Question

You are the manager of College Computers, a manufacturer of customized computers that meet the specifications required by the local university. Over 90 percent of your clientele consists of college students. College Computers is not the only firm that builds computers to meet this university’s specifications; indeed, it competes with many manufacturers online and through traditional retail outlets. To attract its large student clientele, College Computers runs a weekly ad in the student paper advertising its “free service after the sale” policy in an attempt to differentiate itself from the competition. The weekly demand for computers produced by College Computers is given by Q = 800 – 2P, and its weekly cost of producing computers is C(Q) = 1,200 + 2Q2. If other firms in the industry sell PCs at $300, what price and quantity of computers should you produce to maximize your firm’s profits?

Price: $

Quantity: computers

Answer 1

The firm is able to differentiate its product from other firms on basis of its offering of free after sales service.

This differentiation technique indicates that firm is a monopolistically competitive firm.

A monopolistically competitive firm maximizes profit when it produce that level of output corresponding to which MR equals MC.

Demand function is as follows -

Q = 800 - 2P

2P = 800 - Q

P = 400 - 0.5Q

Total revenue function is as follows -

TR = P * Q = [400 - 0.5Q] * Q = 400Q - 0.5Q2

Marginal revenue function is as follows -

MR = dTR/dQ = d(400Q - 0.5Q2)/dQ = 400 - Q

Cost function is as follows -

C = 1,200 + 2Q2

Marginal cost function is as follows -

MC = dC/dQ = d(1,200 + 2Q2)/dQ = 4Q

Equating MR and MC

MR = MC

400 - Q = 4Q

5Q = 400

Q = 80

P = 400 - 0.5Q = 400 - (0.5 * 80) = 400 - 40 = 360

Thus,

In order to maximize profit,

The firm should charge $360 per computer.

The firm should produce 80 computers.