# Cobb-Douglas demand yields a zero marginal revenue, monopolies don't exist?

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 $$p(Q)Q$$.

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

But

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

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?

• 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. – bajun65537 Nov 8 '19 at 17:17