Questions tagged [pure-exchange-economy]
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24
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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:
$u_A = x_A + y_A$
$u_B = 2 ...
- 1,216
5
votes
1
answer
119
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How to find the contract curve when both agents have linear utilities?
I'm trying to solve the following excercise:
Find the contract curve for an exchange economy where agents' ($A$ and $B$) preferences and endowments are given by:
$u_A = x_A + y_A$
$u_B = s x_A + y_A$
$...
- 1,216
2
votes
1
answer
82
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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 ...
- 77
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2
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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 ...
- 98
1
vote
1
answer
52
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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) = ...
- 21
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0
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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?...
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1
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139
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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
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1
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207
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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 −...
- 98
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1
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207
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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 ...
- 98
4
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1
answer
204
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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(...
- 1,539
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1
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40
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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 ...
- 57
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1
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385
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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 ...
- 224
1
vote
1
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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 ...
- 13
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1
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437
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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? ...
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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 ...
- 28k
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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 ...
- 28k
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0
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145
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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&...
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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......
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4
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509
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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 ...
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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 ...
- 1,106
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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 ...
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1k
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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 ...
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0
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150
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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(...
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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=(...
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