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 Q2
the coefficients from the AVC function are used to determine the short-run marginal cost function, SMC = a + 2bQ + 3cQ2
SMC = 20 – 0.006Q Q2
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 Q2.
The quantity where AVC is minimized is –b/(2c)
Min Q = -(-0.003)/(2 * ) = 6000
Now substitute the 6000 output level back into the AVC equation.
Min AVC = 20 – (0.003*6000) + ( *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 Q2
15 = 20 – 0.006Q Q2
0 = 5 – 0.006Q Q2
Since this equation cannot be factored algebraically, it must be solved using the quadratic formula.
Q = (-(-0.006) ± √( – 4*5* )) ÷ (2* )
Q = (0.006 ± ) ÷
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) + ( *9452) = $17.39
AVC7,055 = 20 – (0.003*7055) + ( *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 > $ = 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