Slope of marginal revenue curve

CFA Level I Economics
#1

I’m trying to find the slope of MR curve given quantity demand (QD) for the product is QD = 800 – 0.25 × P (where P is price)

I know that you have to solve for P and I got P = 3200- 4Q so I thought that the slope was -4

However, I had to go further and multiply by Q again

TR = P × Q = 3200 Q - 4 Q2

and Marginal Revenue = ΔTR/ΔQ = 3200 - 8Q

Why is multiplying by Q required and how do you get -8 from that?

#2

You have to multiply by Q to get total revenue – P×Q – because marginal revenue is the derivative with respect to quantity of total revenue (it’s a calculus thing).

The −8 comes from differentiating 3,200Q − 4Q² with respect to Q (it’s that same calculus thing). I could give you a tutorial on differential calculus, but you’re probably better off just taking my word for it: they’re correct that the slope is 3,200 − 8Q.

1 Like
#3

I see. They differentiated it using calculus. Why and when is that used? Is that only use for finding the slope of marginal revenue curve? I don’t remember seeing differentiation being used anywhere through my readings

#4

Differential calculus is used to find slopes – rates of change – in all sorts of financial applications, calculating, for example:

  • marginal cost
  • marginal revenue
  • marginal revenue product
  • modified duration
  • GDP growth rate
  • option delta
  • marginal rate of substitution
  • maximum profit
  • minimum total cost
  • minimum WACC

Integral calculus – integration is the inverse operation of differentiation – is used to find areas, and has financial applications in calculating, for example:

  • consumer surplus
  • producer surplus
#5

Is the factor applied to x always the slope? Would appear so from this and following link: http://www.purplemath.com/modules/slope.htm

… although can’t see the logic.

#6

For a straight line, the coefficient on x (the variable on the horizontal axis) is the slope. For a curve, you have to use calculus to get the slope at a particular point, as the slope changes from point to point.

#7

Thanks. This doesn’t appear to be in the text book?

#8

Here is a pretty good video on this below. I had to look this up as well sinc I haven’t done any simple calculus in 3 years.

http://www.khanacademy.org/economics-finance-domain/microeconomics/perfect-competition-topic/monopolies-tutorial/v/monopolist-optimizing-price--part-1---total-revenue

#9

I was having an issue understanding this concept too, apologies if I’m missing something here. Once the demand function is inverted to get a slope of -4, is it correct to say that doubling this number solves for the slope of marginal revenue since MR is the revenue from selling one additional unit? I understand that differential calculus is ultimately involved but hoping to find a practical rule to apply. Thanks!

#10

It’s true only because the demand curves you get in the CFA curriculum are all straight lines.

#11

Good to know. Thanks all.

#12

You’re welcome.