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 percent of your clientele consists of college students. College computer 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 as 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) = 2,000 +Q^2. If other firms in the industry sell PCs at $600m what price and quantity of computers should you produce to maximize your firm’s profits? What long run adjustments should you anticipate? Explain.
May i have step by step on how the answer is retrieved. I saw it on here already but do not know how to come up with that answer and i need to show my work. thank you

Explanation / Answer

Cost curve is given by, C(Q) = 2000 + Q^2 therefore marginal cost, MC(Q) = 2*Q (differentiating the cost curve function) now, Q = 1000 - P hence, P = 1000 - Q Now return is given by, P*Q = (1000-Q)*Q (price multiplied the quantity) Return = 1000*Q - Q^2 therefore the marginal return, MR(Q) = 1000 - 2*Q (differentiating the return curve function) For optimality, Marginal cost = Marginal Return i.e. 2*Q = 1000 - 2*Q hence, Q = 250 therefore P = 1000 - 250 P = 750 Answer:: The price would be $750 and Quantity would be 250 For long run, Bringing down the cost is an option due to the market competition. Since other firms are selling computers at $600 and we are selling at $750,we would face problems in the long run and must try to reduce the costs and due to which the quantity will grow and we can earn more than before and also try to knock other firms out of the market if possible...

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