<p>Core Allocations are Pareto efficient allocations that must satisfy individual rationality i.e. these allocations must yield at least as much satisfaction to the individuals as their respective endowments. In the given question, core allocations are represented by line connecting <span class="math-container">$(e/2, e/2)$</span> to <span class="math-container">$(e,e)$</span>.</p>
<p>Dashed line on the left graph is representing the set of efficient allocations and on the right graph is representing the Core allocations.</p>
<p><a href="https://i.sstatic.net/ODohY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ODohY.png" alt="Set of efficient Allocations and Core Allocations" /></a></p>

CC BY-SA 4.0
2021-01-11T10:26:59.493Z
2021-01-11T10:26:59.493Z
Amit
<p>Find Pareto optimal allocations and the core for the following economies</p>
<p>Consider an exchange economy with two agents and two goods. Let consumption sets are the nonnegative orthant. Agent 1’s utility is represented by <span class="math-container">$x+y$</span> and agent 2’s utility is <span class="math-container">$xy$</span>. Endowments are (e,0) for agent 1, and (0,e) for agent 2 with  &gt; 0.</p>
<p>When I find MRS and equalize them, I am going to find <span class="math-container">$x_2=y_2$</span>  This is interior point (contract curve. ). By feasibility constraint, <span class="math-container">$x_1=y_1$</span>.</p>
<p>Its core is given as follows. Why?</p>
<p><a href="https://i.sstatic.net/o8FW1.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/o8FW1.jpg" alt="enter image description here" /></a></p>
<p>How can we find (determine) core? What it’s appropriate calculation to find core? For example, why we assume <span class="math-container">$e/2$</span>?</p>

<microeconomics><self-study><pure-exchange-economy>
Exchange economy find core
studentp
# Exchange economy find core

(Asked by: username_0 on 2021-01-10)

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 is represented by $x+y$ and agent 2’s utility is $xy$. Endowments are (e,0) for agent 1, and (0,e) for agent 2 with > 0.

When I find MRS and equalize them, I am going to find $x\_2=y\_2$ This is interior point (contract curve. ). By feasibility constraint, $x\_1=y\_1$.

Its core is given as follows. Why?

[![enter image description here](https://i.sstatic.net/o8FW1.jpg)](https://i.sstatic.net/o8FW1.jpg)

How can we find (determine) core? What it’s appropriate calculation to find core? For example, why we assume $e/2$?

**Tags:** microeconomics, self-study, pure-exchange-economy


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## 1 answers

### Answer by username_1 on 2021-01-11. Score: 1 | Accepted answer

Core Allocations are Pareto efficient allocations that must satisfy individual rationality i.e. these allocations must yield at least as much satisfaction to the individuals as their respective endowments. In the given question, core allocations are represented by line connecting $(e/2, e/2)$ to $(e,e)$.

Dashed line on the left graph is representing the set of efficient allocations and on the right graph is representing the Core allocations.

[![Set of efficient Allocations and Core Allocations](https://i.sstatic.net/ODohY.png)](https://i.sstatic.net/ODohY.png)


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