Hi,
can anyone help me understand how the Marginal Revenue is obtained below?
Thanks!
ABC company is a monopoly that has very high barriers to entry. The quantity demand (QD) for its product is QD = 800 – 0.25 × P (where P is price). The slope of the marginal revenue curve is closest to:
Q = 800 - 0.25 P
P = 3200 - 4Q
TR = P × Q = 3200 Q - 4 Q2
Marginal Revenue = ΔTR/ΔQ = 3200 - 8 Q
Therefore the slope of the curve is -8.
It’s a calculus thing: you’re taking the derivative of TR with respect to Q.
When asked about the slope of the marginal revenue curve, I just remember that it is twice the slope of the demand curve (for a negatively sloped, linear demand curve which is what these questions always seem to refer to) which in this instance is -4: Q = 800 - 0.25P 0.25P = 800 - Q P = 3200 - 4Q Therefore the slope of the marginal revenue curve is -8.
an easier way, at least in my opinion, is taking the slope of the Demand curve (-4) and multiplying by 2. You get the slope of the Demand curve from the inverse Demand function (ie. “Price =” equation). And I believe MR slope is always twice as steep as the demand curve (assuming it’s linear, which is the only demand curve’s we deal with in curriculum); so twice as steep as -4 would be -8
alrighty! I’ll keep that in mind. Thanks!