the purchase of the essence oil. Let the price of cookies be p = 1 and the price of essence oil be pg = 1. Thus, given G₁ and GB, G = GA + GB is the total amount the essence oil that will be purchased, what is the Pareto optimal amount of the total contribution of G ? C a. 15 C b. 10 c. They will be no difference between the individual decision and the Pareto optimal decision. d. 5
There are 6 cups of espresso (x1) and 6 bars of chocolate (x2) in the house. Andrew and Eric have identical preferences, U₁ = alog(x) + (1 - a)log(x), where i = A, E and a € (0, 1). Suppose the Target allocation is ((2, 2), (4, 4)). (a) What is the relationship between UA and UE in the Target? (b) Find the ratio of equilibrium prices at the Target allocation. (c) Determine the lump-sum transfer necessary to achieve the Target if An- drew is initially endowed with (4, 1) and Eric with (2,5). Set x2 as the numeraire, i.e., assume pi 1. Under what condition would require Andrew to transfer to Eric or vice versa? Why? If a > 1/3, Andrew transfers to Eric and vice versa. = p and p2 =
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…
Joe Bob from Workout Problem 4.12 has a cousin Don who consumes goods 1 and 2. Don thinks that 3 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Don's preferences? U(x1, x2) = min{2x1, 3x2}. Ux1, x2) = 20x1 + 30x2 - 10,000. Ux1, x2) = 2x1 + 3x2 + 1000. Ux1, x2) = 4x²2₁ + 12x₁x2 + 9x²₂. More than one of the above does not represent Don's preferences.
For the utility function U = Qx0.15Qy(1-0.15) find the trade-off rate between good X and good Y at Qx= 9 and Qy=13
Bread and doughnuts: The consumer receives positive benefits from the consumption of beans (B) and donuts (K). Utility function of the consumer is the following: U(B,K) = 100∙B0.25 · K0.75 The price of beans (can) is ISK 2,000. but the price of a donut (box) is ISK 4,000. Consumption restrictions are placed on the consumer since his income is ISK 400,000. Put on all form donuts on the x-axis and beans on the y-axis. a) Show an equation for the bean's success rate for a single donut in light of the utility function. Draw the equivalence curve on a picture and explain what the equation is performance ratio is stated at each point on the equivalence curve. Explain with the concept of the efficiency ratio of the curvature of the equivalent curve. b) Find the most efficient consumption combination and draw on the diagram. c) The government decides to support the consumption of beans so its price drops to 1,000. Who is the most economical consumption combination based on the changed price…

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