a) If a business has a long-run cost (TC) function given by TC = aq^3 – bq^2 + ca where q = the rate of output, and a, b and c are all positive parameters, show that average cost is always positive if and only if b^2 < 4ac and a >0.

Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter3: Benefits, Costs, And Decisions
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a) If a business has a long-run cost (TC) function given by
TC = aq^3 - bq^2 + ca
%3D
where q = the rate of output, and a, b and c are all positive parameters, show that
average cost is always positive if and only if b^2 < 4ac and a >0.
Transcribed Image Text:a) If a business has a long-run cost (TC) function given by TC = aq^3 - bq^2 + ca %3D where q = the rate of output, and a, b and c are all positive parameters, show that average cost is always positive if and only if b^2 < 4ac and a >0.
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