More on Perfect Competition
3. How Perfectly Competitive Firms Make Output Decisions
By the end of this section, you will be able to:
- Calculate profits by comparing total revenue and total cost
- Identify profits and losses with the average cost curve
- Explain the shutdown point
- Determine the price at which a firm should continue producing in the short run
A perfectly competitive firm has only one major decision to make - namely, what quantity to produce. To understand why this is so, consider a different way of writing out the basic definition of profit:
Profit = Total revenue − Total cost
= (Price)(Quantity produced) − (Average cost)(Quantity produced)
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. This is already determined in the profit equation, and so the perfectly competitive firm can sell any number of units at exactly the same price. It 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, broken down into fixed and variable costs, are shown in Table 8.1 and also appear in Figure 8.2. The horizontal axis shows the quantity of frozen raspberries produced in packs; 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. All these cost curves follow the same characteristics as the curves covered in the Cost and Industry Structure chapter.
Figure 8.2 Total Cost and Total Revenue at the Raspberry Farm Total revenue for a perfectly competitive firm is a straight line sloping up. 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. The maximum profit will occur at the quantity where the gap of total revenue over total cost is largest.
||Total Cost (TC)
||Fixed Cost (FC)
||Variable Cost (VC)
||Total Revenue (TR)
Table 8.1 Total Cost and Total Revenue at the Raspberry Farm
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. On Figure 8.2, the vertical gap between total revenue and total cost represents either profit (if total revenues are greater that total costs at a certain quantity) or losses (if total costs are greater that total revenues at a certain quantity). In this example, total costs will exceed total revenues at output levels from 0 to 40, and so over this range of output, the firm will be making losses. At output levels from 50 to 80, total revenues exceed total costs, so the firm is earning profits. But then at an output of 90 or 100, total costs again exceed total revenues and the firm is making losses. Total profits appear in the final column of Table 8.1. The highest total profits in the table, as in the figure that is based on the table values, occur at an output of 70–80, when profits will be $56.
A higher price would mean that total revenue would be higher for every quantity sold. A lower price would mean 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. But 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
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).
Ordinarily, marginal cost changes as the firm produces a greater quantity.
Table 8.3 Marginal Revenues and Marginal Costs at the Raspberry Farm
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. From a level of 70 to 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 where marginal revenue is equal to marginal cost - that is, where MR = MC. A profit-seeking firm should keep expanding production as long as MR > MC. But at the level of output where MR = MC, the firm should recognize that it has achieved the highest possible level of economic profits. (In the example above, the profit maximizing output level is between 70 and 80 units of output, but the firm will not know they've maximized profit until they reach 80, where MR = MC). Expanding production into the zone where MR < MC will only reduce economic profits. Because the marginal revenue received by a perfectly competitive firm is equal to the price P, so that P = MR, the profit-maximizing rule for a perfectly competitive firm can also be written as a recommendation to produce at the quantity where P = MC.
Profits and Losses with the Average Cost Curve
First consider a situation where the price is equal to $5 for a pack of frozen raspberries. The rule for a profit-maximizing perfectly competitive firm is to produce the level of output where Price= MR = MC, so the raspberry farmer will produce a quantity of 90, which is labeled as e in Figure 8.5 (a). Remember that the area of a rectangle is equal to its base multiplied by its height. The farm's total revenue at this price will be shown by the large shaded rectangle from the origin over to a quantity of 90 packs (the base) up to point E' (the height), over to the price of $5, and back to the origin. The average cost of producing 80 packs is shown by point C or about $3.50. Total costs will be the quantity of 80 times the average cost of $3.50, which is shown by the area of the rectangle from the origin to a quantity of 90, up to point C, over to the vertical axis and down to the origin. It should be clear from examining the two rectangles that total revenue is greater than total cost. Thus, profits will be the blue shaded rectangle on top.
It can be calculated as:
Or, it can be calculated as:
Now consider Figure 8.5 (b), where the price has fallen to $3.00 for a pack of frozen raspberries. Again, the perfectly competitive firm will choose the level of output where Price = MR = MC, but in this case, the quantity produced will be 70. At this price and output level, where the marginal cost curve is crossing the average cost curve, the price received by the firm is exactly equal to its average cost of production.
The farm's total revenue at this price will be shown by the large shaded rectangle from the origin over to a quantity of 70 packs (the base) up to point E (the height), over to the price of $3, and back to the origin. The average cost of producing 70 packs is shown by point C'. Total costs will be the quantity of 70 times the average cost of $3.00, which is shown by the area of the rectangle from the origin to a quantity of 70, up to point E, over to the vertical axis and down to the origin. It should be clear from that the rectangles for total revenue and total cost are the same. Thus, the firm is making zero profit. The calculations are as follows:
Or, it can be calculated as:
In Figure 8.5 (c), the market price has fallen still further to $2.00 for a pack of frozen raspberries. At this price, marginal revenue intersects marginal cost at a quantity of 50. The farm's total revenue at this price will be shown by the large shaded rectangle from the origin over to a quantity of 50 packs (the base) up to point E” (the height), over to the price of $2, and back to the origin. The average cost of producing 50 packs is shown by point C” or about $3.30. Total costs will be the quantity of 50 times the average cost of $3.30, which is shown by the area of the rectangle from the origin to a quantity of 50, up to point C”, over to the vertical axis and down to the origin. It should be clear from examining the two rectangles that total revenue is less than total cost. Thus, the firm is losing money and the loss (or negative profit) will be the rose-shaded rectangle.
The calculations are:
|Price > ATC||Firm earns an economic profit|
|Price = ATC||Firm earns zero economic profit|
|Price < ATC||Firm earns a loss|
The Shutdown Point
As an example, consider the situation of the Yoga Center, which has signed a contract to rent space that costs $10,000 per month. If the firm decides to operate, its marginal costs for hiring yoga teachers is $15,000 for the month. If the firm shuts down, it must still pay the rent, but it would not need to hire labor. Table 8.5 shows three possible scenarios. In the first scenario, the Yoga Center does not have any clients, and therefore does not make any revenues, in which case it faces losses of $10,000 equal to the fixed costs. In the second scenario, the Yoga Center has clients that earn the center revenues of $10,000 for the month, but ultimately experiences losses of $15,000 due to having to hire yoga instructors to cover the classes. In the third scenario, the Yoga Center earns revenues of $20,000 for the month, but experiences losses of $5,000.
|If the center shuts down now, revenues are zero but it will not incur any variable costs and would only need to pay fixed costs of $10,000.|
|profit = total revenue – (fixed costs + variable cost)
= 0 –$10,000
|The center earns revenues of $10,000, and variable costs are $15,000. The center should shut down now.|
|profit = total revenue – (fixed costs + variable cost)
= $10,000 – ($10,000 + $15,000)
|The center earns revenues of $20,000, and variable costs are $15,000. The center should continue in business.|
|profit = total revenue – (fixed costs + variable cost)
= $20,000 – ($10,000 + $15,000)
This example suggests that the key factor is whether a firm can earn enough revenues to cover at least its variable costs by remaining open. Let's return now to our raspberry farm. Figure 8.6 illustrates this lesson by adding the average variable cost curve to the marginal cost and average cost curves. At a price of $2.20 per pack, as shown in Figure 8.6 (a), the farm produces at a level of 50. It is making losses of $56 (as explained earlier), but price is above average variable cost and so the firm continues to operate. However, if the price declined to $1.80 per pack, as shown in Figure 8.6 (b), and if the firm applied its rule of producing where P = MR = MC, it would produce a quantity of 40. This price is below average variable cost for this level of output. If the farmer cannot pay workers (the variable costs), then it has to shut down. At this price and output, total revenues would be $72 (quantity of 40 times price of $1.80) and total cost would be $144, for overall losses of $72. If the farm shuts down, it must pay only its fixed costs of $62, so shutting down is preferable to selling at a price of $1.80 per pack.
|| Average Variable Cost
Table 8.6 Cost of Production for the Raspberry Farm
The intersection of the average variable cost curve and the marginal cost curve, which shows the price where the firm would lack enough revenue to cover its variable costs, is called the shutdown point. If the perfectly competitive firm can charge a price above the shutdown point, then the firm is at least covering its average variable costs. It is also making enough revenue to cover at least a portion of fixed costs, so it should limp ahead even if it is making losses in the short run, since at least those losses will be smaller than if the firm shuts down immediately and incurs a loss equal to total fixed costs. However, if the firm is receiving a price below the price at the shutdown point, then the firm is not even covering its variable costs. In this case, staying open is making the firm's losses larger, and it should shut down immediately. To summarize, if:
- price < minimum average variable cost, then firm shuts down
- price = minimum average variable cost, then firm stays in business
Short-Run Outcomes for Perfectly Competitive FirmsThe average cost and average variable cost curves divide the marginal cost curve into three segments, as shown in Figure 8.7. At the market price, which the perfectly competitive firm accepts as given, the profit-maximizing firm chooses the output level where price or marginal revenue, which are the same thing for a perfectly competitive firm, is equal to marginal cost: P = MR = MC.
Marginal Cost and the Firm's Supply CurveFor a perfectly competitive firm, the marginal cost curve is identical to the firm's supply curve starting from the minimum point on the average variable cost curve. To understand why this perhaps surprising insight holds true, first think about what the supply curve means. A firm checks the market price and then looks at its supply curve to decide what quantity to produce. Now, think about what it means to say that a firm will maximize its profits by producing at the quantity where P = MC. This rule means that the firm checks the market price, and then looks at its marginal cost to determine the quantity to produce - and makes sure that the price is greater than the minimum average variable cost. In other words, the marginal cost curve above the minimum point on the average variable cost curve becomes the firm's supply curve.
Work It Out
At What Price Should the Firm Continue Producing in the Short Run?
(TFC + TVC)
|Quantity||Price||Total Revenue (P x Q)
|| Profits (TR-TC)
Step 5. Once you have determined the profit-maximizing output level (in this case, output quantity 5), you can look at the amount of profits made (in this case, $40).
Step 6. If the firm is making economic losses, the firm needs to determine whether it produces the output level where price equals marginal revenue and equals marginal cost or it shuts down and only incurs its fixed costs.
Step 7. For the output level where marginal revenue is equal to marginal cost, check if the market price is greater than the average variable cost of producing that output level.
- If P > AVC but P < ATC, then the firm continues to produce in the short-run, making economic losses.
- If P < AVC, then the firm stops producing and only incurs its fixed costs.
In this example, the price of $28 is greater than the AVC ($16.40) of producing 5 units of output, so the firm continues producing.