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 What long-run adjustments should you anticipate?

Answer 1

The price and quantity of computers that should be produced to maximize the firm’s profits will be $360 and 80 computers.

The demand curve for College Computers is given as (Q) = 800 - 2P where, P = 400 - 0.5Q.

Therefore, the weekly total revenue will be:

= (400 - 0.5Q) × Q

= 400Q - 05Q²

Marginal revenue = 400 - Q

Weekly cost of producing computers will be:

= 1200 + 2Q²

Marginal cost = 4Q

Maximum profit will b earned when MR = MC

Therefore, 400 - Q = 4Q

Collect like terms

4Q + Q = 400

5Q = 400

Q = 400/5

Q = 80

Quantity = 80 units

Therefore, the price will be:

P = 400 - 0.5Q

P = 400 - 0.5(80)

P = 400 - 40.

P = 360

The price is $360.

The weekly total revenue will be:

TR = price × quantity.

TR = 360 × 80

TR = $28800

The total cost will be:

TC = 1200 + 2(80)²

TC = 1200 + 12800

TC = 14000

Therefore, the profit will be:

= TR - TC

= $28800 - $14000

= $14800

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