From here and a pile of maths that I've done myself,

$x_1 = \frac{a}{a+b}\frac{m}{p_1} \\ x_2= \frac{b}{a+b}\frac{m}{p_2}$

This yields inverse demand equations, when you have numbers stand in for $a$ , $b$, $m$, and $p_i$, of the form:

$p(x_i) = \frac{STUFF_i}{x_i}$

Dropping the other good and treating $x_i$ as $Q$, we have the marginal revenue equation, the derivative of $p(Q)Q$.

$MR = p'(Q)Q + p(Q) \cdot 1$


$MR = \frac{-STUFF}{Q^2}Q + \frac{STUFF}{Q} = 0$

So something is either wrong or these sorts of functions just don't have marginal revenues. Could someone tell me what sort of basic mistakes, mathematical or conceptual, are being made?

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  • $\begingroup$ You can answer your own question for others to see. I focused on the “easy” part and did not think of the set up for this question. $\endgroup$ – bajun65537 Nov 8 at 17:17

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