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 :slight_smile:


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 :expressionless:

Thanks! 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. .

Differential calculus is the answer!

That last step is just differentiation

Basically differention gives you the rate of change, in this case, the rate of change of revenue to quantity, which is the marginal revenue line.

Check out khan academy or something for some quick differentiation tutorials. Haven’t used it for quite some time myself lol

Ah, that makes a lot of sense now. It really is just basic differentiation after all. Not sure how i missed that as an engineer!

Thanks guys!

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Please provide me the answer to TR/Q = 3200-8 Q. How it become -8

TR = P × Q = 3200 Q - 4 Q^2

using differentiation to find slope,

MR = dy/dx.3200 Q - dy/dx.4 Q^2

it becomes = 3200 (1) - 4*2 Q (as the 2 comes down and is multiplied by 4)

We get MR= 3200-8Q

for more clarity just watch videos on youtube for Differentation concepts


How do you get the TR?
TR = P * Q
TR = 3200 - 4Q * 800-0.25P
TR = 3200800 - 32000.25P - 4Q * 800 - 4Q * -0.25P
TR = …

I know i have a grave conceptual lacking…could anyone explain?