Verifying the Profit Maximum for a Price-Taker Using the Second-Order Condition
To confirm that the production quantity where price equals marginal cost (P = C'(Q)) corresponds to a profit maximum, the second-order condition must be examined. This is accomplished by finding the second derivative of the profit function with respect to quantity. A negative value for the second derivative at the point where P=C'(Q) confirms that it represents a local maximum for profit.
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