Consider a two-person, two good pure exchange economy. A's preferences over consumption bundles (x₁, x₂) are represented by the utility function UA (X₁, X₂) = X₁Xx2 B's preferences over consumption bundles are represented by the utility function UB (X₁, X₂) = x₁ + 2x₂ The initial endowment in goods x, and x2 are given as: Individual A's as e^ = (1,0.5) and Individual B's as e = (1,1.5) 1. Draw an Edgeworth box indicating the endowment and preferences of this problem.

Consider a two-person, two good pure exchange economy. A's preferences over consumption bundles (x₁, x₂) are represented by the utility function UA (X₁, X₂) = X₁Xx2 B's preferences over consumption bundles are represented by the utility function UB (X₁, X₂) = x₁ + 2x₂ The initial endowment in goods x, and x2 are given as: Individual A's as e^ = (1,0.5) and Individual B's as e = (1,1.5) 1. Draw an Edgeworth box indicating the endowment and preferences of this problem.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: 4. Consider an exchange economy of two goods and two individuals. Consumer A has an endowment of 100…

Q: None

A: (a) Draw the Edgeworth boxThe Edgeworth box represents the feasible set of allocations for the two…

Q: Zeynep lives on an island where she produces two goods, apples (x) and bananas (y), according to the…

A: Given Production Possibility Frontier 200 = x2 + y2 Utility funcation U = xy3

Q: 4) Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2). Consumers'…

A: Since you have posted a question with multiple sub-parts, we will solve the first 3 sub-parts for…

Q: Pareto efficient

A: Allow's to make clear Adam's utility features and options. In the given state of affairs, Adam's…

Q: (In this question, differently from our lecture notes, income will be denoted by Y, not W). The…

A: Qx(px,py,Y), the demand of good x for prices px and py and income Y can be found out by the…

Q: (In this question, differently from our lecture notes, income will be denoted by Y, not W). The…

A: Demand: the demand refers to the intention or willingness to purchase a commodity at the prevailing…

Q: Consider an exchange economy with two agents (i = a, b) and two goods (j = 1,2) with the following…

A: A rectangular diagram showing a combination of two goods and two individuals in a closed economy is…

Q: (a) Identify the set of all Pareto efficient allocations. Solution: Let (x,y) be the bundle…

Q: Suppose costumer 1's endowment is (a₁, b₁) endowment is (a2, b₂) = (7,3). Consumer 1 has preferences…

A: In a competitive market, the sum of the consumer preferences is maximized subject to the…

Q: ns Consider an economy with two goods and two states of nature. The states are indexed by s = 1,2.…

A: In economics, the Arrow–Debreu general equilibrium shows that under certain economic assumptions…

Q: Dick, Jane, and their dog, Spot, share an apartment. Their utilities depend upon the cleanliness of…

A: The purpose of this question is to show the cconcept of household work distribution between two…

Q: Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2…

A: The initial endowments are not effcient and improvement is possible as explained below.

Q: Suppose Lan's utility function is U₁(x,y) =x₁y₁¹⁰ and Dan's utility function is Up(x,y) =xD³yD³,…

A: We have to equate marginal rate of substitution of both Lan & Dan

Q: Suppose that Boris is a price taker and the price for each concert is $35. For Boris to maximise his…

A: Marginal benefit(MB)refers to additional benefit a Consumer receive when an additional unit is…

Q: Question 2. Suppose there are two consumers, A and B, and two goods, X and Y. The consumers have the…

A: For consumer AUA=min(2X,Y)XA=5YA=2For consumer BUB=3X+YXB=3YB=6Px=2Py=1

Q: Question 6. Suppose there are two consumers, A and B, and 2 goods, X and Y. The utility functions of…

A: Pareto efficient allocation refers to the point deviating from which no person can be made better…

Q: 4. Consider an economy consisting of two individuals, Ann and Bob, and two goods, scotch and wine.…

A: Ann and Bob are two individuals producing scotch and wine. The endowment for Ann is 5 bottles of…

Q: Armando consumes two goods: grapes and wine. He can purchase both at the market and also possesses a…

A: Utility function : U = x2 y Price of x : p1 Price of y : p2 Budget Constraint : p1x1 + p2y = w…

Q: Suppose a consumer’s utility function is given by U(X,Y) = MIN (5X, Y). Also, the consumer has $60…

A: U=Min(5X,Y)Px=5Py=1M=60

Q: Pankti consumes two goods, x and y. Her utility function is given by U(x, y) = ln(xy). (a) Are…

A: If preferences are homothetic, a proportional increase in x and y would result in no change in…

Q: Consider the following consumer’s problem: max…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: wo grad students go out to lunch and decide to split the bill evenly between them. Each student has…

A: The claim that both students eat too much is false, both students eat nothing at all Explanation -…

Q: Alberto's utility function is u(xã, YA) = min{¤Ã, YA}, where ï and yд are his consumptions of goods…

A: Consumer 1 u=min(xA,yA) px=1 py=p Budget Constrain : px.xA+py.yA=M M is the money income. xA+p.yA=M…

Q: Suppose that consumer is alway's ready to trade 4 units of X and 7 units of Y. Suppose also that Px…

A: Perfectly substitutable goods, also known as perfect substitutes, refer to two or more goods that…

Q: 3. Christina loves pizza and hates burger. Her utility function is U(p – b) =p – →b´, | where p is…

Q: Consider an one person, two good, one input economy. This is "Lea's Economy". Lea's utility function…

A: Utility function can be defined as the measure for a group of goods and services preferred by…

Q: Graph make graph

A: The objective of the question is to understand the concept of marginal rate of substitution and…

Q: Consider a pure exchange economy with two goods k = 1,2 and two households = A, B. Consider the…

A: We are going to calculate marginal rate of substitution for household A

Concept explainers

Welfare Analysis

Welfare analysis of the society is related to welfare economics. From the economic point of view former welfare economics refers to that subject which uses the techniques of microeconomics to analyse and evaluate the welfare at the economic or aggregate level.

Question

Consider a two-person, two good pure exchange economy. A's preferences over
consumption bundles (x₁, x₂) are represented by the utility function
UA (X₁, X₂) = x₁Xz
B's preferences over consumption bundles are represented by the utility function
UB (X₁, X₂) = x₁ + 2x₂
The initial endowment in goods x, and x₂ are given as: Individual A's as e^ = (1,0.5)
and Individual B's as eB= (1, 1.5)
1. Draw an Edgeworth box indicating the endowment and preferences of this problem.
2. Find the set of Pareto Optimal Allocations in this economy and depict these in the
Edgeworth box.
MRSA =
JUA/ƏX₁ X2
aUA/aX₂ X1
ƏUB/0x₁
MRSB =
= 2
aUB/0x₂
Therefore, the set of all points where the MRS are equal are given by
= 2 → X₂ = 2x1
Show Transcribed Text
Advanced Microeconomics.
Solve step by step so that I grasp the concept

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Describe the problem

VIEW

Step 2: Draw Edgeworthbox and depict the preferences

VIEW

Step 3: Find and depict set of all pareto optimal allocations

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.
= 5. Consider an economy with a single (representative) agent with utility function u(x, lc) = x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.
5.18 In a two-good, two-consumer economy, utility functions are u¹ (x₁, x₂) = x₁(x₂)², u² (x₁, x₂) = (x₁)²x₂. Total endowments are (10, 20). (a) A social planner wants to allocate goods to maximise consumer 1's utility while holding con- sumer 2's utility at u² = 8000/27. Find the assignment of goods to consumers that solves the planner's problem and show that the solution is Pareto efficient. (b) Suppose, instead, that the planner just divides the endowments so that e¹ = (10, 0) and e² = (0, 20) and then lets the consumers transact through perfectly competitive markets. Find the Walrasian equilibrium and show that the WEAs are the same as the solution in part (a).
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?
Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 5 units of good Y. Consumer B is given an initial endowment of 5 units of good X and 3 units of good Y. Consumer A's utility function is given by: UA(X,Y)= X + 4Y, and consumer B's utility function is given by UB(X,Y)= MIN (X, 2Y). If the prices are Px = 1 and Py = 3, if each consumer sells her initial endowment and buys back her optimal bundle, which of the following statements is true? Group of answer choices Both Markets are in Equilibrium There is Excess Demand in the Market for Good X = 2.4 There is Excess Demand in the Market for Good Y = 0.8 There is Excess Supply in the Market for Good Y = 1.6 There is Excess Supply in the Market for Good X = 1.6 E
6.