Question

A monopolist with constant average and marginal cost equal to 8 (AC = MC = 8) faces demand Q = 100 - P, implying that its marginal revenue is MR = 100 - 2Q.

Its profit-maximizing quantity is:

a) 8 b) 46 c) 50 d) 92

Answer 1

b) 46

Step-by-step explanation:

Provided that

AC = MC = 8

Q = 100 - P

Or P = 100 - Q

MR = 100 - 2Q

So the total revenue would be

= Price × Quantity

So if we put the values of p in the total revenue so the equation would be

= 100 × Q – Q^2

Now we have to take the differentiation with respect to marginal revenue which equal to

= d(Total revenue) ÷ d(Quantity)

If we differentiated than the value would come

= 100 - 2Q

And

We know that

MR = MC

100 - 2Q = 8

2Q = 92

Q = 46