Monopolist Question

The money the monopolist makes on each unit is (p - 20). Agreed?

The profit is equal to the money made on each unit multiplied by the number of units sold. Let's call the profit "y", because I don't want to copy-paste a capital pi into this post. So y = q(p - 20).

Substitute "60 - p" into my profit equation for q, to get y = (60 - p)(p - 20) = -p^2 + 80p - 1200.

To find the value of p that maximizes y(p), take the derivative of y with respect to p, and set it equal to zero:

0 = y'(p) = -2p + 80.

p = 40 solves this equation.

Awesome thank you!