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Questions tagged [pure-exchange-economy]

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Trying to understand Walrasian equilibrium (Brown & Matzkin 1996)

I'm trying to understand page 6-7 of the Brown & Matzkin paper. Here is an example: Consider a 2-person, 2-good pure exchange economy $E=(u_i,w_i)_{i=1}^2$ where both utility functions are ...
0 votes
0 answers
27 views

Increase in income in an economy would increase

Increase in income in an economy would increase the following except Consumption Savings Imports Exports
8 votes
1 answer
366 views

Pure exchange economy: Set of multiple equilibria endowments

Initial endowments which can result in multiple equilibria in a pure exchange economy are explained here. Given a pure exchange economy, that is given the utility functions (which fulfil the usual ...
5 votes
2 answers
2k views

Pure exchange economy with two consumers and non differentiable utility functions

We have a pure exchange economy, two consumers $A,B$ and two goods $x,y$. The utility functions are as follows $$u_A=\min\{x_A,y_A\}\qquad u_B=\min\{x_B,\sqrt{y_B}\}$$ The endowments are $$\omega_A=(...
1 vote
1 answer
244 views

Finding the competitive equilibrium in an exchange economy with two perfect complements

I am currently in a Microeconomics class and have come across the problem described below. I have tried to solve the problem algebraically but only get to the intercept (x1a,x2a)=(8,4). I know that ...
1 vote
1 answer
374 views

How do I find the set of pareto optimal allocations?

Suppose there are 2 individuals and 2 goods. $u_1(x_1,y_1)=x_1+2y_1$, and $u_2(x_2,y_2)=x_2+y_2$. There are 2 units of good $x$ and 1 unit of good $y$ in total. How do I find the set of Pareto optimal ...
2 votes
1 answer
206 views

Why doesn't this exchange economy have a walrasian equilibrium?

Consider an exchange economy with $n$ individuals and 2 goods $x,y$. All individuals have the same utility function $u(x,y)=x^2+y^2$ and the same endowment $w=(1,1)$. I tried to solve the problem with ...
0 votes
1 answer
67 views

Edgeworth Box for exchange economy

Could you please tell me, if the Edgeworth Box I have drawn for the exchange economy is correct? My professor's solution is really unclear. Thank you!
2 votes
1 answer
203 views

Core in a replicated economy

I'm trying to solve the following problem on general equilibrium: Consider an economy with two individuals with utility functions $u^A(x^A,y^A) = \min \{ x^A, y^A \}$ and $u^B(x^B,y^B) = \min \{ x^B, ...
1 vote
2 answers
268 views

General equilibrium with market power

I'm trying to solve the following problem: Consider an exchange economy with two consumers, $A$ and $B$, whose utility functions are: \begin{align*} u_{A} & = x_1^A x_2^A \\ u_{B} & = x_1^B (...
0 votes
0 answers
53 views

difference between "crawling like arrangement" and "stabilized arrangement"

What is the difference between "crawling like arrangement" and "stabilized arrangement" ? what about margins ? both less than + or -1% ?
1 vote
0 answers
140 views

Utility Possibility Set and Utility Possibility Frontier

Consider an Exchange economy with two individuals $a$ and $b$ and two goods $1$ and $2$. Denote consumption of good $j$ by individual $i$ as $x_{ij}$ for $i\in\{a,b\}$ and $j\in\{1,2\}$ The utility ...
2 votes
2 answers
403 views

Exchange economy with two agents, what's the competitive equilibrium?

I'm currently doing this assignment but I'm keep getting stuck by this question. I put the Lagrange function for both agents and get the MRS / Price ratio but what should I do from there?
1 vote
1 answer
143 views

Is there/can we define a notion of Giffen goods in pure exchange economies?

I was checking some questions I recently answered here on General Equilibrium, and a result from this one (Exchange economy with two agents, what's the competitive equilibrium?) drew my attention: ...
1 vote
1 answer
288 views

How to find the Walrasian equilibrium for non monotonic utility functions?

I just say Amit's comment on this question: The second welfare theorem without monotonicity so I got curious and tried to find both the contract curve for that particular problem, and the Walrasian ...
5 votes
1 answer
1k views

How to find the contract curve when both agents have linear utilities?

I'm trying to solve the following excercise: Find the contract curve for an exchange economy where agents' ($A$ and $B$) preferences and endowments are given by: $u_A = x_A + y_A$ $u_B = s x_A + y_A$ $...
2 votes
2 answers
257 views

Finding Walrasian equilibria when Walrasian demands are not unique

I'm trying to solve the following excercise: Find the Walrasian equilibria for a pure exchange economy where agents' ($A$ and $B$) preferences and endowments are given by: $u_A = x_A + y_A$ $u_B = 2 ...
2 votes
1 answer
511 views

How to find the competitive equilibrium?

Consider a $2$-good, $2$-person pure-exchange economy where $A$ is endowed with $(0,5)$ and $B$ is endowed with $(5,0)$. If the utility functions are $u_A = xy$ and $u_B = \min\{x,y\}$, what are all ...
2 votes
2 answers
462 views

Finding Pareto optimal allocations and Walrasian equilibrium allocations in the case of 3 goods

We have 3 people and 3 goods $$U_A(x,y,z)=x_Ay_Az_A^2$$ $$U_B(x,y,z)=x_B^2y_Bz_B$$ $$U_C(x,y,z)=x_Cy_C^2z_C$$ Endowments are $W_A= (1,1,1)$ $W_B= (2,1,3)$ $W_C= (1,5,1)$ I am confused due to the ...
7 votes
2 answers
2k views

Pure exchange economy: Given an initial endowment are multiple equilibria possible?

Consider a pure exchange economy with two goods ($x_1,x_2$) and two consumers $A,B$. Both users have an initial endowment, $(\omega_1^A,\omega_2^A)$ and $(\omega_1^B,\omega_2^B)$ respectively. A price ...
1 vote
1 answer
99 views

Net and gross market clearing in endowment economy

My question relates to an endowment economy. We assume perfect competition and markets clear, i.e. supply = demand. The way my professor defined it, he said endowment (per good) = supply (per good) = ...
1 vote
0 answers
88 views

Visualisation of a 3-person 3-good economy

Are there any theoretical or practical ways to visualise such an economy? I understand that a 2-person 3-good economy is visualised by a 3D Edgeworth Box (a cube), but what about a 3-person 3-good one?...
0 votes
1 answer
288 views

Calculating the Competitive Equilibrium in a pure exchange economy with 3 comodities and 2 agents [closed]

Consider a pure exchange economy with three commodities and two households with individual endowments $e_{1}=(1,2,3) \text { and } e_{2}=(3,2,1)$ respectively, and utility functions $u_{1}\left(x_{11},...
1 vote
1 answer
285 views

Find Pareto optimal allocations and the core for the following economies

Find Pareto optimal allocations and the core for the following economies. There are two consumers and two goods. Utility functions are $u_1(x_1,y_1)= 10x_1-(y_1-2)^2$ and $u_2(x_2,y_2) = 10y_2 − (x_2 −...
0 votes
1 answer
545 views

Exchange economy find core

Find Pareto optimal allocations and the core for the following economies Consider an exchange economy with two agents and two goods. Let consumption sets are the nonnegative orthant. Agent 1’s utility ...
4 votes
1 answer
276 views

Contract curve and Pareto frontier

Consider an exchange economy with two agents. Each agent $i \in \{1,2\}$ derives utility $u^i(x_1,x_2) \in \mathbb R$ by consuming $(x_1,x_2) \in \mathbb R_+^2$. Let $u_j^i(x_1,x_2) = \partial u^i(...
0 votes
1 answer
48 views

Why can’t we know the specific outcome of an exchange economy with initial resource endowment?

In a 2-person exchange economy we define the contract curve as the subset of all Pareto-efficient outcomes within the ‘lens’ bounded by both agents’ indifference curves through $\vec{R}$ which is the ...
2 votes
1 answer
439 views

Utility Possibility Frontier with two consumers and 3 commodities

I am trying to solve the following problem: Consider a pure exchange economy with three commodities and two households with individual endowments: $$e_1=(1,2,3), e_2=(3,2,1),$$ respectively, and ...
1 vote
1 answer
215 views

A question about the exchange economy

The question I am given is the following: Consider an economy that has only three goods, mineral water, orange juice, and wine available in fixed amounts, and three agents, A, B and C. So in this ...
8 votes
4 answers
526 views

Fair and efficient allocation of "family goods"

Consider an exchange economy with two goods, e.g. home furniture (x) and electrical equipment (y). The interesting thing about these goods is that, when a family owns a bundle, all members of the ...
-1 votes
1 answer
501 views

Pareto-optimal allocations in the Edgeworth box

If agent A has utility function $u(x_1, x_2)$ and agent B has utility function $v(x_1, x_2)$, what are the equation(s) that characterize the Pareto-efficient allocation of goods in the Edgeworth box? ...
2 votes
0 answers
152 views

Endowment increases but utility reduces

In an Edgeworth economy with two agents and two goods, Player A has endowment $\left(a,\,0\right)$ and utility $u_{A}\left(x_{1},\,x_{2}\right)=\min\left(\gamma x_{1},\,x_{2}\right)$ in which $\gamma&...
0 votes
1 answer
2k views

Competitive equilibrium in an exchange economy with lexicographic preferences [closed]

I am really stuck with this problem and not able to approach it. Any help will be much appreciated. I tried to draw edgeworth box with initial endowment point. I do know that for competitive ...
0 votes
2 answers
3k views

Does the contract curve always have to connect the initial points on an edgeworth box? Why or why not?

What if the contract curve goes out of bounds? In that case, do I assume it superimposes itself on the axes it is closest to? I hope this was clear. Not sure how to explain this other than visually......
1 vote
1 answer
9k views

How does an import quota affect the demand / supply of currency?

An import quota in an open economy might not have the desired affect of increasing the GDP as it increases the demand of domestic currency in the open market raising exchange rate. How does it happen ...
3 votes
1 answer
1k views

Price ratio determined by endowments only?

Am I right to say in an Exchange Economy with two consumers with identical preferences, the equilibrium price (WEA) of the two goods would be determined by availability of two goods, i.e, total ...
3 votes
0 answers
154 views

How to find walrasian asignations? [closed]

In a economy Arrow Debreau of pure exchange with two agents and two goods. With utility function of Leontief for agent B, where $U_b(x_b,y_b)=\min(x_b,y_b)$; and for agent A a simple Cobb-Douglas $U_a(...