<p>In the economy described above, set of efficient allocations is given by the blue curve. Just do the slope of ICs comparisons at the boundaries and you will get that.</p>
<p><a href="https://i.sstatic.net/OllPdnz1.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OllPdnz1.png" alt="enter image description here" /></a></p>

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2021-01-19T11:17:34.253Z
2024-06-18T06:31:26.680Z
2024-06-18T06:31:26.680Z
Amit
<p>Find Pareto optimal allocations and the core for the following economies.</p>
<p>There are two consumers and two goods. Utility functions are <span class="math-container">$u_1(x_1,y_1)= 10x_1-(y_1-2)^2$</span> and <span class="math-container">$u_2(x_2,y_2) = 10y_2 − (x_2 − 2)^2$</span>. The endowments are (0,4) for agent 1 and (4,0) for agent 2.</p>
<p>I have its intuitive solution but I don’t understand this.</p>
<p><a href="https://i.sstatic.net/goX22.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/goX22.jpg" alt="enter image description here" /></a></p>
<p>Please help me to provide a solution by calculation. Thanks a lot.</p>

<microeconomics><utility><self-study><optimization><pure-exchange-economy>
Find Pareto optimal allocations and the core for the following economies
studentp
# Find Pareto optimal allocations and the core for the following economies

(Asked by: username_0 on 2021-01-18)

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 $u\_2(x\_2,y\_2) = 10y\_2 − (x\_2 − 2)^2$. The endowments are (0,4) for agent 1 and (4,0) for agent 2.

I have its intuitive solution but I don’t understand this.

[![enter image description here](https://i.sstatic.net/goX22.jpg)](https://i.sstatic.net/goX22.jpg)

Please help me to provide a solution by calculation. Thanks a lot.

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

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## 1 answers

### Answer by username_1 on 2021-01-19. Score: 2 | Accepted answer

In the economy described above, set of efficient allocations is given by the blue curve. Just do the slope of ICs comparisons at the boundaries and you will get that.

[![enter image description here](https://i.sstatic.net/OllPdnz1.png)](https://i.sstatic.net/OllPdnz1.png)


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