Lecture Notes 4: Perfect Competition
While there are very few markets that satisfy all of the assumptions of perfect competition, perfect competition is nevertheless a benchmark for the ideal conditions under which a market can operate. As we will see in this unit, perfectly competitive markets attain efficiency in a number of senses, so it is instructive to start there. To the degree that markets violate perfectly competitive assumptions, they will typically not attain these desirable efficiency properties.
What is a perfectly competitive market?
The following are the characteristics of perfect competition.
1. There is a large number of firms.
2. All firms produce a homogeneous (identical product). There is no differentiation by branding, quality, location, etc…
3. Buyers and sellers have perfect information.
4. There are no transactions costs or switching costs. Buyers can easily move between different sellers, and vice versa for sellers.
5. Firms and buyers are price takers. No buyer or seller can influence the market price. 6. There is easy entry and exit in the market, in the long-run.
The price-taking assumption basically means that each firm and consumer views the price as beyond its control. If a firm tries to charge a price higher than the market price, all its customers can costlessly move to a different firm. At the same time, there is no reason to consider prices below the market price because the firm can sell as much as it wants at the market price. Each firm’s output is too small to influence market conditions.
Firm Behavior
The key is that firms in a perfectly competitive market take the price as given. Then, given the selling price, the objective of each firm is to choose its output to maximize profit.
For example, consider a firm facing a market price of $20 and total cost function 𝑇𝑇𝑇𝑇 = 5 + 𝑞𝑞2. How much output should the firm produce in order to maximize profit?
Let’s first set up the profit function. Remember that revenue is Price × Quantity.
Π = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑇𝑇
The firm chooses 𝑞𝑞 to maximize profit.
𝑑𝑑Π
𝑑𝑑𝑞𝑞 = 20 − 2𝑞𝑞 = 0 ⇒ 𝑞𝑞 = 10
This firm produces 10 units of output. Its revenue is 𝑇𝑇𝑇𝑇 = $20 ⋅ 10 = $200. Its total costs are given by 𝑇𝑇𝑇𝑇 = 5 + 102 = $105. Thus, the firm earns a profit of $95.
Economists often find it convenient to characterize profit-maximization graphically using marginal conditions. In general, the profit function is:
Π = 𝑇𝑇𝑇𝑇 − 𝑇𝑇𝑇𝑇 = 𝑃𝑃𝑞𝑞 − 𝑇𝑇𝑇𝑇
Profit is maximized where the derivative of Π with respect to output is set equal to zero. To find
the derivative, recall that the definition of marginal cost is 𝑀𝑀𝑇𝑇 = 𝑑𝑑
𝑑𝑑𝑑𝑑(𝑇𝑇𝑇𝑇). To maximize profit:
𝑑𝑑Π
𝑑𝑑𝑞𝑞 = 𝑃𝑃 − 𝑀𝑀𝑇𝑇 = 0 ⇒ 𝑃𝑃 = 𝑀𝑀𝑇𝑇
• In order to maximize profit, a perfectly competitive firm sets its output where price equals marginal cost.
Marginal revenue is the additional revenue from selling one more unit. For a perfectly competitive firm, the marginal revenue is just equal to the market price. Each time the firm sells one more unit, it sells it for a price of $20 and earns $20 of additional revenue.
As long as the $20 price exceeds the cost of producing the next unit of output (the marginal cost), it is worth it for the firm to increase its output – it makes more additional revenue from selling the unit than it costs to produce it. However, the firm should not produce units where the marginal cost is greater than $20. Thus, for the firm shown on the diagram, the profit-maximizing level of output is 1350 units – exactly where price equals marginal cost.
To calculate the firm’s profit from the diagram, the firm sells each unit of output for $20, but its cost per unit of production is only $15 (the average total cost). Thus, the firm earns a profit of $5 for each unit that it sells. This $5 profit per unit, multiplied over the 1350 units that it produces generates a total profit of $6750. The profit is shaded on the diagram below.
Now we know what price a competitive firm will set – the market price. How much output the firm will choose to produce – where price equals marginal cost. And how to calculate its profit.
Next question – When will the firm operate and when will it choose to shut down? Your first inclination might be to say that the firm will operate if it is making money and shut down when it is losing money. But that’s not quite right, at least in the short-run.
Consider a firm that earns revenues of $7000 weekly. Over the week, its fixed costs are $5000 and its variable costs are $3000. With a total cost of $8000, the firm actually loses $1000 a week by staying open. Should it shut down? Absolutely not! Even if the firm shuts down, it still has to pay the $5000 fixed cost. Thus, by shutting down it loses $5000. But by operating it loses only $1000.
it does. Thus, the only relevant question is whether the firm earns enough revenue to cover its
variable costs of operating. As long as it does, the firm is better off to operate.
By contrast, a firm with $7000 of revenues but $9000 of variable costs should shut down. It doesn’t even make enough money to cover its variable costs, so it’s better off to shut down and not pay the variable costs at all. In summary:
• A firm in the short run should operate as long as the revenues are sufficient to cover the variable costs.
It’s often more convenient to express this in per-unit terms rather than overall cash flows. The firm’s revenue per unit sold is the price and the firm’s variable cost per unit is the average variable cost. Thus, another way to state the rule is that:
• A firm should operate in the short run as long as the price is greater than the average variable cost. If the market price falls lower than the firm’s average variable cost, it should shut down.
Our firm shown in the diagram above should shut down if the price ever goes below $5 – the lowest possible average variable cost.
Finally, we want to map out the firm’s supply curve. The supply curve shows the firm’s output as a function of the market price. For any price, the firm will set its output level where price equals marginal cost. Thus, the firm’s supply curve is its marginal cost curve, but only if the firm is operating. If the price goes below average variable cost, then the firm shuts down and produces nothing.
Short Run Market Equilibrium
In the short run, the market supply curve is upward sloping. The number of firms is fixed in the short run, and each firm will supply more output as the market price rises.
The equilibrium price is determined by the intersection of the market supply curve and the market demand curve. In the short-run, this equilibrium price could be high enough to allow firms to earn a profit (if the price exceeds the average total cost of production) or it might be so low that firms earn a loss (if the price is less than the average total cost of production).
The diagram below shows a short-run equilibrium with firms earning a profit. The market equilibrium price at P* is above firms’ average total cost, so each firm earns a short run profit.
Long Run Market Equilibrium
Unfortunately, the short run profit is not going to last. The key feature of perfectly competitive markets in the long run is that they feature easy entry and exit. Other firms are going to see this opportunity to earn an economic profit and they are going to enter the market. This entry of new firms (which is possible only in the long run) is going to increase market supply of the product and push down prices. And the entry will continue all the way until profits reach zero!
For the firm we considered earlier, a $20 market price permitted the firm to earn profits. Thus, over the long run, new firms will enter until the price drops to the zero-profit price of $14, which is the long run equilibrium price.
To emphasize one more time, the short run equilibrium price in a market can be such that firms earn profits or losses. But if firms earn profits, then new firms will enter in the long run, reducing the price. Conversely, if firms suffer losses, then firms will exit over the long run, which raises market supply and increases the price. Thus,
• The long run equilibrium price in a perfectly competitive market is the zero-profit price.
What does this imply about the long run supply curve? Well, suppose there is a short run spike in demand. In the short-run, the price will spike from P0 to P1, as shown in the diagram above. This higher price enables firms to earn a profit. But in the long run, new firms will enter, increasing the supply curve to S’ and dropping the price back to the zero-profit level P0.
Is the long run supply curve really horizontal?
In theory, free entry and exit of identical firms imply that the long run supply curve is horizontal at the zero-profit price. At any level of demand, firms will enter and exit to restore the zero-profit price.
The problem is that, practically, we do tend to observe that the long run supply curve is upward sloping. In other words, increasing supply in a market comes with a higher market price, even in the long run. What gives? Something about our model must be oversimplified.
There are two main problems. First, the model assumes that all existing firms and potential entrants are identical in the sense that all have the same zero-profit price. But this might not be the case. Imagine farming. The first farmers to start growing oranges will choose the best land and will probably be those who have the best skills for growing oranges. But as consumers want more and more oranges, we will start having to use land which isn’t quite as good or farmers who aren’t quite as talented at growing oranges – all of which comes with rising costs.
So, for example, the first bloc of orange farmers might be willing to enter the market at a market price of $3 per pound for oranges – that is their zero-profit price. But the second bloc of potential orange farmers aren’t quite as efficient, so they’re willing to enter, but only at a price of $4 per pound. Thus, higher demand can be accommodated, but at a higher price. This creates an upward sloping supply curve – getting more oranges supplied requires a market price of $4 instead of $3.
Notice that the first bloc of firms would earn an economic profit in this scenario. But this doesn’t violate the zero-profit condition. Strictly, the zero-profit condition means that marginal entrants don’t have any incentive for new entry.
A second problem with the horizontal long run supply curve is the following. While each firm is too small to have any influence on production costs, at a market level this may not be the case. In other words, entry of new firms might push input costs up because the firms are bidding for scarce resources. If we double orange production, then the farmers will bid up the cost of seed, workers, equipment, etc… Thus, increasing output has to come at a higher price in order for firms to maintain zero profits. Again, the supply curve would be upward sloping in this case. More output means a scarcer supply of inputs, raising production costs and raising the zero-profit price.
A third potential issue is that there might be some kind of limit on entry by new firms; government regulations, for example. If this is the case, then increasing supply in the long-run requires incentivizing existing firms to produce more output (rather than entry of new firms), which does
What does zero-profit mean?
Some people object to the idea that firms will operate in a market with zero profit, but this is just a misunderstanding of what zero profit means.
When economists talk about zero profit, we are referring to economic profits, not to accounting
profits. For example, consider a firms that earns $60,000 of revenues annually. It has explicit costs of $20,000 and implicit costs of $40,000.
• The firm’s accounting profit is $40,000 – revenue net of explicit costs.
• The firm’s economic profit is $0 – revenue net of explicit and implicit costs.
So now we see what zero-profit really means. The firm actually puts a $40,000 accounting profit in the bank, but the economic profit is zero because the implicit costs are exactly equal to the accounting profits.
What are implicit costs? They represent the opportunity cost of the firm’s next-best use of its resources. In other words, if our firm exited and found some other use of its resources, that next-best use of its resources is $40,000 – which is exactly the accounting profit that the firm earns by staying right where it is! In other words, zero economic profit really means that the firm earns exactly the same profit it would earn with the next-best use of its resources – but not a dollar more. In other words, the firm earns exactly enough profit to prevent it from wanting to shift its resources into some other use. Zero economic profit covers the opportunity cost of the firm’s resources.
So, yes, firms earn zero economic profit in long run equilibrium. But what this really means is that new firms have no incentive to move into the industry – profit is equal to the profit that could be earned with alternative uses of the firm’s resources.
Efficiency
Perfectly competitive markets in long run equilibrium attain a number of efficiency conditions.
First, notice that output at the long run equilibrium price is at the minimum of the average total cost curve. Producing at the lowest possible cost per unit is the definition of productive efficiency.
• In long run equilibrium in perfect competition, firms are productively efficient
Secondly, perfectly competitive firms price at marginal cost. Thus, perfectly competitive markets attain the gold standard for allocative efficiency – price equal to marginal cost of production. This is really good for society. Expressed in an informal way, price equal to marginal cost gets the incentives right on both sides of the market. Buyers get the product exactly when what they are willing to pay exceeds the cost of producing the product. Sellers enter the market when they can produce at a cost less than or equal to what the product is worth to the buyer.
• Perfectly competitive markets attain allocative efficiency because the price is equal to the marginal cost of production.
Residual Demand Analysis – Is the firm’s demand really perfectly elastic?
One of the key assumptions of perfect competition is that firms act as price takers. In other words, their demand curves are horizontal – They take the market price as given and assume that their output has no influence on the market price.
But surely this can’t be literally true. At some point, if a firm increases its output too much, it would push the market price down. The truth is that each firm does have an impact on overall market conditions, but it’s so tiny as to be practically imperceptible to the firm.
Here is an example to illustrate the point. Consider a market where 500 firms each supply 200 units of output at an equilibrium price of $5. In other words, market demand at $5 is for 100,000 units of output. But if the price dropped to $4, market demand would rise to 110,000 units of output. This implies that the elasticity of demand in the market is 𝜀𝜀 = −0.5, a reasonable value.1
𝜀𝜀𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 =% Δ quantity% Δ price =−0.2 = −0.50.1
What does this mean for a single firm? In order to create a drop in price from $5 to $4, the firm would have to increase its output by 10,000 units – from 200 units to 10,200 units – which is a 5000% increase in the firm’s output! Thus, the elasticity of demand that the firm faces is as follows:
𝜀𝜀𝑓𝑓𝑓𝑓𝑚𝑚𝑚𝑚 = % Δ quantity% Δ price = −0.2 = −25050
What’s the point? It may not be technically true that each firm faces a perfectly elastic demand (perfectly horizontal demand curve). But this firm would have to increase its output by 250% to
1 Quantity sold increases 10% since 110,000−100,000
100,000 = 0.1. Price dropped 20% since 4−5
see even a 1% drop in the price. The firm’s demand so elastic that it basically treats itself as a price taker. One single firm’s output practically has no influence on the market price.
What we have learned here is that the elasticity of demand that each firm faces will will be many, many times greater than the market elasticity. And typically this firm elasticity is so great that we are safe treating the firm as a price-taker with perfectly elastic demand.
Here is an example. The market elasticity of demand for apples is about 𝜀𝜀 = −0.20. But there are more than 28,000 apple growers in the US, and the price elasticity of any single firm is estimated to be 𝜀𝜀 = −5600! That may not be perfectly elastic, but it’s so close that it’s safe to assume that a single grower treats his demand as perfectly elastic.
Perfectly Contestable Markets
In some markets, the overall size of the market is small, so it doesn’t support many firms, yet the firms seem to earn zero profits and behave like perfect competitors. It turns out that a perfectly contestable market is just as good.
A perfectly contestable market is one in which firms can freely enter and exit without sunk costs. Indeed, in this case, even if the firm in operation is a monopoly, it can never earn economic profits. Another firm could always jump in to undercut the operating firm.
As an example, suppose that only one restaurant in West Chester sells venison burgers. The restaurant theoretically has a monopoly, but it’s contestable – another restaurant could start making venison burgers without any huge entry cost. The reason that there is only one firm is just that there isn’t much demand for the product. Even though the restaurant has a monopoly in selling venison burgers, it can’t charge an extremely high markup, because another restaurant could easily jump in and undercut them.
The important point of this discussion is that it puts the spotlight on the real enemy of perfect competition – entry barriers. For example, if our restaurant held the only license to sell venison burgers, then it could charge a high markup since no other firms could contest.
Barriers to Entry
Economists point to many different sources of barriers to entry. We will talk about many of them extensively throughout the course, but here are a few just to get started:
• Patents – a license that makes you the exclusive seller of some product
• Cost advantages – operating firms have lower costs than new entrants
• Economies of scale – firms have to attain a large size to be competitive, making it difficult for new entrants to attain a size sufficient to compete
• Product differentiation – if branding is very good, consumers might not view new entrants as good substitutes
Economists have done lots of work on barriers to entry. Here, I will just briefly summarize some of the research findings.
• Entry in agriculture, construction and retail sales tends to be quite easy. Firms in these industries cannot earn large economic profits.
• Entry and exit are more difficult in manufacturing and mining. There is a lot of regulation and firms have to make significant industry-specific sunk costs to enter.
• Most new entrants are small relative to the overall market size. But, a little bit of competition tends to reduce prices very quickly, even if the entrants are small.
• Many industries evolve in big jumps, not smoothly. In other words, there is a massive entry over a short period of time, followed by a shake-up that reorganizes the industry. A good example is the auto industry.
• Barriers to entry having to do with cost differences tend to go away over time as technology disperses. Barriers to entry having to do with product differentiation tend to be the most persistent.
• The time horizon matters. A firm might not care that its long run profits are going to be driven to zero if it can accumulate a sufficient profit stream before it happens.
Are there really any perfectly competitive industries?
Exercises
Problem 1
A firm sells its output in a perfectly competitive market with a market price of $80 per unit. The firm faces the cost function 𝑇𝑇𝑇𝑇 = 40 + 8𝑞𝑞 + 2𝑞𝑞2.
a. How much output should the firm produce in order to maximize profit? b. What price will the firm set?
c. How much profit does the firm earn?
d. What kind of adjustments might you expect in this market over the long run?
Problem 2
Consider a firm that earns revenues of $3000 and faces a total cost of $5000.
a. Suppose that the firm’s variable costs are $4000. Should the firm operate or shut down? b. Suppose instead that the firm’s fixed costs are $4000. Should the firm operate or shut down?
Problem 3
You open a copy store. You rent store space (signing a one-year lease), purchase 10 copiers and make a profit. Two months into your lease, another store opens a block away from yours. As a result, the revenue you earn, while enough to cover the wages of your employees and the cost of supplies, doesn’t cover all of your rent. Should you shut down your store in the short run?
Problem 4
This problem refers to the perfectly competitive firm below, facing a market price of $30.
a. How much output should this firm produce? b. Calculate the firm’s profit or loss.
c. Should the firm operate or shut down in the short run?
