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    Find consumer's surplus at maximum profit level.

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    A monopoly has a total cost function c = 250 + x^2 + 5x for its product, which has demand function p = (-1/3)x^2 - 2x +30.

    Find the consumer's surplus at the point where the monopoly has a maximum profit.

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    Solution Preview

    First we graph the demand curve and cost curve.

    You may want to look at http://en.wikipedia.org/wiki/File:Monopoly-surpluses.svg; this picture will tell you where everything is (labeled clearly). Our graph (attached) will look something like ...

    Solution Summary

    The solution finds consumer's surplus at maximum profit level.