# Slope of Marginal Revenue Curve

Hi there,

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.

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 Thanks!

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. .