Chapter 11: Competitive Markets

1. Chapter 11: Competitive Markets Profit Maximization Example Profit Maximization at Beau Apparel: An Illustration

2. Profit Maximization at Beau Apparel • Beau Apparel, Inc., is a clothing manufacturer that produces moderately priced men’s shirts. • Beau Apparel is a price-taker • Beau Apparel is one of many firms that produce a fairly homogeneous product, and none of the firms in this moderate-price shirt market engages in any significant advertising. • To choose the quantity that maximizes its profits, Beau Apparel needs estimates of the market price and its costs

3. Price and Cost Forecasts • In December 2010, the manager of Beau Apparel prepares the firm’s production plan for the first quarter of 2011. • The Marketing/Forecasting Division forecasts a 2011 price of $15 • The manager of Beau Apparel estimates a cubic equation for short-run cost AVC = 20 – 0.003Q + 0.00000025Q2 • the coefficients from the AVC function are used to determine the short-run marginal cost function, SMC = a + 2bQ + 3cQ2 SMC = 20 – 0.006Q + 0.00000075Q2 • Now that the firm knows the price and estimates of AVC and MC: • Should the firm produce or shut down? • If it produces, what is the profit maximizing quantity?

4. The Shutdown Decision • To answer the shut down question, the manager determines • the quantity that minimizes AVC • and the value of AVC at that quantity. • It was previously determined that • AVC = 20 – 0.003Q + 0.00000025Q2. • The quantity where AVC is minimized is –b/(2c) • Min Q = -(-0.003)/(2 * 0.00000025) = 6000 • Now substitute the 6000 output level back into the AVC equation. • Min AVC = 20 – (0.003*6000) + (0.00000025*60002) = $11 • AVC is minimized at $11 while producing 6000 units.

5. The Shutdown Decision Cont. • The manager now compares this minimum AVC with the forecasted price of $15. • Since $15 > $11, the firm should produce and not shutdown.

6. The Output Decision • To maximize profits or minimize loss, marginal revenue (price for a price-taker) should equal marginal cost. • P = SMC = 20 – 0.006Q + 0.00000075Q2 • 15 = 20 – 0.006Q + 0.00000075Q2 • 0 = 5 – 0.006Q + 0.00000075Q2 • Since this equation cannot be factored algebraically, it must be solved using the quadratic formula. • Q = (-(-0.006) ± √(0.0062 – 4*5*0.00000075)) ÷ (2*0.00000075) • Q = (0.006 ± 0.004583) ÷ 0.0000015 • There are two solutions: Q = 945 and Q = 7,055

7. The Output Decision Cont. • Calculate AVC for each quantity, Q = 945 and Q = 7,055 • AVC945 = 20 – (0.003*945) + (0.00000025*9452) = $17.39 • AVC7,055 = 20 – (0.003*7055) + (0.00000025*70552) = $11.28 • Compare the price to AVC for each quantity. • At Q = 945, price = $15 < $17 = AVC. The manager would not produce here, since the AVC is higher than the price. • At Q = 7,055, price = $15 > $ 11.28 = AVC. The manager will produce 7,055 units, because price is greater than AVC. • Now that the manager has determined the profit maximizing quantity, he calculates the profit or loss.

8. Computing Total Profit or Loss • Remember • TR = P*Q • TVC = AVC*Q • TC = TVC + TFC = (AVC*Q) + TFC • TP = TR – TC = (P*Q) – [(AVC*Q) + TFC] • The manager expects TFC to be $30,000. • For P = $15, we have already calculated that AVC = $11.28 and Q = 7,055 units. • TP = (15*7055) – (11.28*7055) -30,000 • TP = -$3,755 • Even though Beau is experiencing a loss at $15, they should continue to produce, since the loss of -$3,755 is much less than the $30,000 in fixed costs that would still have to be paid even if production stopped. • AVC ≤ P < ATC