Profit Maximization in a Perfectly Competitive Market

Learning Objectives

  • Determine profits and costs by comparing total revenue and total cost
  • Use marginal revenue and marginal costs to find the level of output that will maximize the firm’s profits

How Perfectly Competitive Firms Make Output Decisions

A perfectly competitive firm has only one major decision to make—namely, what quantity to produce. To understand why this is so, consider the basic definition of profit:

[latex]\begin{array}{l}\text{Profit}=\text{Total revenue}-\text{Total cost}\hfill \\ \text{ }=\left(\text{Price}\right)\left(\text{Quantity produced}\right)-\left(\text{Average cost}\right)\left(\text{Quantity produced}\right)\hfill \end{array}[/latex]

Since a perfectly competitive firm must accept the price for its output as determined by the product’s market demand and supply, it cannot choose the price it charges. Rather, the perfectly competitive firm can choose to sell any quantity of output at exactly the same price. This implies that the firm faces a perfectly elastic demand curve for its product: buyers are willing to buy any number of units of output from the firm at the market price. When the perfectly competitive firm chooses what quantity to produce, then this quantity—along with the prices prevailing in the market for output and inputs—will determine the firm’s total revenue, total costs, and ultimately, level of profits.

Determining the Highest Profit by Comparing Total Revenue and Total Cost

A perfectly competitive firm can sell as large a quantity as it wishes, as long as it accepts the prevailing market price. Total revenue is going to increase as the firm sells more, depending on the price of the product and the number of units sold. If you increase the number of units sold at a given price, then total revenue will increase. If the price of the product increases for every unit sold, then total revenue also increases.

As an example of how a perfectly competitive firm decides what quantity to produce, consider the case of a small farmer who produces raspberries and sells them frozen for $4 per pack. Sales of one pack of raspberries will bring in $4, two packs will be $8, three packs will be $12, and so on. If, for example, the price of frozen raspberries doubles to $8 per pack, then sales of one pack of raspberries will be $8, two packs will be $16, three packs will be $24, and so on.

Total revenue and total costs for the raspberry farm are shown in Table 1 and also appear in Figure 1.

Table 1. Total Revenue, Total Cost, and Profit at the Raspberry Farm
Quantity

(Q)

Total Revenue (TR) Total Cost (TC) Profit

0 $0 $62 −$62
10 $40 $90 −$50
20 $80 $110 −$30
30 $120 $126 −$6
40 $160 $138 $22
50 $200 $150 $50
60 $240 $165 $75
70 $280 $190 $90
80 $320 $230 $90
90 $360 $296 $64
100 $400 $400 $0
110 $440 $550 $−110
120 $480 $715 $−235

In Figure 1, the horizontal axis shows the quantity of frozen raspberries produced. The vertical axis shows both total revenue and total costs, measured in dollars. The total cost curve intersects with the vertical axis at a value that shows the level of fixed costs, and then slopes upward, first at a decreasing rate, then at an increasing rate. In other words, the cost curves for a perfectly competitive firm have the same characteristics as the curves that we covered in the previous module on production and costs.

Try It

The graph shows that firms will incur a loss if the total cost is higher than the total revenue. The x-axis is the quantity of raspberry packs. The y-axis is the total cost/total revenue. The description of the graph is located in the paragraph below the table.

Figure 1. Total Revenue, Total Cost and Profit at the Raspberry Farm. Total revenue for a perfectly competitive firm is an upward sloping straight line. The slope is equal to the price of the good. Total cost also slopes up, but with some curvature. At higher levels of output, total cost begins to slope upward more steeply because of diminishing marginal returns. Graphically, profit is the vertical distance between the total revenue curve and the total cost curve. This is shown as the smaller, downward-curving line at the bottom of the graph. The maximum profit will occur at the quantity where the difference between total revenue and total cost is largest.

Based on its total revenue and total cost curves, a perfectly competitive firm like the raspberry farm can calculate the quantity of output that will provide the highest level of profit. At any given quantity, total revenue minus total cost will equal profit. One way to determine the most profitable quantity to produce is to see at what quantity total revenue exceeds total cost by the largest amount.

Figure 1 shows total revenue, total cost and profit using the data from Table 1. The vertical gap between total revenue and total cost is profit, for example, at Q = 60, TR = 240 and TC = 165. The difference is 75, which is the height of the profit curve at that output level. The firm doesn’t make a profit at every level of output. In this example, total costs will exceed total revenues at output levels from 0 to approximately 30, and so over this range of output, the firm will be making losses. At output levels from 40 to 100, total revenues exceed total costs, so the firm is earning profits. However, at any output greater than 100, total costs again exceed total revenues and the firm is making increasing losses. Total profits appear in the final column of Table 1. Maximum profit occurs at an output between 70 and 80, when profit equals $90.

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A higher price would mean that total revenue would be higher for every quantity sold. Graphically, the total revenue curve would be steeper, reflecting the higher price as the steeper slope. A lower price would flatten the total revenue curve, meaning that total revenue would be lower for every quantity sold. What happens if the price drops low enough so that the total revenue line is completely below the total cost curve; that is, at every level of output, total costs are higher than total revenues? In this instance, the best the firm can do is to suffer losses. However, a profit-maximizing firm will prefer the quantity of output where total revenues come closest to total costs and thus where the losses are smallest.

Comparing Marginal Revenue and Marginal Costs

The approach that we described in the previous section, using total revenue and total cost, is not the only approach to determining the profit maximizing level of output. In this section, we provide an alternative approach which uses marginal revenue and marginal cost.

Firms often do not have the necessary data they need to draw a complete total cost curve for all levels of production. They cannot be sure of what total costs would look like if they, say, doubled production or cut production in half, because they have not tried it. Instead, firms experiment. They produce a slightly greater or lower quantity and observe how it affects profits. In economic terms, this practical approach to maximizing profits means examining how changes in production affect marginal revenue and marginal cost.

As mentioned before, a firm in perfect competition faces a perfectly elastic demand curve for its product—that is, the firm’s demand curve is a horizontal line drawn at the market price level. This also means that the firm’s marginal revenue curve is the same as the firm’s demand curve. Every time a consumer demands one more unit, the firm sells one more unit and revenue increases by exactly the same amount equal to the market price. In this example, every time the firm sells a pack of frozen raspberries, the firm’s revenue increases by $4, as you can see in Table 2. This condition only holds for price taking firms in perfect competition where:

[latex]\text{marginal revenue = price}[/latex]

The formula for marginal revenue is:

[latex]\text{marginal revenue = }\frac{\text{change in total revenue}}{\text{change in quantity}}[/latex]
Table 2. Marginal Revenue for Raspberries
Price Quantity Total Revenue Marginal Revenue
$4 1 $4
$4 2 $8 $4
$4 3 $12 $4
$4 4 $16 $4

Try It

Notice that marginal revenue does not change as the firm produces more output. That is because the price is determined by supply and demand and does not change as the farmer produces more (keeping in mind that, due to the relative small size of each firm, increasing their supply has no impact on the total market supply where price is determined).

The firm-level graph shows how a firm uses the market price to determine its profit-maximizing level of output.

Figure 2. Market Price. The equilibrium price of raspberries is determined through the interaction of market supply and market demand at $4.00.

Since a perfectly competitive firm is a price taker, it can sell whatever quantity it wishes at the market-determined price. Marginal cost, the cost per additional unit sold, is calculated by dividing the change in total cost by the change in quantity. The formula for marginal cost is:

[latex]\text{marginal cost = }\frac{\text{change in total cost}}{\text{change in quantity}}[/latex]

Unlike marginal revenue, ordinarily, marginal cost changes as the firm produces a greater quantity of output. At first, marginal cost decreases with additional output, but then it increases with additional output. Again, note this is the same as we found in the module on production and costs.

Table 3 presents the marginal revenue and marginal costs based on the total revenue and total cost amounts introduced earlier. The marginal revenue curve shows the additional revenue gained from selling one more unit, as shown in Figure 3.

Table 3. Marginal Revenues and Marginal Costs at the Raspberry Farm
Quantity Total Revenue Marginal Revenue Total Cost Marginal Cost Profit
0 $0 $4 $62 -$62
10 $40 $4 $90 $2.80 -$50
20 $80 $4 $110 $2.00 -$30
30 $120 $4 $126 $1.60 -$6
40 $160 $4 $138 $1.20 $22
50 $200 $4 $150 $1.20 $50
60 $240 $4 $165 $1.50 $75
70 $280 $4 $190 $2.50 $90
80 $320 $4 $230 $4.00 $90
90 $360 $4 $296 $6.60 $64
100 $400 $4 $400 $10.40 $0
110 $440 $4 $550 $15.00 -$110
120 $480 $4 $715 $16.50 -$235

In the raspberry farm example, marginal cost at first declines as production increases from 10 to 20 to 30 packs of raspberries. But then marginal costs start to increase, due to diminishing marginal returns in production. If the firm is producing at a quantity where MR > MC, like 40 or 50 packs of raspberries, then it can increase profit by increasing output. The reason is since the marginal revenue exceeds the marginal cost, additional output is adding more to profit than it is taking away. If the firm is producing at a quantity where MC > MR, like 90 or 100 packs, then it can increase profit by reducing output. The firm’s profit-maximizing level of output will occur where MR = MC (or at a level close to that point).

The market-level graph shows that the equilibrium price ($4.00) is determined through the interaction between market demand and market supply.

Figure 3. Marginal Revenues and Marginal Costs at the Raspberry Farm. For a perfectly competitive firm, the demand curve s a horizontal line equal to the market price of the good, Since price doesn’t change with additional output, the demand curve is also the marginal revenue (MR) curve. The marginal cost (MC) curve is sometimes initially downward-sloping, but is eventually upward-sloping at higher levels of output as diminishing marginal returns kick in. The firm will maximize profit at the level of output where MR = MC. In the case of the raspberry farm, this occurs at 80 packs of strawberries.

In this example, the marginal revenue and marginal cost curves cross at a price of $4 and a quantity of 80 produced. If the farmer started out producing at a level of 60, and then experimented with increasing production to 70, marginal revenues from the increase in production would exceed marginal costs—and so profits would rise. The farmer has an incentive to keep producing. At a level of output of 80, marginal cost and marginal revenue are equal so profit doesn’t change. If the farmer then experimented further with increasing production from 80 to 90, he would find that marginal costs from the increase in production are greater than marginal revenues, and so profits would decline.

The profit-maximizing choice for a perfectly competitive firm will occur at the level of output where marginal revenue is equal to marginal cost—that is, where MR = MC. This occurs at Q = 80 in the figure.

Does Profit Maximization Occur at a Range of Output or a Specific Level of Output?

Table 1 showed that maximum profit occurs at any output level between 70 and 80 units of output. But MR = MC occurs only at 80 units of output. How can do we explain this slight discrepancy? As long as MR > MC. a profit-seeking firm should keep expanding production. Expanding production into the zone where MR < MC reduces economic profits. It’s true that profit is the same at Q = 70 and Q = 80, but it’s only when the firm goes beyond that that see that profits fall. Thus, MR = MC is the signal to stop expanding, so that is the level of output they should target.

Because the marginal revenue received by a perfectly competitive firm is equal to the price P, we can also write the profit-maximizing rule for a perfectly competitive firm as a recommendation to produce at the quantity of output where P = MC.

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Watch It

Watch this video to practice finding the profit-maximizing point in a perfectly competitive firm. Mr. Clifford reminds us that in a perfectly competitive market, the demand curve is a horizontal line, which also happens to be the marginal revenue. You can use the acronym MR. DARP to remember that marginal revenue=demand=average revenue=price. The ideal production point is the place where MR=MC.

Glossary

marginal revenue:
the additional revenue gained from selling one more unit of output
profit:
 the difference between total revenues and total costs
profit-maximizing rule for a perfectly competitive firm:
produce the level of output where marginal revenue equals marginal cost