Consider a pure exchange economy with two goods k = 1,2 and two householdsi = A, B. The total available amount of good 1 and 2 is 9 and 12 units, respectively.Utility functions for households A and B areUA (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. Findthe competitive equilibrium.(c) Is the competitive equilibrium allocation in the Pareto Optimal set? Why thisresult should not surprise us?

The two goods in the economy is given as The total amount of good 1 available is 9 units.The total…

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) = TAITA2 and UB(B1, B2) = XB1³2. (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?

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) = TAITA2 and UB(B1, B2) = XB1³2. (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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Suppose you find that MU1(X1Xx2)=2x2 and MU₂(x1+x₂)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional-marginal-unit of good 1.) Question 21 Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer: Good 1 and good 2 are perfect complements Good 1 and good 2 are perfect substitutes Good 1 and good 2 are both essential goods None of the above
10) If prices and income in a two-good model double, what will happen to the budget line? A) The intercepts of the budget line will increase. B) The intercepts of the budget line will decrease. C) The slope of the budget line may either increase or decrease. D) There will be no effect on the budget line. E) Insufficient information is given to determine what effect the change will have on the budget line.
Consider an economy with 100 pieces of apple (A) and 150 pieces of banana (B) that must be completely distributed to individuals 1 and 2. The utility function of the two individuals, U1 & U2, is given by U1 (A1,B1) = 2A2 + B2 & U2 (A2,B2) = 2A2B2, respectively. With this information, recommend an efficient allocation of the two goods between the two individuals. Discuss and show the necessary solution to support your recommendation
The utility derived by a consumer from the consumption of two commodities is given by the function U (A, B) = 0.5In (A) + 0.5 In (B) where A are the number of units of the first commodity consumed and B are the number of units of the second commodity consumed each month. A unit of the first commodity costs $8 and a unit of the second commodity costs $ 4 using the Lagrange multiplier method determine the optimal quantity of each of the commodities consumed each month given that consumer has $32 to spend on both commodities each month
Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3x2A; UB(X1B,X2B)=x1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (W1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (WIB,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? O a. An amount 7 of wealth should be transferred from consumer A to consumer B. O b. None of the other answers. An amount 3 of wealth should be transferred from consumer A to consumer B. O c. d. An amount 3 of wealth should be transferred from consumer B to consumer A. An amount 7 of wealth should be transferred from consumer B to consumer…
Suppose you find that MU1(X1Xx2)=2x2 and MU₂(x1+x₂)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional-marginal-unit of good 1.) Question 20 Suppose you find that the expressions of the marginal utilities for a consumer are given by MU1 (1,2)= 2 and MU₂ (1,2)= 7. Then you can conclude that: This consumer has Cobb-Douglas tastes For this consumer good 1 and good 2 are perfect complements For this consumer good 1 and good 2 are perfect substitutes None of the above Question 21 Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer: Good 1 and good 2 are perfect complements Good 1 and good 2 are perfect substitutes Good 1 and good 2 are both essential goods None of the above
Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3X2A; UB(X1B,X2B)=X1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (w1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (w1B,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? An amount 7 of wealth should be transferred from consumer A to consumer B. O a. O b. None of the other answers. O c. An amount 3 of wealth should be transferred from consumer A to consumer B. O d. An amount 3 of wealth should be transferred from consumer B to consumer A. e. An amount 7 of wealth should be transferred from consumer B to…
3 Consider a pure exchange economy with 2 consumers and 2 goods. Consumer ? owns 8 units of good 1 and 1 unit of good 2, and his preference is represented by the following utility function: uA(x1, x2) = x1*x2. Consumer ? owns 2 units of good 1 and 4 units of good 2, and his preference is represented by the following utility function: uB(x1,x2)=x1+x2. Assume that the two consumers are allowed and able to trade with each other, and that good 1 is the numeraire. In this case, both consumers act as price-takers. Price takers: a market participant that is not able to dictate the prices in a market. Therefore, a price taker must accept the prevailing market price. Please find the competitive equilibrium of this pure exchange economy.
Suppose that consumer has the following utility function: U(X,Y) - X1/2y1/4. Suppose also that P 2, P -3 and 1=144. What would be the optimal consumption of X and Y at the equilibrium. respectively? 36, 24 12,40 24,32 48.16
Please teach not just solve
A small exchange economy is comprised of two of individuals, A and B, and two types of goods, x, ,x,. The individuals' preferences over two goods are can be represented by the following utility functions: U*(x;,.x; ) = min (2.x,x; ) and U* (x;,x;) = min(x;.2x, ). Initial endowments are 10 x, (individual A), and 10 x, (individual B). Calculate the price ratio which yields an equilibrium in the exchange market.
Joe and Martin, two roommates, have access to music in digital and analog formats. Each are initially endowed with 8 GB of high-resolution digital music and 4 vinyl LP's (analog) per month (there are a total of 16 GB's of music in digital and 8LP's in this case). Joe's preferences for music in digital and analog formats are represented by the utility function u, (D, A) = 2D + 2A, where D is the amount of digital music in GB's and A is the numberofLP's. Martin's utility function is um(D,A)=D+4A. 1. Draw an Edgeworth box to show the initial endowments and the indifference curves (going through the initial endowments) for Joe and Martin. What are their utility levels from the initial endowments? 2. Calculate the marginal rates of substitution for Joe and Martin. Provide an economic interpretation. 3. Do the initial endowments represent a Pareto efficient allocation? Discuss. 4. If Joe convinces Martin to exchange music at terms which would leave Martin at his initial utility level (i.e.,…