## Perfectly Competitive Markets December 10, 2012

Posted by tomflesher in Micro, Teaching.
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When solving economic problems, the type of firm you’re dealing with can lead you to use different techniques to figure out the firm’s rational choice of action. This week, I’ll set up a thumbnail sketch of how to solve different firms’ types of problems, since a common exam question in intermediate microeconomics is to set up a firm’s production function and ask a series of different questions. The important thing to remember about all types of markets is that every economic agent is optimizing something.

In a perfectly competitive market, three conditions hold:

• All goods are identical. If the seller is selling apples, then all apples are the same – there are no MacIntosh apples, no Red Delicious apples, just apples.
• There are lots of sellers, so sellers can’t price-fix because there will always be another seller who will undercut.
• There are lots of buyers, so a buyer boycotting won’t make a difference.

The last two conditions sum up together to mean that no one has any market power. That means, essentially, that no action an individual buyer or seller takes can affect the price of the goods. If ANY of these conditions isn’t true, then we’re not dealing with a perfectly competitive market – it might be a monopoly or a monopsony, or it might be possible to price-discriminate, but you’ll have to do a bit more to find an equilibrium.

Speaking of that, an equilibrium in microeconomics happens when we find a price where buyers are willing to buy exactly as much as sellers are willing to sell. Mathematically, an equilibrium price is a price such that QS(P) = QD(P), where QS is the quantity supplied, QD is the quantity demanded, and the (P) means that the quantities depend on the price P. Since the quantity is the same, economists sometimes call an equilibrium quantity Q* and the equilibrium price P*.

Consumers are optimizing their utility, or happiness. This might be represented using something called a utility function, or it might be aggregated and presented as a market demand function where the quantity demanded by everyone in the world is decided as a function of the price of the good. A common demand function would look like this:

QD(P) = 100 – 2*P

That means if the price is \$0, there are 100 people willing to buy one good each; at a price of \$1, there are (100 – 2*1) = 98 people willing to buy one good each; and so on, until no one is willing to buy if the price is \$50. Demand curves slope downward because as price goes up, demand goes down. Essentially, a demand function allows us to ignore the consumer optimization step. Demand represents the marginal buyer’s willingness to pay; price equalling willingness to pay is something to remember.

Firms optimize profit, which is defined as Total revenue, minus total costs. If we have a firm’s costs, we can figure out how much they’d need to charge to break even on each sale. Let’s say that it costs a firm \$39 to produce a each good. They won’t produce at all until they’ll at least break even – or, until their marginal benefit is at least equal to their marginal cost, at which point they’ll be indifferent. Then, as the price rises above \$39, charging more will lead to more profit. Even if the firm’s marginal cost changes as they produce more unity, the price of the marginal unit will need to be at least as much as the marginal cost for that unit. Otherwise, selling it wouldn’t make sense.

The first condition to remember when solving microeconomics problems is that in a perfectly competitive market, a firm will set Price equal to Marginal Cost. If you have price and a marginal cost function, you can find the equilibrium quantity. If you have supply and demand functions, set QS(P) = QD(P) and solve for the price, or simply graph the functions and figure out where they meet.