How does perfect competition work?

Question

I have made several other posts about this topic, but all the answers I got confused me even more. This is my attempt at making a comprehensive post that highlights my confusion about perfect competition.

1. “No individual firm can influence the market price”

This is highly confusing. The market price is the equilibrium price determined by market supply and market demand. Market supply and market demand are composed of individual supply schedules and individual demand schedules respectively. So given this, why would a change in an individual producer’s supply schedule not lead to a shift in the equilibrium market price? Here are some actual figures for a concrete example:

If producer K decided they would produce 2 cakes at all prices from 1 dollar to 10 dollars instead of just 1 cake, would this not change the overall quantity supplied curve, which would, in turn, change the equilibrium price?

2. “Individual firms can sell ANY quantity at the market price”

How can an individual firm sell literally any quantity at the market price? I understand that it’s impossible for a producer to supply an infinite quantity, but even theoretically, how could there be an infinite quantity demanded for an individual firm when the market quantity demanded for the entire market (including the individual firm) is a finite number? Also, why would an individual producer not just produce the quantity that corresponds to the equilibrium price on their supply schedule? For instance, using the graph above, let’s say the equilibrium price is 5 dollars and I’m producer O. According to my individual supply schedule, I would be willing to make 1 cake at that price of 5 dollars. So why would I not just make 1 cake at the equilibrium price?

Answer 1

Answer to 1

The example you provide has only few firms. In perfectly competitive market there are infinite amount of firms so you can't simply use simple table to visualize that since your table lacks infinite amount of rows.

Mathematically market supply is:

$$S=\sum_{i=1}^n q_i $$

This is what your table does, sums quantities produced, here we just do it mathematically so we can deal with infinity. Now if we want to subtract one firm from total supply (e.g. thought experiment where 1 firm withholds its whole supply from market) we get:

$$S=\sum_{i=1}^n q_i -q_{-i}$$

Now in perfect competition all firms are exactly identical, and hence they all produce identical quantities. $q_1 =q_2=...=q_n=q\geq 0$ so we can simplify this:

$$S=q(n -1)$$

Now since we have infinite amount of firms we have to figure out what S is as $n \to \infty$. If we take a limit of $S$ as $n$ goes to infinity:

$$\lim_{n \to \infty} [q(n-1)] = \infty$$

This is exactly, the same as if the firm would not withhold supply from the market where we would have:

$$S=\sum_{i=1}^n q_i = qn \quad \lim_{n \to \infty} [qn]= \infty$$

Hence as you can see in perfect competition supply is so massive that it is the same whether the firms supplies goods to the market or not. Of course, in reality supply cannot be infinity. Perfect competition model is a model, you can view it as a Platonic form (e.g. there are no real triangles in universe, there are only approximations to triangles). The justification for the model is that if a number of firm is very large firms will behave as if there were infinite firms out there since it would be impossible to track every other firm.

For example, suppose there are 1 million lumber mills each supplying 1 ton of lumber to world market meaning total supply at world market is 1 million ton. If one firm cuts on production or supplies less there will still be approximately 1 million ton supplied to the market. This change is too small for other firms to notice and react to it.

Answer to 2

I understand that it’s impossible for a producer to supply an infinite quantity,

It is actually not impossible to do that in mathematical model, although that will usually not happen in model of perfect competition.

how could there be an infinite quantity demanded for an individual firm when the market quantity demanded for the entire market (including the individual firm) is a finite number?

Quantity demanded can exceed quantity supplied both in real life and theoretical model. Also quantity demanded for a good can be infinite. For example, at a negative price that would pay for the storage cost my quantity demanded of gold bars would be infinite, even if quantity of gold is limited.

Also, why would an individual producer not just produce the quantity that corresponds to the equilibrium price on their supply schedule?

This is exactly what perfectly competitive firm does. Individual supply of a perfectly competitive firm is given by marginal costs $MC$. In perfect competition the optimal quantity of individual firm is exactly such that:

$$p=MC$$

So individual firm, in perfect competition, will supply exactly as many products as given by intersection between price and its own supply.

Answer 2

I can understand that this can be confusing. A better way to re-state those two statements is: In a competitive environment,

• No individual firm believes that it can influence the market price.
• Individual firms believe that they can sell ANY quantity at the market price

This defines the competitive behavior of the firm. In other words, any firm will act as a price-taker, and decides how much to supply taking as given the market price. This is a behavioral assumption on the way the firms act in a competitive environment. And this is kind of true and can be observed in situations where there are many suppliers of a homogeneous good or service, as they perceive themselves to have no power to influence the going price. Consequently, the market supply is derived by aggregating the individual supply decisions of the firms at each price. Ultimately, competitive equilibrium is defined as the intersection of the market demand and supply curves.