Slope of marginal revenue curve

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releasets

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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?
 
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.
 
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
 
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
 
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.
 
Thanks. This doesn’t appear to be in the text book?
 
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!
 
bostoncfa2014 wrote: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!
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It’s true only because the demand curves you get in the CFA curriculum are all straight lines.
 
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