Perfect Competition

A QUICK REVIEW (AND EXAMPLE) OF PERFECT COMPETITION

Perfectly competitive firms are so small they don't have any market power (power to set price). Instead, these little firms respond as best they can to market conditions, trying to make a profit with the price that prevails in the market. Of course, the price is established by demand and supply in the industry as a whole, but no individual producer has an ability to move this price up or down.

Imagine that we have a market demand function given by P = 1010 - .08Q, where P is the market price in the industry and Q is the total output of the good by producers in this particular industry. The demand curve is downward sloping, because consumers are willing to consume more of this good at lower prices but less of this good at higher prices (income and substitution effects).

Let's say that the total cost function faced by all firms is TC = 10,000 + 10q + q2 (they all have access to best-practice technology which affects these costs, and they are all able to hire workers and other inputs to produce goods and services. Therefore, every firm has the same costs....no one has a special technological or cost advantage). In this function, q is the amount of output by the individual firm. That means that the marginal cost (or MC) function is MC = 10 + 2q.

There are 100 firms in this industry. As we remember from first year, the marginal cost curve of the individual firm tells us how much that firm will be willing to supply at different possible prices. If the firm faces a price that is below its AVC, it would prefer to temporarily shut down, rather than not even be able to cover its variable costs with revenue. But apart from this qualification, the MC curve is the supply curve of the individual firm (it tells us how much the firm will supply at different prices it might face).

If the MC curve is the supply curve of the firm, and if all 100 firms have identical MC curves, we simply need to add all of these MC curves horizontally together to get the supply curve of the whole industry. If 100q = Q, then q = .01Q. We can substitute into the MC curve to get P = 10 + 2(.01Q) = 10 + .02Q, which is the overall industry supply curve (short run).

We now have the industry supply curve and the industry demand curve so we can find the equilibrium price that all firms will face (and the equilibrium quantity of output in the market as a whole). 1010 - .08Q = 10 + .02Q, so that Q* = 10,000 and P* = 1010 - .08(10,000) = $210. Since there are 100 firms in the industry, each one will be producing 10,000/100 = 100 units of output at a price of $210.

The following diagram is not necessarily drawn to scale, but it gives a sense of the graphical depiction of the firm situation and industry situation we have described:

The one additional line on this graph which is of special interest is the SLR line, otherwise known as the long-run supply curve for the industry. In order to draw the line as a horizontal one (rather than positively sloped), we would have to know that this industry is a "constant cost" industry. A constant cost industry is one in which the price of the inputs do not rise as the industry expands (therefore, the cost of its inputs remain constant). This long run supply curve is drawn as a horizontal line at the price where the average cost curve of the firm reaches its minimum. Individual firms will be forced by competitive pressures to produce at the lowest-cost level of output in the long run (i.e., they will produce at the minimum point on the average cost curve).

How do we know that the equilibrium we have calculated above is actually at this minimum-AC point? We don't yet, but it's easy to figure out. We could either calculate what the level of profit of the firm is, or we could find the minimum value of AC and compare it to the equilibrium price of $210. Either way, we would find that we are currently in both short run and long run equilibrium with firms earning an economic profit of zero.

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