I’m having some difficulty understanding the answer explanations for one of the questions in the CFAI Mock Exam. Any help would be appreciated

Q.

A power generation company is a monopoly that has very high barriers to entry. The quantity demand (Q__D) for its product is Q__D = 800 – 0.25 × P (where P is price). The slope of the marginal revenue curve is closest to:

A. –8.00.

B. –0.25.

C. –4.00.

Answer = A

Solve for P from the quantity demanded: Q = 800 - 0.25 P

P = 3200 - 4Q

TR = P × Q = 3200 Q - 4 Q2

and Marginal Revenue = ΔTR/ΔQ = 3200 - 8 Q Therefore the slope of the curve is -8.

I’m fine up until the last sentence where they somehow come up with the equation:

ΔTR/ΔQ = 3200 - 8 Q

How exactly did they come up with the right-hand side of that equation? I feel like there’s something very obvious that i’m somehow overlooking

http://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91330310 My understanding is you can double the inverted demand function slope to solve for the slope of marginal revenue. I’m not clear on the exact logic (differentiated calculus?), but I think of this as though adding one additional unit of marginal revenue doubles the slope. This is probably inherently wrong but desparate times call for desparate measures. .