Finding the Profit-Maximizing Quantity Using the First-Order Condition (dΠ/dQ = 0)
The profit-maximizing quantity (Q*) is found by applying the first-order condition, which involves setting the first derivative of the profit function (Π) with respect to quantity (Q) equal to zero (dΠ/dQ = 0). This mathematical step identifies the point on the profit function graph where the slope is zero, indicating a potential maximum. This first-order condition is algebraically equivalent to the economic principle that a firm should produce at a level where marginal revenue equals marginal cost (MR = MC).
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Finding the Profit-Maximizing Quantity Using the First-Order Condition (dΠ/dQ = 0)
Figure 7.4b: Cheerios Profit Function Graph (Profit-Quantity Diagram)
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Finding the Profit-Maximizing Quantity Using the First-Order Condition (dΠ/dQ = 0)
Learn After
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Figure 7.4b: Cheerios Profit Function Graph (Profit-Quantity Diagram)
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- At Q = 1,000 units, they find dΠ/dQ = +$15.
- At Q = 2,000 units, they find dΠ/dQ = -$10.
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