We will now analyze the profit-maximizing decision of firms that are pure monopolies. Keep in mind that the fundamentals of this monopoly decision apply to a large extent to all firms with market power. The manager of a monopoly treats the market demand curve as the firm’s demand curve. As was the case for perfect competition, we assume that the manager wishes to maximize profit. Thus the manager of a monopoly firm chooses the point on the market demand curve that maximizes the profit of the firm. While the manager of a monopoly does, in fact, determine the price of the good, price cannot be chosen independent of output. The manager must choose price and output combinations that lie on the market demand curve.
In Figure 12.1, for example, if the manager wishes to charge a price of $14 per unit, the monopoly firm can sell (consumers will buy) only 900 units of the product. Alternatively, if the manager decides to sell 900 units, the highest price that can be charged for this output is $14. So, while the monopolist can choose both price and output, the two choices are not independent of one another.
In practice, some monopolists choose price and let market demand determine how many units will be sold, whereas other monopolists choose the level of output to produce and then sell that output at the highest price market demand allows. Consider your electric utility company. Electric utilities set the price of a unit of electricity, say, 10 cents per kilowatt-hour, and then stand ready to supply as many kilowatt-hours as consumers wish to buy at that price. You can be sure that your electric company has estimated its demand function and knows approximately how much electricity will be demanded at various prices.
Alternatively, an automobile manufacturer might decide to produce 300,000 cars of a particular model in a given year. The manufacturer sells these cars at the highest possible price given the existing market demand. Again, you can be sure that the automobile manufacturer has estimated the demand for its cars and knows approximately the average price at which each car can be sold.
Given the demand curve facing a monopolist, choosing price to maximize profit is equivalent to choosing output to maximize profit. To be consistent with our discussion of profit maximization under perfect competition, we will view the monopolist as choosing output to maximize profit.
The basic principle of profit maximization—profit is maximized by producing and selling the output at which marginal cost equals marginal revenue—is the same for the monopoly as for the competitive firm. Amanager can increase profit by expanding output as long as the marginal revenue from the expansion exceeds the marginal cost of expanding output. A manager would reduce output if marginal revenue is less than marginal cost. The fundamental difference for a monopolist is that marginal revenue is not equal to price.
Principle A monopolist chooses the point on the market demand curve that maximizes profit. If marginal revenue exceeds marginal cost, a profit-maximizing monopolist increases output. If marginal revenue is less than marginal cost, the monopolist does not produce these additional units.
Demand and Marginal Revenue for a Monopolist
A monopoly, facing a downward-sloping demand, must lower the price in order to sell more. As shown in Figure 12.1, marginal revenue is less than price for every unit sold except the first. You will recall that marginal revenue is the change in the firm’s total revenue from an additional unit of sales; symbolically, MR= ΔTR/ΔQ. In Figure 12.1, if the firm sells 900 units at $14 each, you can see from the marginal revenue curve that the marginal or additional revenue from selling the 900th unit is $8. This means that reducing the price just enough to increase sales from 899 to 900 adds $8 to the firm’s revenue, rather than the $14 price at which the 900th unit is sold. The reason is that in order to sell the 900th unit, the firm must reduce the price on the 899 units it could have sold at the slightly higher price.
Although we set forth a technical analysis of the relation between MR and P, we can perhaps give you a bit more understanding of why MR is less than P with a hypothetical example. Suppose you manage a small appliance store that has been selling 20 radios a day at $50 apiece. You want to increase your sales of radios, so one day you reduce the price to $49. Sure enough, you sell 21 radios that day at the reduced price. So you sold one more at $49. You check the cash register and compare the receipts with those from previous days. You had been receiving $1,000 (= $50 * 20). Now you see that you have taken in $1029 (= $49 * 21) from selling radios. Your revenue increased by $29, but what happened to the $49 at which the additional radio was sold? Did someone steal $20 from the register? What happened was that, in order to sell the 21st radio, you had to take a $1 price reduction on the 20 you could have sold at $50. This $1 price reduction accounts for the “missing” $20.
Figure 12.1 illustrates the relation between demand and marginal revenue for a linear demand curve. When demand is linear, marginal revenue is twice as steep as demand and consequently lies halfway between demand and the vertical axis. When MR is positive, between 0 and 1,500 units, demand is elastic. When MR is negative, above 1,500 units, demand is inelastic. When MR equals 0, at 1,500 units, demand is unitary elastic.
Relation The market demand curve is the demand curve for the monopolist. Because the monopolist must lower price in order to sell additional units of output, marginal revenue is less than price for all but the first unit of output sold. When marginal revenue is positive (negative), demand is elastic (inelastic). For a linear market demand, the monopolist’s marginal revenue is also linear, with the same vertical intercept as demand, and is twice as steep.
Maximizing Profit at Southwest Leather Designs: An Example
Southwest Leather Designs specializes in the production of fashionable leather belts for women. Southwest’s original designs are sometimes imitated by rival leather goods manufacturers, but the Southwest logo is a registered trademark that affords the company some protection from outright counterfeiting of its products. Consequently, Southwest Leather enjoys a degree of market power that would not be present if imitators could make identical copies of its belts, trademark and all.
Table 12.1 presents the demand and cost conditions faced by the manager of Southwest Leather Designs. Columns 1 and 2 give the demand schedule for 1,000 through 9,000 units of output (leather belts) in discrete intervals of 1,000. Column 3 shows the associated total revenue schedule (price times quantity). The total cost of producing each level of output is given in column 4. The manager computes profit or loss from producing and selling each level of output by subtracting total cost from total revenue. Profit is presented in column 7. Examination of the profit column indicates that the maximum profit ($56,020) occurs when Southwest Leather Designs sells 6,000 belts at a price of $18.92.
The manager of Southwest Leather Designs can reach the same conclusion using the marginal revenue–marginal cost approach. Marginal revenue and marginal cost are shown, respectively, in columns 5 and 6. The marginal revenue from selling additional leather belts exceeds the marginal cost of producing the additional belts until 6,000 units are sold. After 6,000 units the marginal revenue for each of the next 1,000 belts is $5.48 per belt while the marginal cost for each of the next 1,000 belts is $6.25 per belt. Clearly, increasing output and sales from 6,000 to 7,000 belts would lower profit. Thus profit must increase until 6,000 units are produced; then profit decreases thereafter. This is the same solution that was obtained by subtracting total cost from total revenue: An output of 6,000 belts maximizes profit.
The example in Table 12.1 is shown graphically in Figure 12.2. Since marginal revenue and marginal cost are per-unit changes in revenue and cost over discrete changes in output of 1,000 units, we plot these values in the middle of the 1,000- unit interval. For example, marginal revenue for the first 1,000 units sold is $35 per unit for each of these 1,000 units. We plot this value of marginal revenue ($35) at 500 units of output. We do this at all levels of output for both marginal revenue and marginal cost.
In Figure 12.2, marginal revenue equals marginal cost at 6,000 units of output, which, as you saw from the table, is the profit-maximizing level of output. The demand curve shows that the price that Southwest Leather Designs will charge for the 6,000 belts is $18.92.
We turn now from a specific numerical example of profit maximization for a monopolist to a more general graphical analysis of a monopolist in the short run. In this case, we will assume for analytical convenience that output and price are continuously divisible
Short-Run Equilibrium: Profit Maximization or Loss Minimization
A monopolist, just as a perfect competitor, attains maximum profit by producing and selling the rate of output for which the positive difference between total revenue and total cost is greatest; or it attains a minimum loss by producing the rate of output for which the negative difference between total revenue and total cost is least. As long as total revenue covers total avoidable cost, this condition occurs when marginal revenue equals marginal cost. As was the case for the perfectly competitive firm, when price is less than average variable cost, the manager shuts down production in the short run. We will first discuss profit maximization and then loss minimization.
The position of short-run equilibrium is easily described graphically. Figure 12.3 shows the relevant cost and revenue curves for a monopolist. Because AVC and AFC are not necessary for exposition, they are omitted. Note that demand is the downward-sloping market demand curve. Marginal revenue is also downwardsloping and lies below the demand curve everywhere except at the vertical intercept. Figure 12.3 shows a situation in which price exceeds average total cost, and thus the monopolist earns an economic profit.
The monopolist maximizes profit by producing 200 units of output where MR = SMC. From the demand curve, the monopolist can (and will) charge $7 per unit. Total revenue is $1,400 (= $7 * 200), or the area of the rectangle 0ABE. The average total cost of producing 200 units of output is $5. Total cost of producing 200 units is $1,000 (= $5 * 200), or the area of the rectangle 0DCE. Economic profit is TR minus TC, $400 (= $1,400 - $1,000), or the shaded area ABCD. Since price is greater than average total cost at the equilibrium output of 200 units, the monopolist earns an economic profit. This need not be the case, however.
People often have the idea that monopoly firms can always make a profit; if the firm is making losses, it can simply raise price until it makes a profit. It is, however, a misconception that all monopolies are ensured a profit. Figure 12.4 illustrates a monopolist that makes losses in the short run. Marginal cost equals marginal revenue at 50 units of output, which, from the demand curve, can be sold for $75 each. Total revenue, then, is $3,750 (= $75 * 50), or the area 0DCE. Since average total cost is $80 per unit, total cost is $4,000 (= $80 * 50), or the area 0ABE. Since total cost exceeds total revenue, the firm experiences a loss of $250 (= $4,000 - $3,750), which is the shaded area ABCD.
Note that in Figure 12.4 the monopolist would produce rather than shut down in the short run since total revenue (area 0DCE) exceeds the total variable cost of $3,250 (= $65 * 50), or area 0GFE. After all variable costs have been covered, there is still some revenue, $500 (area GDCF), left over to apply to fixed cost. Since total fixed cost in this example is $750 (= $15 * 50), or area ABFG, the firm loses less by producing 50 units than by shutting down. If the monopolist shuts down, it would, of course, lose its entire fixed cost of $750.
If demand decreases so that it lies below AVC at every level of output and the monopolist could not cover all its variable cost at any price, the firm would shut down and lose only fixed cost. This is exactly the same shutdown rule as that of the perfect competitor.
We should note that a monopolist would never choose a situation in which it was producing and selling an output on the inelastic portion of its demand. When demand is inelastic, marginal revenue is negative (see Table 6.4, page 225). Since marginal cost is always positive, it must equal marginal revenue when the latter is also positive. Thus the monopolist will always be on the elastic portion of demand.
In the short run, the primary difference between a monopoly and a perfect competitor lies in the slope of the demand curve. Either may earn a pure profit; either may incur a loss.
Principle In the short run, the manager of a monopoly firm will choose to produce the output where MR = SMC, rather than shut down, as long as total revenue at least covers the firm’s total avoidable cost, which is the firm’s total variable cost (TR ≥ TVC). The price for that output is given by the demand curve. If total revenue cannot cover total avoidable cost, that is, if total revenue is less than total variable cost (or, equivalently, P < AVC), the manager will shut down and produce nothing, losing an amount equal to total fixed cost.
A monopoly exists if there is only one firm in the market. Among other things, this statement implies that entry into the market is closed. Thus, if a monopolist earns an economic profit in the short run, no new producer can enter the market in the hope of sharing whatever profit potential exists. Therefore, economic profit is not eliminated in the long run, as was the case under perfect competition. The monopolist, however, will make adjustments in plant size as demand conditions warrant, in order to maximize profit in the long run.
Clearly, in the long run, a monopolist would choose the plant size designed to produce the quantity at which long-run marginal cost equals marginal revenue. Profit would be equal to the product of output times the difference between price and long-run average cost:
π = P * Q - LAC * Q = Q (P - LAC)
New entrants cannot come into the industry and compete away profits—entry will not shift the demand curve facing the monopolist.
Demand conditions may change for reasons other than the entry of new firms, and any such change in demand and marginal revenue causes a change in the optimal level of output in both the short run and the long run. Suppose demand does change, due perhaps to a change in consumer income. In the short run, the manager will adjust output to the level where the new marginal revenue curve intersects the short-run marginal cost curve (or it will shut down if P < AVC). This short-run adjustment in output is accomplished without the benefit of being able to adjust the size of the plant to its optimal size. The plant size that minimizes the cost of production varies with the level of output. Hence, in the long run, the manager would adjust plant size to the level that minimizes the cost of producing the optimal level of output. If there is no plant size for which long-run average cost is less than price, the monopolist would not operate in the long run and would exit the industry.
Principle The manager of a monopoly firm maximizes profit in the long run by choosing to produce the level of output where marginal revenue equals long-run marginal cost (MR = LMC). unless price is less than long-run average cost (P < LAC), in which case the firm exits the industry. In the long run, the manager will adjust plant size to the optimal level; that is, the optimal plant is the one with the short-run average cost curve tangent to the long-run average cost at the profitmaximizing output level.
This principle is illustrated in Figure 12.5. The level of output that maximizes profit in the long run is 350 units, the point at which MR = LMC. In the long run, the manager adjusts plant size so that 350 units are produced at the lowest possible total cost. In Figure 12.5, the optimal plant size is the one with shortrun average total cost and marginal cost curves labeled ATC1 and SMC1, respectively. Thus the average cost of producing 350 units is $50 per unit. The manager will sell the 350 units at a price of $55 to maximize profit. Long-run profit is $1,750 [= Q * (P - LAC) = 350 * ($55 - $50)], or the area ABCD. By the now-familiar argument, this is the maximum profit possible under the given revenue and cost conditions.
I L L U S T R AT I O N 1 2 . 2
Quasi-Fixed Costs and Pricing Decisions by Stainless Steel Makers
The CEO of Universal Stainless & Alloy Products Inc., a capital-intensive manufacturer of specialty steel products that possesses some degree of market power (specialty stainless steel is not a homogeneous commodity) raised its prices twice over a 30-day period, according to a recent article in The Wall Street Journal. According to the CEO, the price hikes were in direct response to falling demand for stainless steel products. Can raising price be the optimal response to falling demand? The short answer: No. In this Illustration we will examine the confusion experienced by Universal and several other stainless steel makers when they raised their prices to counter falling demand for stainless steel product.
The source of confusion for the stainless steel CEOs concerns their apparent misunderstanding of the role fixed costs play in decision making, both fixed and quasi-fixed costs in the stainless steel industry. “Regular” fixed costs do not matter for decision-making purposes. Managers should never make production or pricing decisions for the purpose of spreading fixed costs over more units of output. Furthermore, the firm’s decision to shut down in the short run (or to exit in the long run) is decided by comparing revenue to avoidable costs: When total revenue covers total avoidable costs, keep producing; if not, shut down (or exit in the long run). Fixed costs play no role in the short-run shutdown decision or the pricing and production decisions because they must be paid even if output is zero. In contrast, any quasi-fixed costs a firm might incur do matter, but only for making the shutdown decision in the short run. Since quasi-fixed costs can be avoided if output is zero, the firm’s avoidable costs include both variable costs and quasi-fixed costs. Thus, a stainless steel firm that employs quasi-fixed inputs will produce in the short run only if total revenue covers total avoidable cost, which is the sum of variable costs of production plus the quasi-fixed costs. As you can see, the existence of quasi-fixed costs increases the amount of revenue (i.e., raises the shutdown price) that must be reached in order to continue producing rather than shut down in the short run.
The WSJ article quotes several of the CEOs as they explain their reasoning for raising their specialty steel prices. One stainless steel executive explains his price hike as follows:
Unlike (price) increases announced in recent years, this is obviously not driven by increasing global demand, but rather by fixed costs being proportioned across significantly lower demand.
In other words, decreasing demand caused a drop in the quantity of stainless sold, and this reduction in output caused an increase in average fixed costs since there were fewer tons of stainless steel over which to spread or “proportion” the fixed costs. The figure below shows the demand for a stainless steel maker that possesses some degree of market power and earns positive profit before falling demand causes a loss. The original demand and marginal revenue conditions, denoted DA and MRA, require price to be set at point a on demand in order to maximize profit prior to the decrease in demand (SMC = MRA at Q*A). (Notice that point a lies slightly above ATC, creating a positive profit for the steel firm.) When demand decreases to DB, which also causes marginal revenue to shift to MRB, the new optimal price is at point b on DB (SMC = MRB at Q*B ). As you can see, moving from point a to point b must reduce total revenue because both price and quantity fall. Even if the firm kept price unchanged after the decline in demand (see point f ), total revenue would still decline. In either case, at point f or point b, profit is now negative since price is lower than average total cost.
What should the stainless steel maker do once demand decreases? At least one mistake, raising the price of stainless steel, was made, and perhaps a second mistake was made: continuing to produce stainless steel rather than shutting down operations. Let’s first consider the price hike. Raising price after a decrease in demand (i.e., setting price somewhere above point f along DB), does several undesirable things. Raising price above point f on DB instead of lowering price to point b only adds to the loss of sales when demand for stainless falls. The global recession caused demand for steel to shift leftward, which is something management can do nothing about, but as you can see clearly in the figure, management’s decision to raise prices made matters even worse. Not only will there be fewer tons of steel to spread fixed costs over—a completely irrelevant concern in any case—but stainless steel demand is elastic here and raising price also reduces total revenue! Specifically, by choosing, incorrectly, to set price higher than point f instead of at point b, some total revenue is needlessly sacrificed since demand is elastic at point b (i.e., MR is positive).
On the second issue of shutting down stainless steel production, the CEO must distinguish between fixed cost and quasi-fixed cost, because stainless steel production involves substantial quasi-fixed costs. At Universal’s facility an enormous blower serves as a pre-heater by blasting 2,300 degree Fahrenheit hot air at the giant ladle holding the molten steel. The preheater must continue running even when no steel is being produced in order to prevent a melt-down of the refractory bricks that heat the ladle and to avoid damage caused by starting and stopping the motors. The cost of running the giant pre-heater is the same whether Universal makes one batch or a dozen batches of steel.
It is clear from this description of stainless steel production that running the huge blower represents a quasi-fixed cost: A lump amount of “blowing" is needed for the first ton and this amount is constant as more tons are produced. And, in contrast to “regular” fixed costs, the quasi-fixed cost of running the blower is avoidable if the plant shuts down. Unless the now lower total revenue can cover all the variable costs plus the quasi-fixed costs of running the pre-heater, the stainless steel firm should shut down operation in the short run and lose only its total (unavoidable) fixed cost. According to the article, the stainless steel makers are continuing to produce in the short run, so we will assume that total revenue is indeed sufficient to cover all avoidable costs. We show this situation in our figure. As you can verify at point b, the new price, P*B, is greater than the sum of average variable cost (AVC) plus average quasi-fixed cost (AQFC) at point c on the curve labeled “AVC + AQFC ”.
Now we can explain why raising price (incorrectly) might also cause the firm to make the wrong shutdown decision. Based on the figure we have constructed, the optimal price exceeds average avoidable cost (i.e., point b lies above point c), so total revenue from selling Q*B tons of steel at price P*B will indeed cover total avoidable cost. However, since the CEO made the wrong pricing decision by setting price somewhere above point f on DB, we cannot be sure that total revenue at the wrong price will be sufficient to warrant continued production in the short run. While the WSJ article does not tell us whether or not the firm’s revenue is covering all of its avoidable costs, you can see from this Illustration, nonetheless, how making the wrong pricing decision could cause the firm needlessly to shut down in the short run and lose more than the minimum possible loss.
We can summarize this rather complicated Illustration with two general points. First, as a general rule, when the demand for your product falls, raising price is not the optimal response if profit-maximization is your aim. We cannot help but wonder why the CEO at Universal Stainless & Alloy Products made this decision twice. Perhaps he raised price again after the first price hike failed to raise revenue or reduce average fixed costs. Second, making an incorrect pricing decision by setting price higher than optimal will result in lower total revenue, which could lead the manager mistakenly to shut down.