Questions tagged [edgeworth-box]
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23 questions
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Find the Pareto Efficient allocations and Competitive Equilibrium when both agents have funky functions
I'm trying to solve this General Equilibrium excercise which I find quite challenging as both agents have funky utility functions.
Find the Pareto Efficient allocations and Competitive Equilibra for ...
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2
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1
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123
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Shape of the contract "curve"
In the edgeworth box model, is the pareto set / contract curve necessarily shaped like a monotonically increasing function? This seems to be stated / implied in various places (such as Wikipedia), but ...
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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!
- 27
2
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1
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220
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Find the set of Pareto efficient allocations. $U_1 = -|x_1-2|$ and $U_2 = −|x_2 − 8|$
A professor has 20 hours to allocate between two PhD students. Let x1 and x2 be the time allocated to the two students. The utility of each student is as follows:
$U_1 = −|x_1 − 2|$ and $U_2 = −|x_2 − ...
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0
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Equilibrium in Edgeworth box with Cobb-Douglas utility function
Given an Edgeworth box environment, with two individuals and two goods $(x,y)$ with maximum quantities $Q_x$ and $Q_y$. Suppose that the utility functions for each individual are
$$ U_1(x,y) = x^\...
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1
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How to find the contract curve for a funky utility involving the min operator?
Suppose a pure exchange economy where agents’ ($A$ and $B$) preferences are given by the following utility functions:
$u_A = \min(3x+y,x+3y)$
$u_B = x^\frac{1}{2} y^\frac{1}{2}$
Find the contract ...
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1
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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 ...
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2
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2
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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:
$u_A = x_A + y_A$
$u_B = 2 ...
- 2,351
5
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1
answer
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How to find the contract curve when both agents have linear utilities?
I'm trying to solve the following excercise:
Find the contract curve for an exchange economy where agents' ($A$ and $B$) preferences and endowments are given by:
$u_A = x_A + y_A$
$u_B = s x_A + y_A$
$...
- 2,351
1
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1
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Second welfare theorem: can it be used to show there does not exist any competitive equilibrium? (exchange economies)
The one version of the Second Welfare Theorem states that: if there exists a competitive/Walrasian equilibrium and an endowment $X$ is Pareto efficient, then there is a price vector $\hat{P}$ for ...
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Edgeworth Box (Non-Convex preference)
Consider a situation that agent A's indifference curves are concave, while B’s indifference curves are convex and both sets of indifference curves have exactly the same shape. A northeast movement ...
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1
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900
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Find the set of Pareto efficient allocations
There is an exchange economy with two people and two goods.
Utility functions are
$u_A(x_A, y_A)=\max\{x_A, y_A\}$
$u_B(x_B, y_B)=\max\{x_B, y_B\}$
Endowments are $w_A(1,\alpha)$ and $w_B(1,\alpha)$ ...
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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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Shape of contract curve in an Edgeworth-Box economy
I've noticed that contract curves for preference functions $u_{1,2}=(x_1x_2)^{1/2}$ and $u_{1,2}=x_1(x_2)^{1/2}$ is the diagonal of the Edgeworth Box. A general question arose, and I can't figure it ...
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In a box diagram, why does efficiency locus lie on one side of the diagonal, if both sectors haves constant returns to scale function?
The following is what I understand, so far.
If we measure labour in the $x$-axis and capital in the $y$-axis, the slope of diagonal of the box is the capital-labour ratio $K/L$ in the economy. Let $A$ ...
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2
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1
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Computing the competitive equilibrium from the edgeworth box
Consider the following Edgeworth economy. There are two consumers $i \in {1,2}$ and two goods x and y. Consumer $i$ consumes $(x_i,y_i)$, where $x_i ≥0$ and $y_i ≥0$. Endowments are $ω_1 =(a,0)$ and $...
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1
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558
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Leontif case for Edgeworth box
Consumer 1 has utility $u_1=min\{x_1,y_1\}$, Consumer 2 has utility $u_1=min\{x_1,2y_1\}$, their endowments are $w_1=(a,0)$ and $w_1=(b,0)$ and in this case $a=b$.
I know the offer curves look like ...
- 1,048
2
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1
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350
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Offer curves in general equilibrium
I'm having trouble understanding how to find the offer curves in general equilibrium. Is there a general way that we can use to find it?
I can understand the Pareto set and contract curve but when it ...
- 1,048
2
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1
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153
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CES utility function in an Edgeworth box
Two consumers have the CES utility function $x_1^\beta +x_2^\beta$, for $0<\beta<1$, their initial endowments are $w^1=(1,0)$, $w^2=(0,1)$ Draw the Core of this economy in an Edgeworth box. Note ...
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How to find the Utility Possibility Frontier when there are Perfect Substitutes?
I am trying to derive the Utility Possibility Frontier (UPF) when both utility functions display perfect substitutes (in an Edgeworth economy with to consumers and two goods).
The specific problem:
$...
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194
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Pareto Set with strictly convex preferences
Suppose the agents A and B have the following utility functions $x_A y_A+12x_A+3y_A $ and $x_By_B +8x_B+9y_B$ respectively with endowments (8,30) and (10,10).
The contract curve's equation turns out ...
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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 $u_j^i(x_1,x_2) = \partial u^i(...
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2
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Pure exchange economy: Given an initial endowment are multiple equilibria possible?
Consider a pure exchange economy with two goods ($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 ...
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