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Determine the profit-maximizing output and price under 3 scenarios.

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Using the function C(Q) = 400+50Q+5Q^2 determine the profit-maximizing output and price and discuss its long-run implications under 3 scenarios.

1) The firm is a perfect substitute with a similar product offered by Firm B, Firm C that have similar cost functions and that currently sell for $200 each.

2) The firm firm has NO substitutes and so is a monopolist, and the demand for the Firm is expected to be forever Q=30-(1/5)P (note use earlier listed cost function)

3) The firm has no substitutes and currently the demand for the firms product is Q = 80-(1/5)P but the firm anticipates that other firms can develop close substitutes in the future.

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Solution depicts the steps to estimate the optimal output and price combination in the given cases.

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Using the function C(Q) = 400+50Q+5Q^2 determine the profit-maximizing output and price and discuss its long-run implications under 3 scenarios.

1) C(Q)=400+50Q+5Q^2
Marginal Cost=MC=dC(Q)/dQ=50+10Q

Since the product of given firm is a perfect substitute of the product of other given firms. Given firm will behave as perfectly competitive firm and will set its output such that MC=Prevailing market price i.e.
MC=50+10Q=200

Q=(200-50)/10=15 units
Price of product=Prevailing market price=$200

Total ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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