The estimated short-run cost function of a Japanese beer manufacturer is C(q) = 0.55q 1.67 + 800/q

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The estimated short-run cost function of a Japanese beer manufacturer is C(q) = 0.55q1.67 + 800/q (see the application Short-Run Cost Curves for a Japanese Beer Manufacturer). At what positive quantity does the average cost function reach its minimum? If a $400 lump-sum tax is applied to the firm, at what positive quantity is the after-tax average cost minimized?

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