Question

The total cost (TC) of a monopolistic firm is a linear function of output (q), expressed as TC=20q. Market demand for the firm is p=100-2q.

a. Determine the monopolistic firm's profit-maximizing output and price.

Answer 1

The profit-maximizing output for a monopolistic firm is approximately 4.55 units, and the price is approximately $90.90.

Step-by-step explanation:

The profit-maximizing output and price for a monopolistic firm can be determined using the marginal revenue (MR) and marginal cost (MC) approach. The firm will produce the quantity where MR = MC. In this case, MR is based on the demand curve, which is p=100-2q. MC, on the other hand, is given as TC=20q.

To find the quantity where MR = MC, we equate the two equations:

100 - 2q = 20q

100 = 22q

q = 100/22

q ≈ 4.55 (rounded to the nearest decimal place)

So, the profit-maximizing output is approximately 4.55 units.

To find the price, we substitute the value of q back into the demand equation:

p = 100 - 2(4.55)

p ≈ 100 - 9.1

p ≈ 90.9

So, the profit-maximizing price is approximately $90.90.