A monopolist’s demand curve is given by p = 100 – 2q. Find the marginal revenue function. Find the relationship between the slopes of the average revenue and marginal revenue curves. At what price is marginal revenue zero?
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Demand curve is given by
P = 100 - 2q
Total revenue will be given by
TR = P×q = (100-2q)×q = 100q - 2q²
(a) marginal revenue is the derivative of TR. So
MR= \frac{d(TR)}{dq} = \frac{d}{dq}(100q-2q^2) =100-4qMR=
dq
d(TR)
=
dq
d
(100q−2q
2
)=100−4q
So marginal revenue is 100-4q.
(b) MR = 0
⇒ 100 - 4q = 0
⇒ 4q = 100
⇒ q = 100/4 = 25
At q=25,
TR = 100q - 2q²
= 100×25 - 2×25²
= 2500 - 1250
= 1250
Marginal Revenue is 0 at Price 1250.
Step-by-step explanation:
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