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Calculating optimal output levels

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Syracuse Paper supplies printer paper in upstate New York. Like the output of other wholesale distributors, Syracuse Paper must meet strict guidelines and the printer paper supply industry can be regarded as perfectly competitive. Total and marginal cost relations are:

TC = $3,600 + $5Q + $0.01Q2
MC = dTC/ dQ = $5 + $0.02Q

where Q is cases of printer paper per day.

A. Calculate the firm's optimal output and profits if prices are stable at $20 per case.
B. Calculate optimal output and profits if prices rise to $25 per case.
C. If Syracuse Paper is typical of firms in the industry, calculate the firm's equilibrium output, price, and profit levels.

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Solution Summary

Solution describes the steps to calculate optimal output levels and associated profits at the given price levels.

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A. Calculate the firm's optimal output and profits if prices are stable at $20 per case.

Perfectly competitive firm sets its output such that MC=Price to maximize its profits.
Put MC=Price=$20
20= 5 + 0.02Q
0.02Q=15
Q=750

Total Revenue=P*Q=20*750=$15000
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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