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

Answer - College computer are facing a monopolistically competitive market. College Computers weekly demand curve is (Q) = 800 - 2P

P = 400 - 0.5Q

Weekly total revenue (TR) = P*Q

TR = 400Q - 0.5Q²

MR = TR / Q

MR = 400 - Q

Weekly cost of producing computers is C(Q) = 1200 + 2Q²  

MC = C(Q) / Q

MC = 4Q

The firm will earn maximum profit when MR = MC. Equate marginal revenue and marginal cost.

400 - Q = 4Q

Add 'Q' both side

400 = 5Q

Q = 80 computers

Optimal output for College Computers is 80 units.

The will set optimal price at,

P = 400 - 0.5(80)

P = 400 - 40

P = $360 per computer

Weekly total revenue (TR) = 360 * 80

TR = $28800

TC = 1200 + 2(80)²

TC = 1200 + 12800

TC = $14000

College computer total profit = TR - TC

Profit = 28800 - 14000

Profit = $14800

The firm will sell 80 computers and chagre $360 in order to maximize its profit in the market.