You are the manager of College Computers, a manufacturer of customized computers

Question

You are the manager of College Computers, a manufacturer of customized computers that meet the specifications required by the local university. Over 90% of your customers consist of college students. College Computers is not the only firm that builds computers to meet this university’s specifications; indeed, it competes with many manufactures 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 = 1,000 – P and its weekly cost of producing computers is C(Q) = 2000 + Q2. Its marginal revenue is MR = 1000 -2Q and its marginal cost is MC = 2Q. The other firms in the industry sell PCs at $600.

1.        What is the market model and the rule for determining the quantity and price of output which maximize your firm’s profits in the short run?

2.        What is the optimal level of output?

3.        What is the optimal price level?

4.        What is the profit level give the output and pricing determined above?

5.        What long term adjustments do you anticipate?

Explanation / Answer

1. Here, the College Computers is the monopolistically competitive firm.

The weekly demand function is:  Q = 1,000 – P

The inverse demand function is : P = 1,000 – Q

TR = P x Q = 1,000Q - Q2

MR = 1,000 - 2Q

TC = 2000 + Q2

MC = 2Q

The rule for determining the quantity and price of output which maximize your firm’s profits in the short run is: MR = MC

2. MR = MC

1,000 - 2Q = 2Q

This implies:

4Q = 1,000

Q = 250

Therefore, the optimal level of output is 250 units.

3. Substituting the value of Q in inverse demand function:

  P = 1,000 – Q = P = 1,000 – 250 = $750

  Therefore, the optimal level of price is $750.

4. Profit = TR - TC

= P x Q - (2000 + Q2)

= 750 x 250 - (2000 - 2502)

= 187,500 - 60,500 = $127,000

5. In the firm would increase production so as to get normal profit.

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