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Building on this question, regarding the answer from Bkay:

Is it a general statement that when $m < \frac{p_y^2}{4 p_x}$, all income will be allocated to $x_M$? What about the case when the marginal utility of $x$ is smaller than the marginal utility of $y$ (which is 1 in this case)? $x>0.25$ would satisfy this. Would it mean that the $x$ will be consumed up to 0.25 unit, before all other income are allocated to $y$?

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