Question

Suppose that the boutique has a monopoly on Miss Me jeans. The market demand for the jeans P = 500 – 3Q and MR = 500 – 6Q. The marginal cost of selling the jeans is MC = 20 + 2Q. What is the profit-maximizing price the monopolist should charge for the jeans and how many will they sell?

Answer 1

The boutique has a monopoly on Miss Me jeans.

The market demand for jeans is given as

P = 500 - 3.Q

The Marginal Revenue is given as

MR = 500 - 6.Q

The Marginal Cost of selling a jeans is given as

MC = 20 + 2.Q

We know that, a monopolist maximizes profit at that point where Marginal Revenue (MR) equals Marginal Cost (MC) i.e.

MR = MC

or, 500 - 6.Q = 20 + 2.Q

or, 8.Q = 480

or, Q* = 60

Hence, the monopolist will sell 60 jeans.

Now, from the demand curve, putting Q*=60 we get,

P = 500 - 3.Q* = 500 - 3×60

or, P = $320

Hence, the profit maximizing price that the monopolist should charge is $320

Hope the solution is clear to you my friend.