<p>Since this is just a picture and it does not specify the utility functions and the endowments, we have incomplete data and we cannot derive the competitive equilibrium with this much information. Whether the equilibrium exists or not will depend on the choice of utility functions and endowments. However, given the budget line in the picture we can certainly say that X is not a competitive equilibrium. The reason is that person A will not demand point X at those prices, he will demand point Y, and B demands point X. So at those prices, there is excess demand for Good 1 and excess supply of good 2.</p>
<p>Situation in the picture provided in the question is similar to the one described in the following <span class="math-container">$2$</span> consumers, <span class="math-container">$2$</span> goods economy:</p>
<ul>
<li><span class="math-container">$u_1(x_1,y_1)=\max(\min(2x_1,y_1),\min(x_1,2y_1))$</span></li>
<li><span class="math-container">$u_2(x_2,y_2)=x_2y_2$</span></li>
<li>Endowment allocation is <span class="math-container">$\alpha=((0.25,0.5),(0.75,0.5))$</span></li>
</ul>
<p>Observe that <span class="math-container">$\alpha$</span> is Pareto efficient, but it is not a competitive equilibrium. Reason is similar to the one provided above. In fact, in this economy, competitive equilibrium does not exist.
<a href="https://i.sstatic.net/DXLxT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DXLxT.png" alt="enter image description here" /></a></p>

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2023-10-04T05:26:21.653Z
2023-10-04T06:34:20.857Z
2023-10-04T06:34:20.857Z
Amit
<p><a href="https://i.sstatic.net/Z2omQ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Z2omQ.png" alt="enter image description here" /></a>
This is a figure from <em>Microeconomics(Hal Varian)</em> and I'm not sure about its market equilibrium and pareto efficiency. I'm sure that X is a point with pareto efficiency, but I'm not sure if it can be called a competitive equilibrium since it's <span class="math-container">$MRS_{XY}^A = MRS_{XY}^B = \frac{P_X}{P_Y}$</span>. I know that X point isn't reachable through the market. I'm just not sure if we can derive a market equilibrium in this economy or not. Anybody has an idea about it?</p>

<microeconomics>
Equilibrium allocation 'reachable' and 'existence'
user45188
# Equilibrium allocation 'reachable' and 'existence'

(Asked by: username_0 on 2023-10-04)

[![enter image description here](https://i.sstatic.net/Z2omQ.png)](https://i.sstatic.net/Z2omQ.png)
This is a figure from *Microeconomics(Hal Varian)* and I'm not sure about its market equilibrium and pareto efficiency. I'm sure that X is a point with pareto efficiency, but I'm not sure if it can be called a competitive equilibrium since it's $MRS\_{XY}^A = MRS\_{XY}^B = \frac{P\_X}{P\_Y}$. I know that X point isn't reachable through the market. I'm just not sure if we can derive a market equilibrium in this economy or not. Anybody has an idea about it?

**Tags:** microeconomics

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## 1 answers

### Answer by username_1 on 2023-10-04. Score: 3 | Accepted answer

Since this is just a picture and it does not specify the utility functions and the endowments, we have incomplete data and we cannot derive the competitive equilibrium with this much information. Whether the equilibrium exists or not will depend on the choice of utility functions and endowments. However, given the budget line in the picture we can certainly say that X is not a competitive equilibrium. The reason is that person A will not demand point X at those prices, he will demand point Y, and B demands point X. So at those prices, there is excess demand for Good 1 and excess supply of good 2.

Situation in the picture provided in the question is similar to the one described in the following $2$ consumers, $2$ goods economy:

* $u\_1(x\_1,y\_1)=\max(\min(2x\_1,y\_1),\min(x\_1,2y\_1))$
* $u\_2(x\_2,y\_2)=x\_2y\_2$
* Endowment allocation is $\alpha=((0.25,0.5),(0.75,0.5))$

Observe that $\alpha$ is Pareto efficient, but it is not a competitive equilibrium. Reason is similar to the one provided above. In fact, in this economy, competitive equilibrium does not exist.
[![enter image description here](https://i.sstatic.net/DXLxT.png)](https://i.sstatic.net/DXLxT.png)


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