Question

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? ​

Answer 1

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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