CHAPTER • Profit Maximization and Competitive Supply 285 Cost, revenue, profit (dollars per year) C(q) R(q) A F IGURE 8.1 PROFIT MAXIMIZATION IN THE SHORT RUN B A firm chooses output q*, so that profit, the difference AB between revenue R and cost C, is maximized At that output, marginal revenue (the slope of the revenue curve) is equal to marginal cost (the slope of the cost curve) q0 q* q1 π (q) Output (units per year) For the firm illustrated in Figure 8.1, profit is negative at low levels of output because revenue is insufficient to cover fixed and variable costs As output increases, revenue rises more rapidly than cost, so that profit eventually becomes positive Profit continues to increase until output reaches the level q* At this point, marginal revenue and marginal cost are equal, and the vertical distance between revenue and cost, AB, is greatest q* is the profit-maximizing output level Note that at output levels above q*, cost rises more rapidly than revenue— i.e., marginal revenue is less than marginal cost Thus, profit declines from its maximum when output increases above q* The rule that profit is maximized when marginal revenue is equal to marginal cost holds for all firms, whether competitive or not This important rule can also be derived algebraically Profit, p = R - C, is maximized at the point at which an additional increment to output leaves profit unchanged (i.e., ⌬p/⌬q = 0): ⌬p/⌬q = ⌬R/⌬q - ⌬C/⌬q = ⌬R/⌬q is marginal revenue MR and ⌬C/⌬q is marginal cost MC Thus we conclude that profit is maximized when MR - MC = 0, so that MR(q) = MC(q) Demand and Marginal Revenue for a Competitive Firm Because each firm in a competitive industry sells only a small fraction of the entire industry output, how much output the firm decides to sell will have no effect on the market price of the product The market price is determined by the industry demand and supply curves Therefore, the competitive firm is a price taker Recall that price taking is one of the fundamental assumptions of perfect competition The price-taking firm knows that its production decision will have no effect on the price of the product For example, when a farmer is deciding how many acres of wheat to plant in a given year, he can take the market price of wheat—say, $4 per bushel—as given That price will not be affected by his acreage decision