Question #51666

A monopolist’s demand curve is given by P = 100 – 2q.

(a) Find his marginal revenue function.

(b) At what price is marginal revenue zero

(a) Find his marginal revenue function.

(b) At what price is marginal revenue zero

Expert's answer

(a). First of all it is necessary to calculate total revenue as a

function of quantity.

TR = P * Q= (100 – 2q)*q = 100q – 2q^2

So, the marginal revenue function can be calculating as derivative

form total revenue:

MR = d TR /d Q = 100 – 4q

(b). If MR = 0

100 – 4q = 0

4q = 100

q = 25

P = 100 – 2q = 100 – 50 = 50

function of quantity.

TR = P * Q= (100 – 2q)*q = 100q – 2q^2

So, the marginal revenue function can be calculating as derivative

form total revenue:

MR = d TR /d Q = 100 – 4q

(b). If MR = 0

100 – 4q = 0

4q = 100

q = 25

P = 100 – 2q = 100 – 50 = 50

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