We now turn to the output decision facing the manager of a price-taking firm op- erating in a competitive industry in the short run. Recall that the short run is the time period during which a firm employs one or more fixed inputs and any num- ber of variable inputs. The fixed costs are sunk and must be paid even if the firm decides to cease production. The variable costs increase with the level of output and can be avoided if the manager decides to cease production.1
A manager must make two decisions in the short run. The first decision is whether to produce or shut down during the period. Shut down means the manager decides to produce zero output by hiring no variable inputs (and no quasi-fixed inputs, if the firm uses any). When production is zero, the only costs incurred by the firm are the unavoidable fixed costs. To make the decision to pro- duce a positive level of output rather than shut down, the manager considers only the avoidable variable costs that will be incurred if the firm produces some posi- tive quantity of goods or services. As you will see in this section, a manager will choose to produce a positive amount of output only if doing so generates enough total revenue to cover the firm’s avoidable total variable costs of production.
Now try Technical Problem 1.
shut down
A firm produces zero output in the short run but must still pay for fixed inputs.
1Firms sometimes incur quasi-fixed costs that do not vary with output but can be avoided if the manager decides to cease production in either the short run or long run. When there are quasi-fixed inputs, total avoidable cost is the sum of total variable cost plus total quasi-fixed cost. To keep our discussions as simple as possible throughout this chapter and the rest of the book, we will treat total variable cost as the only component of total avoidable cost, unless we specifically state the firm employs quasi-fixed inputs.
If the manager makes the first decision to produce rather than shut down, the second decision involves choosing the optimal level of output. Using the terminology presented in Chapter 3, the optimal level of output is the quantity that maximizes the firm’s net benefit function, which is economic profit (p). Un- der some circumstances, which we discuss later, a manager will choose to incur losses (i.e., profit is negative) yet continue to produce rather than shut down.
In such a situation, the manager will choose the output that minimizes the loss of the firm. Because minimizing a loss is equivalent to maximizing a negative profit, the decision rule for finding the optimal level of production is exactly the same regardless of whether profit is positive or negative. For this reason, we will speak of profit maximization even though the rule applies to a firm that is minimizing a loss.
In this section, we first discuss the firm’s output decision when it can earn positive economic profit. We apply marginal analysis to find the profit- maximizing output. We then explain the conditions under which the manager should choose to shut down rather than produce. Next, we return to a central theme from Chapter 3: sunk costs, fixed costs, and average costs are irrelevant for making optimal decisions. We then finish this section by deriving the supply curve for a competitive, price-taking firm.
The Output Decision: Earning Positive Economic Profit
Figure 11.3 shows a typical set of short-run cost curves: short-run marginal cost (SMC), average total cost (ATC), and average variable cost (AVC). Average fixed cost is omitted for convenience and because, as we demonstrated in Chapter 3 and show you again in this section, fixed costs are irrelevant for decision-making purposes. Let’s suppose the market-determined price, and therefore mar- ginal revenue, is $36 per unit. What level of output should the firm produce to maximize profit?
One of the more common mistakes managers make when choosing a firm’s production level is to select the quantity that generates the highest possible profit margin for the firm, rather than the maximum profit. Profit margin is the differ- ence between price and average total cost, P 2 ATC. When all units of output are sold for the same price, profit margin is equivalent to average profit.2 Average profit is simply total profit divided by output, pyQ, and thus measures profit per unit. The equivalence of average profit and profit margin is easy to see with only a bit of algebra
Average profit 5 p __Q 5 (P 2 ATC)Q
___________
Q 5 P 2 ATC 5 Profit margin
profit margin
The difference between price and average total cost: P 2 ATC.
average profit Total profit divided by quantity: p/Q. Measures profit per unit and is equivalent to profit margin when all units sell for the same price.
2The practice of charging the same price for every unit sold is called uniform pricing. In Chapter 14, we will examine some pricing techniques that involve charging different prices for different units of the same good or service. In these instances, profit margin will vary for different units sold and thus will not be equivalent to average profit.
Panel A — Common mistake: maximizing profit margin
Price and cost (dollars) 16
Quantity N
N
B A u
t
r F
SMC H
ATC AVC B A F
u r
s
SMC
D: MR 5 P 5 $36
D: MR 5 P 5 $36 ATC
AVC 36
0 100 400 600
Lost profit (5 $2,200) Profit 5 $8,000 Profit
margin 5 $20
Profit margin 5 $17
Panel B — Correct decision: maximizing total profit 16
19
Price and cost (dollars)
Quantity 36
40
0 100 400 600 630
Profit 5 $10,200 F I G U R E 11.3
Profit Maximization when P 5 $36
I L L U S T R AT I O N 1 1 . 1 Chevron Focuses on Profit Margin:
Can It Maximize Profit Anyway?
We commented previously in this chapter that man- agers sometimes mistakenly believe that increasing or even maximizing profit margin should be one of their principle objectives in managerial decision making.
Perhaps these managers believe maximizing profit and maximizing profit margin are coinciding goals.
They certainly are not.
In an interview with The Wall Street Journal,a Mike Wirth, executive vice president for global refining and marketing operations at Chevron Corporation, announced that Chevron is currently “focused … on being able to widen our (profit) margins” for refin- ing crude oil into gasoline, diesel, jet fuel, and other valuable refined products. As you saw in Figure 11.3, maximizing profit margin—or equivalently, maximizing profit per unit or average profit—is generally inconsistent with the goal of maximizing profit and value of the firm. In this Illustration we will examine Chevron’s plans to expand its profit margin to highlight the pitfalls of making mana- gerial decisions based on pushing up profit margin rather than pushing up profit. While The Wall Street Journal article doesn’t provide all of the quantitative
details we’d like to have, we can nonetheless show you, in general terms, why Chevron’s management can choose to either maximize profit margin or maxi- mize profit along with the value of Chevron stock—it cannot do both.
To allow for multiple refined products in the sim- plest possible way, the nearby graph measures refined output on the horizontal axis as the number of barrels of a blend of the various products, such as gasoline, die- sel, jet fuel, and so on. Obviously, refineries would not actually combine or “package” gasoline, diesel, and jet fuel in the same 42-gallon barrel, it nonetheless simpli- fies our graphs of demand and cost to assume that each barrel of output contains portions of every product.
Subject to some constraints associated with the petro- chemistry of refining processes, refiners are able to vary their blends of products coming from the crude oil input in a way that maximizes the total revenue generated from selling multiple products. We will not need to worry about how Chevron chooses the optimal blend here; we will just assume the blending decision has been made optimally. Because Chevron Corp. sells its petroleum products in markets that closely resemble perfect competition, the demand for Chevron’s refined products is shown in the nearby figure as perfectly elastic (i.e., horizontal). The price per barrel of refined product on the vertical axis equals the number of dol- lars needed to buy the blend of products found in each barrel, based on the prevailing market-determined prices for gasoline, diesel, jet fuel, etc.b The figure also shows a typical set of <-shaped short-run cost curves.
Before Chevron decided to pursue higher refinery profit margins, as stated in The Wall Street Journal article, let’s suppose Chevron was making its out- put decision correctly to maximize profit at point a where P 5 SMC. At Q*, Chevron’s initial profit mar- gin is equal to the vertical distance between points a and b in our figure.
Now let’s see what happens when Chevron’s management decides to increase profit margin, as announced by Mr. Wirth. As a means of achieving higher profit margins, The Wall Street Journal reports that Chevron is restructuring its costs by making long-run investments to lower production costs (recall how this works from our discussion of long-run restructuring P
m
Q Q* Q*'
b a
SMC ATC
D: P 5 MR
c m'
b' a'
SMC'
ATC'
Price and cost of refined product (dollars/barrel)
Quantity of refined product (barrels) Source: Jessica Resnick-Ault, “Chevron Focuses on Refiner- ies,” WSJ.com, May 13, 2009.
in Chapter 9). Chevron has undertaken “an invest- ment program, that’s long overdue” to create cost sav- ings by upgrading its refineries “to extract as much capacity as possible from its refineries.” The effort, known as “Reliability Refinery,” raised capacity utilization of refinery capital by 6.6 percent, compared to a year ago, and raised throughput by 60,000 bar- rels per day for the same time period. As you learned in Chapter 8, a rise in productivity of refineries will cause a reduction in production costs at every level of refined output. In the figure, we show the effect of Chevron’s Reliability Refinery project by shifting costs downward to ATC9 and SMC9.c
Now you can clearly see why Chevron cannot maximize both profit and the spread between P and ATC. If the company continues to produce Q* bar- rels of refined product, profit margin will indeed in- crease because unit costs are now lower. In the figure, the vertical distance between P and ATC9 (distance a to c) is larger than before the Reliability Refinery effort reduced refining costs (distance a to b). Mr. Wirth is correct when he claims that by lowering cost and rais- ing profit margin, Chevron now makes more profit on Q* units. But herein lies the problem we wish to illus- trate: While Chevron has truly succeeded in squeezing more (total) profit out of the same amount of refined product, the company is nonetheless making an error in its output decision by focusing on profit margin. Be- cause of the reduction in marginal production costs, Chevron must increase its output of refined product to make the greatest possible profit—even though in- creasing output will lower its profit margin. As you can see clearly in the nearby figure, the new profit- maximizing quantity occurs at the higher output level, Q*', where P 5 SMC' at point a'. Profit margin at Q*', which is the distance a' to b', is less than profit margin at Q*, which is the distance a to c.
Based on The Wall Street Journal article, we do not know whether Chevron took advantage of its lower marginal cost to expand output at its refiner- ies. However, it is not farfetched at all to imagine that production managers at Chevron would be un- willing to ramp up output and risk upsetting some other manager at Chevron who sees profit margins getting squeezed as output expands from Q* to Q*'.
In fact, if Chevron’s management team truly focuses all of its attention on profit margin, as Mr. Wirth
suggests, then managers might even make matters worse by reducing output from Q* to __Q . This would maximize Chevron’s profit margin, but reduce its profit and the value of the corporation. Again, we do not have enough information from The Wall Street Journal interview to know exactly what decision process was followed at Chevron. However, we know enough to be able to lay out the troubles and pitfalls that Chevron’s managers would face if they get side- tracked by concerns over profit margin. The Reliability Refinery project was not a mistake for Chevron; it lowered cost and increased profit. The mistake here, if in fact any mistake was even made, was to let profit margin creep into the output decision.
As you can see from this Illustration and our presentation in Figure 11.3, businesses cannot maxi- mize both (total) profit, TR 2 TC, and profit margin, P 2 ATC, at the same time (i.e., at the same level of output).d For this reason, managers should ignore profit margin when making output decisions. We are not aware of any studies or quantitative estimates of corporate value lost by managers who mistakenly try to maximize profit margin, but in view of the seemingly widespread desire by managers to earn higher profit margins, we suspect the cost could be substantial.
aThis Illustration is based on the online article by Jessica Resnick-Ault, “Chevron Focuses on Refineries,” WSJ.com, May 13, 2009.
bSuppose, for example, each 42-gallon barrel of blend contains 24 gallons of gasoline, 16 gallons of jet fuel, and 2 gallons of worthless gunk. Further suppose market prices for gasoline and jet fuel are, respectively, $3/gallon and
$2/gallon. The price for a barrel of this blend of refined products is $104 per barrel, which is the amount of revenue each barrel generates when the gasoline and jet fuel are sold at market prices [i.e., $104 5 ($3 3 24) 1 ($2 3 16)].
cTheoretically, the quantity where ATC reaches its mini- mum value could rise, fall, or stay the same. Strictly for convenience, we shifted ATC down in a way that leaves the minimum point on ATC’ unchanged at __Q .
dThere is only one very narrow exception to this rule: When market price happens to be equal to minimum average total cost, then price also equals marginal cost and profit will be maximized (and equal to zero) at the same output that maximizes profit margin.
This relation between average profit and profit margin also holds in the long run;
just substitute LAC for ATC.
The output that maximizes profit margin (P 2 ATC) does not also maximize profit (TR 2 TC), with only one superficial exception.3 For this reason, profit- maximizing managers should ignore profit margin (or profit per unit) when making their production decisions. Suppose the manager of a firm facing the costs shown in Figure 11.3 chooses to produce only 400 units of output in Panel A, because the manager sees the difference between price and average total cost is maximized at 400 units (i.e., where ATC is minimized). Notice in Panel A that the vertical distance from point F to point N, which measures profit margin (and aver- age profit) at 400 units, is $20 ($36 2 $16). By visual inspection, you can verify that
$20 must be the highest possible profit margin because price is $36 for every unit sold and average total cost reaches its minimum value, $16, at point N.
Let’s now compute the profit when the manager mistakenly chooses to produce 400 units. As you can see in Panel A, at 400 units, total revenue is $14,400, which is price times quantity ($36 3 400), and total cost is $6,400, which is average total cost times quantity ($16 3 400). Profit, then, is $8,000 (5$14,400 2 $6,400) when the firm produces 400 units and maximizes profit margin.4 So, what’s wrong with making a profit of $8,000?
The answer is simple: This firm could make even more profit—$10,200 to be precise—by producing 600 units, as shown in Panel B. By expanding production from 400 to 600 units, total profit (p) rises as profit margin falls or, equivalently, as average profit falls. Plenty of highly paid CEOs find this outcome puzzling.
Hardly a day passes that you will not see, somewhere in the business news, an executive manager bragging about raising profit margins or promising to do so in the future. We will now clear up this confusion by employing the logic of mar- ginal analysis presented in Chapter 3.
Return to point N in Panel A where the firm is producing and selling 400 units.
Let the manager increase production by 1 unit to 401 units. Because this firm is a price-taking firm for which price equals marginal revenue (P 5 $36 5 MR), sell- ing the 401st unit for $36 causes total revenue to rise by $36. Producing the 401st unit causes total cost to rise by the amount of short-run marginal cost, which is
$16 (approximately). By choosing to produce and sell the 401st unit, the manager adds $36 to revenue and adds only $16 to cost, thereby adding $20 to the firm’s total profit. By this same reasoning, the manager would continue increasing pro- duction as long as MR (or, equivalently, P) is greater than SMC. From 401 units to 600 units at point A, each unit adds to total profit the difference between P and SMC. Thus, output should be increased to 600 units, as shown in Panel B, where P 5 MR 5 SMC 5 $36. At 600 units, total revenue is $21,600 (5$36 3 600).
3When market price is exactly equal to minimum average total cost (P 5 minimum ATC), price also equals marginal cost (P 5 SMC) and only at this unique quantity is it possible to maximize both profit margin and total profit.
4Notice that total profit can also be calculated by multiplying profit margin (average profit) by quantity: $8,000 5 $20 3 400.
Total cost is $11,400 (5$19 3 600). Thus, the maximum possible profit is $10,200 (5$21,600 2 $11,400). In Panel A, the gray-shaded area below MR and above SMC is equal to the value of the lost profit when only 400 units are produced instead of 600 units. We can summarize this very important discussion in a principle:
Principle Managers cannot maximize both profit and profit margin at the same level of output. For this reason, profit margin—or, equivalently, average profit—should be ignored when making profit-maximizing decisions. When a firm can make positive profit in the short run, profit is maximized at the output level where MR (5 P ) 5 SMC.
This principle applies to choosing the profit-maximizing level of any decision variable: quantity, price, input usage, advertising budget, Research and Develop- ment (R&D) spending, and so on.
So far, we have focused our attention on the loss of profit when managers pro- duce less than the profit-maximizing amount. Now suppose the manager makes the mistake of supplying too much output by producing and selling 630 units in Panel B. As you can see, marginal revenue (price) is now less than marginal cost: Price is $36 and marginal cost of the 630th unit is $40 (point H). The manager could de- crease output by 1 unit and reduce total cost by $40 (the cost of the extra resources needed to produce the 630th unit). The lost sale of the 630th unit would reduce revenue by only $36, so the firm’s profit would increase by $4. By the same rea- soning, the manager would continue to decrease production as long as MR (5 P) is less than SMC (back to point A). The gray-shaded area in Panel B is the lost profit from producing 630 units instead of 600 units. It follows from this discussion that the manager maximizes profit by choosing the level of output where MR (5 P) 5 SMC.
This rule is, of course, the rule of unconstrained maximization set forth in Chapter 3 (MB 5 MC) with profit serving as the net benefit (TB 2 TC) to be maximized.
Figure 11.4 shows the total revenue (TR), total cost (TC), and profit (p) curves for the situation presented in Figure 11.3. Notice in Panel A that TR is linear with slope equal to $36 (5 P 5 MR) because each additional unit sold adds $36 to total revenue. Also note that in Panel B, at 401 units, the slope of the profit curve is $20, which follows from the preceding discussion about producing the 401st unit. At 600 units, the maximum profit is $10,200, which occurs at the peak of the profit curve (point A') where the slope of the profit curve is zero. The points U and V in Figure 11.4 (100 units and 950 units) are sometimes called break-even points because total revenue equals total cost and the firm earns zero profit.
Because the total cost of producing 600 units ($11,400) includes the opportunity cost of the resources provided by the firm’s owners (i.e., the implicit costs), the owners earn $10,200 more than they could have earned if they had instead em- ployed their resources in their best alternative. The $10,200 economic profit, then, is a return to the owners in excess of their best alternative use of their resources.
The Output Decision: Operating at a Loss or Shutting Down
Sometimes the price of a competitive firm’s product is less the average total cost (P , ATC) for all output levels. This means that total revenue (P 3 Q) will fall
break-even points Output levels where P 5 ATC and profit equals zero: points U and V in Figure 11.4.