Questions tagged [pure-exchange-economy]

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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 ...
Ludwig Gershwin's user avatar
3 votes
1 answer
149 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 ...
Ludwig Gershwin's user avatar
1 vote
1 answer
70 views

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 ...
Ludwig Gershwin's user avatar
0 votes
1 answer
42 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!
AJl's user avatar
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2 votes
1 answer
165 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, ...
Walrasian soldier's user avatar
1 vote
2 answers
204 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 (...
Walrasian soldier's user avatar
0 votes
0 answers
31 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% ?
Leila Zniber's user avatar
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0 answers
89 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 ...
mynameparv's user avatar
1 vote
1 answer
134 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: ...
Nicolas Torres's user avatar
2 votes
2 answers
284 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?
carlos21's user avatar
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1 answer
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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 ...
Nicolas Torres's user avatar
2 votes
2 answers
196 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 ...
Nicolas Torres's user avatar
5 votes
1 answer
662 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: $u_A = x_A + y_A$ $u_B = s x_A + y_A$ $...
Nicolas Torres's user avatar
2 votes
1 answer
214 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 ...
user avatar
2 votes
2 answers
374 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 ...
studentp's user avatar
  • 120
1 vote
1 answer
66 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) = ...
Nick's user avatar
  • 21
1 vote
0 answers
74 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?...
Nick The Dick's user avatar
0 votes
1 answer
231 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},...
User_in's user avatar
1 vote
1 answer
259 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 −...
studentp's user avatar
  • 120
0 votes
1 answer
384 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 ...
studentp's user avatar
  • 120
4 votes
1 answer
251 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(...
clueless's user avatar
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0 votes
1 answer
45 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 ...
Panhaboth K's user avatar
2 votes
1 answer
421 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 ...
Vizag's user avatar
  • 224
1 vote
1 answer
204 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 ...
Haode Wang's user avatar
-1 votes
1 answer
487 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? ...
Siddhartha's user avatar
7 votes
0 answers
336 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 ...
Giskard's user avatar
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7 votes
2 answers
1k 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 ...
Giskard's user avatar
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2 votes
0 answers
150 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&...
Erik Apostol's user avatar
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......
TheEconomist's user avatar
8 votes
4 answers
519 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 ...
Erel Segal-Halevi's user avatar
1 vote
1 answer
8k 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 ...
Sub-Optimal's user avatar
  • 1,106
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 ...
Bob's user avatar
  • 263
0 votes
1 answer
1k 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 ...
Amit K Anand's user avatar
3 votes
0 answers
152 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(...
Laura Canon's user avatar
5 votes
1 answer
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=(...
Charlie's user avatar
  • 153