Question

Suppose the demand for a product faces by a monopolist firm is given by P= 120 - 2Q. If the marginal cost of producing the product is $20, what is the profit maximization price the firm should charge for the product? What are the firm's profits? Show the work.

Answer 1

Here, given the demand function of a monopolist such as P= 120 - 2Q, and the marginal cost as $20.

• The profit maximizing price of a monoolist can be calculated by equating marginal revenue and marginal cost such as:

Total revenue=price*quantity

Total revenue= (120 - 2Q)*Q

Marginal revenue= d/dt(120 - 2Q)*Q

MR=120-4Q

According to the profit maximization sitiation:

MR-MC

120-4Q=20

120-20=4Q

100=4Q

100/4=Q

Q=25

Therefore, the profit maximizing quanity would be 25.

To find the profit maximizing price, substitute Q as 25, we get

P=120-2(25)

P=120-50

P=70

So, the firm would charge $70 for the product.

• The firms profit can be calculated by subtracting total cost from total revenue.

Therefore,

Total revenue=P*Q

TR=$70*25

TR=$1,750

And,

Total cost=MC*Q

TC=$20*25

TC=$500

So, the profit of the monopolist would be:

Total revenue-Total cost=$1,750-$500

=1,250

The profit of the monopolist would be $1,250.