In an exchange economy, there are two people, A and B, and two goods,X1 and X2. Their respective utility functions and endowments are u (x, x ) = min (xf, 2x ) u (xf, x) = xf +x oA = (4,9), w = (4, 0). %3D %3D %3D %3D Note: The As and Bs in the equations above are not powers but rather superscripts to indicate each agent. The minimum and maximum possible amounts of Xx^2 on the contract curve are Minimum x %3D Maximum X %3D 0; 4 O 4; 8 O 4; 4

In an exchange economy, there are two people, A and B, and two goods,X1 and X2. Their respective utility functions and endowments are u (x, x ) = min (xf, 2x ) u (xf, x) = xf +x oA = (4,9), w = (4, 0). %3D %3D %3D %3D Note: The As and Bs in the equations above are not powers but rather superscripts to indicate each agent. The minimum and maximum possible amounts of Xx^2 on the contract curve are Minimum x %3D Maximum X %3D 0; 4 O 4; 8 O 4; 4

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.5P

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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.
d) An exchange economy has two goods (apples, bananas) and two types of agents (1, 2). Endowment of agent 1 is (3 bananas, 3 apples), and endowment of agent 2 is (4 bananas, 2 apples). Both goods are divisible goods, so that it is possible to consume frac- tions of each good (e.g. 4.92 bananas and apples). Each type 1 agent's preferences are represented by the utility function U(x,x) = min{x, x}, where x and x denote the agent's consumption of bananas and apples, respectively. Each type 2 agent's preferences are represented by the utility function U(x3, x²) = 7min{x3, x4} where x and r² denote the agent's consumption of bananas and apples, respectively. Use an Edgeworth's Box to depict the set of Pareto efficient allocations in this economy. Please capture consumption of bananas on the horizontal axis.
4. Consider an exchange economy of two goods and two individuals. Consumer A has an endowment of 100 units of good 1 and 12 units of good 2 wA = (100,12), while consumer B has an endowment of 100 units of good 1 and 3 units of good 2 wB = (100, 3). The consumers' utility functions are given by: UA х,4 + Inx,A and UB x,B + 2lnx,B %3D Which of the following allocations is not efficient? a. (x,4,x24) = (100,5), (x,³, x2³) = (100,10) b. (x,4, x24) = (50,5), (x,®, x,³) = (150,10) c. (x,4, x24) = (0,4), (x,³, x,") = (200,11) d. (x,4, x24) = (100,0), (x1",x,") = (100,15) %3D
Problem 3: Consider a pure exchange economy with two consumers (4 and B) and two goods (X and Y). Suppose consumers A and B have the utility functions: UA (XA, YA) u³ (XB, YB) = a1-a 81-8 = XBYB a. Derive the equation of the contract curve. b. Let the endowments of the economy be 1 unit of X and 2 units of Y. Show that an equal division of goods (an egalitarian outcome) is not Pareto optimal. What condition on the parameters of the utility functions is required for equal division of goods to be Pareto optimal? 0 < a < 1 0 < 3 <1 3
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.
1. Consider a pure exchange economy with two goods and two consumers. Let F denote food and C denote clothing. Lacy has the utility function U(F, C) = F¹/32/3. Roy has the utility function V (F, C) = F2/3¹/3. Each consumer has an initial endowment consisting of 9 units of F and 9 units of C. Normalize the price of F to one. Let P denote the price of C. (a) Is the initial endowment a Pareto efficient allocation of F and C between the two con- sumers? Explain briefly. (b) What is each consumer's demand for F and C as a function of P? [Hint: the wealth of each consumer is 9 + 9P.] (c) What is the price of C in a competitive equilibrium? (d) What is the allocation of F and C between the two consumers in a competitive equilibrium?
A5
Suppose $10 is to be allocated between two people, A and B. Their preferences over A's income, xA, and B;s income, are the following:
E1
Kip is trying to decide whether to take a one-day martial arts class at Rex Kwan Do. The fee for the class is $400. Kip will also have to pay his brother Napoleon $150 for that day in return for giving him a ride into town. Instead of taking the class Kip could spend all day on the computer chatting with his girl, LaFawnduh. This gives him a value of $300. On the other hand, he could spend all day working with his Uncle Rico and making sweet moolah. Uncle Rico has promised to pay him $350 on that day if he works with him. What is Kip’s marginal cost of joining Rex Kwan Do? Group of answer choices $650 $550 $400 $300 $350 $150 $900
Kip is trying to decide whether to take a one-day martial arts class at Rex Kwan Do. The fee for the class is $400. Kip will also have to pay his brother Napoleon $150 for that day in return for giving him a ride into town. Instead of taking the class, Kip could spend all day on the computer chatting with his girl, LaFawnduh. This gives him a value of $300. On the other hand, he could spend all day working with his Uncle Rico and making sweet moolah. Uncle Rico has promised to pay him $350 on that day if he works with him. What is Kip’s marginal cost of joining Rex Kwan Do? Correct answer: $900 why don't you include 300 also? explanation