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:
D0
P
MC
SAC
P
SSR
SAVC
D0 P0*
P0
SLR
D1
q
q0
Q
Q0*
FIRM
INDUSTRY
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.
What would happen in perfect competition if the demand in the industry were to
rise…if consumers wanted more of the good at every possible price? Let’s say
that the industry demand curve shifted to the right, so that it’s new equation was
P = 1210 - .08Q. In the short run, the existing firms in the industry will try to
adjust their production to meet this demand, and in the long run, new firms may
enter the industry to meet this additional demand.
In the short run, we look for the intersection between this new demand curve
and the short-run supply industry curve to tell us what will happen. We know
the short run industry supply curve is P = 10 + .02Q. Put this together with the
new demand curve and we get 1210 - .08Q = 10 + .02Q or .1Q = 1200 or Q1* =
12,000. The new equilibrium price is P = 10 + .02(12,000) = 250. In other words,
P1* = $250. This tells us that the new short run equilibrium will bring forth an
additional 2,000 units of output but the price will rise by $40 to make this
happen. We can calculate the profit of firms at this new price. There are still 100
firms in the industry (firms are assumed to enter in the long run, but not the
short run). Therefore, each one is producing 120 units of output. The profit of
the firm is therefore TR – TC = (250 x 120) – (10,000 + [10 x 120] + [120 x 120]) =
$4,400. This profit (it was zero in the former long run equilibrium) is what
induces these firms to work hard to increase their output in the short run.
In the long run, new firms will enter this industry to try to gain access to these
higher-than-normal profits. As these firms enter, they will add their supply to
the existing supply, in effect pushing the short run industry supply curve to the
right. We can calculate the new long run equilibrium as the intersection of the
new industry demand curve and the long run industry supply curve. The
demand curve is P = 1210 - .08Q and the long run supply curve is a horizontal
line at P = $210, so its equation is P = $210. Therefore, 1210 - .08Q = 210 or the
new long run Q is 12,500 (an additional 500 units of output beyond the short run
equilibrium, and the equilibrium price in the long run is back down to $210).
Since each firm must be at the lowest cost size in the long run (at the minimum
point on their average cost curve), each firm must be producing 100 units of
output (you can check this by finding the output at the min point on the AC
curve, but we know it from the original LR equilibrium anyway). That means
that there are now 12500/100 = 125 firms in the industry. In other words, 25 new
firms entered this industry in the long run to produce the extra output
demanded by consumers. We could check to confirm that profit is back down to
zero in the new LR equilibrium.
We could also use this example to calculate the consumer surplus and producer
surplus in the original equilibrium, the new short-run equilibrium and the new
long-run equilibrium. You should do this as an exercise.