A firm's market is characterized by an inverse demand function of P = 200 - 4Q, and its total cost of production is given by C(Q) = 500 + 20Q. An analyst for the firm has determined that the profit function, expressed solely in terms of quantity (Q), is Π(Q) = -300 - 24Q.
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A firm's profit (Π) is a function of the quantity (Q) it produces. This function can be derived from its total cost function, C(Q), and the market's inverse demand function, P(Q), using the formula Π(Q) = [P(Q) * Q] - C(Q). Match each set of cost and demand functions to the correct resulting profit function.
A firm's market is characterized by an inverse demand function of P = 200 - 4Q, and its total cost of production is given by C(Q) = 500 + 20Q. An analyst for the firm has determined that the profit function, expressed solely in terms of quantity (Q), is Π(Q) = -300 - 24Q.
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Finding the Profit-Maximizing Quantity Using the First-Order Condition (dΠ/dQ = 0)