Marginal Revenue Curve Slope Question (CFA Level 1)

CFA Level I Economics
#1

Just a few days before the exam and I can’t seem to wrap my head around this question.

This concept is not well documented in the book or in schweser notes.

Could someone please clarify how they get change in TR and change in Q?

Thanks very much

A power generation company is a monopoly that has very high barriers to entry. The quantity demand Qd for its products is Qd=800-0.25 x P (where P is price). The slope of the marginal revenue curve is:

A) -8

B) -0.25

C) -4

Answer: A

Solve for P from quantity demanded

Q = 800-0.25P

P = 3200 - 4Q

TR = P*Q = 3200Q - 4Q^2

I can get this far, not sure how they jump to the below with the information given in the question.

Marginal Reveune = Change in TR / Change in Qd = 3200 - 8Q

Therefor the slop of the curve is -8

#2

I wouldn’t have gone through that calculation. Since the demand is downward sloping therefore the absolute slope value of MR curve must be greater( as MR Curve is always steeper) than demand curve. Since slope of demand curve is -4 so the slope of MR must be -8.

#3

Thank you. That’s a helpful short cut.

#4

Qd = 3.200 - 8Q is simply the first derivative of the revenue function (TR) which basically the definition of marginal revenue. The minus 8 is then the second derivative of the revenue function which is equal to the slope of the marginal revenue curve.

Best, Oscar

#5

What Oscar’s telling you is that it’s a calculus thing.

You’re not supposed to need calculus for the CFA exams, so whoever wrote that question was being a twit.

#6

Shouldn’t the first derivative of the TR function be giving the slope of MR? If I remember correctly, first derivative will give the marginal changes in revenue due to changes in quantity.

#7

Yes: the first derivative with respect to quantity.

#8

Thanks all.

#9

thanks for this … I was knocking my brains out on this !!