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I have such a question:

In an economy with $𝐼 \ge 2 $ consumers, each agent’s utility functions are given as:

$$ 𝑈(x_1 ,x_2) =max\{2min\{2x_1,x_2\},min\{x_1,4x_2\} \} $$

The endowments in the economy are given as: $ (𝜔_1 ,𝜔_1) = (1+3𝛼,2-𝛼)$ with $𝛼$ $∈$ $(0,1)$

Find the conditions on $𝛼$ which ensure that a Walrasian equilibrium exists for this economy. How does $𝐼$ relate to the size of the set of $𝛼$ for which Walrasian equilibrium is ensured to exist?

I encounter first time with that type of question so I couldnt attempt to solve it. I appreciate it if you can help.

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    $\begingroup$ Try to find the demand first. You can use the approach posted here: qr.ae/pvDf9H $\endgroup$
    – Amit
    Dec 22, 2022 at 4:55
  • $\begingroup$ Thank you for your guidance really Dear Amit. you save my life literally :) $\endgroup$
    – Tatanik501
    Dec 22, 2022 at 6:30

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