Tutorial 9: Firms With No Market Power
Now we have traveled from the production function to the
costs of production. That gives us half the information
we need to model a firm producing goods in a capitalist
economy. But a firm produces goods and services in order
to sell them in the hope that the revenue the goods bring
exceeds the cost, both direct and opportunity, of producing
them. In Tutorial 9 we explore how to model the revenue
earned by firms from the sale of their output.
Then we combine that revenue model with the cost model
developed in Tutorial 8, and use the new model to see how
the firm with no market power goes about determining how
much output to produce. Then, as always, we will alter the
models parameters and see how the firm's price, output,
and economic profit changes in response.
Why are firm's in business? To earn an income for the firm's
owner(s). This income is called profit and its role
is quite often misunderstood. To some, profit is used synonymously
with greed, and it is assumed that most firms earn an enormous
(read "unfair") profit. Profit is simply the difference
between the revenue brought in from the sale of goods, and
the cost of producing those goods, including opportunity
cost. It serves as the reward to the owners for taking risk.
And it is surprisingly small: the national average rate
of return on invested capital (i.e., profit) is about 7%.
So for every $100 the firm invests in the business, it will,
on average, get a return of $7.
It is through this reward that goods and services get produced.
So it is not surprising that the first assumption economists
make about the firm's interest in profit, it that the firm
seeks to maximize profit.
Marginal Revenue, Marginal Cost, and Profit Maximization
We define economic profit, P(Q),
as the difference between total revenue from the
sale of a given level of output, R(Q), less the total
cost of producing that output, C(Q), including opportunity
costs. That is, P(Q) = R(Q) -
C(Q). We learned how to calculate C(Q) in Tutorial 8, now
we'll learn how to calculate R(Q).
Total revenue is calculated as the price of
each item sold times the quantity of units sold per time
period, i.e., R(Q) = P · Q. Note that this equation
is written with price as a constant. This may seem odd at
first, because we know from the law of demand that as price
varies the quantity demanded varies inversely. But we are
not talking about market demand here. Rather, we
are focused only on the demand for the output of a single
firm in a competitive market. Now a competitive market is
made up of large numbers of buyers and sellers. Any one
seller, therefore, produces a small percentage of the total
market output. So even if our representative firm produced
the maximum quantity possible in the short run (when capital
is fixed), its total output is not large enough to make
the market notice its coming or going. So we can safely
assume here that the firm takes the market price as given
and does not vary price with the quantity it wants to sell.
We also assume the firm produces a product that is identical
to that of the other firms in the market.
If the market determines the price the firm must set for
each unit of output it sells, then marginal revenue,
MR(Q), the additional revenue from the sale of one more
unit of output, is equal to that market price, P. Mathemagically,
MR(Q) = DR/DQ.
If the firm takes price as given, then the
change in total revenue is equal to the change in output
times the price the firm gets for each unit. So
MR(Q) = (P · DQ)/DQ
\ MR(Q) = P
Graphically, the price charged for a given unit of output
does not vary with the level of output. In Figure 1, the
market price is $175 per unit. The firm calculates its total
revenue as R(Q) = $175·Q. So marginal revenue, MR1
in Figure 1, is plotted as a horizontal line at the price
level, P*, set by the market, i.e., $175.
Because the firm takes the market price as given, we say
it has 'no market power'. One implication of this is that
the firm is not able to set a price different from its rival
sellers. For example, if the firm charges a price higher
than the market price, say, $176 per unit, it would sell
nothing -- buyers would find another of the thousands of
sellers producing the identical product, and buy from them.
If the firm charged a lower price, say $174 per unit, it
could still sell no more than the maximum it could produce.
So why sell that output at $174 each when the firm could
easily get $175 each? Hence the firm faces a demand curve
that is perfectly elastic at the market price P*.
To sum up, a firm with no market power sells a non unique
product in a competitive market and produces so little of
the total market output that it is forced to charge a price
equal to the market determined price. That market price,
P*, is equal to MR and is the demand curve for the firm's
output, P* = MR = d.
by a Competitive Firm
The firm's goal is to choose that level of output that
maximizes economic profit. How do we model that activity,
that is, how do we model how the firm selects the level
of output that it produces? Let's start from the top. Economic
profit is defined as the difference between revenue and
cost, including opportunity costs:
P(Q) = R(Q) -
Each unit of output that a firm produces adds to its total
cost (i.e., marginal cost is positive). Each unit of output
it sells adds to its total revenue (i.e., marginal revenue
is positive and, we now know, is equal to market price).
The difference between the additional cost of one more unit
of output and the additional revenue from the sale of that
output is additional profit for the firm.
We know from the law of diminishing returns that the marginal
cost of output will eventually be rising as output increases.
That means that at some level of output MR will equal MC
and the addition to profit from the last unit of output
sold will be zero. Continuing with our mathemagical model:
DP = DR
If we divide both sides of the equation above by DQ:
or marginal profit = MR - MC,
When economic profit is at a maximum, the
additional profit from the sale of one more unit of output
equals zero. (Using calculus to find a local maximum, you
would differentiate the total profit function and set it
equal to zero.) So at a maximum economic profit:
i.e., MR(Q) = MC(Q).
Because MR(Q) = P, the maximum economic profit occurs at
an output level such that P = MC(Q). In other words, the
firm continues to produce and sell more output, until the
rising marginal cost of production reaches the price the
firm is forced by the market to charge.
In this first part of Tutorial 9 we have learned that profit,
in a capitalist economic system, is the reward for taking
a risk and gathering resources to produce a good or service.
Economic profit is the difference between total revenue
from the sale of goods and the explicit PLUS opportunity
costs of producing those goods. A firm seeking to maximize
economic profits should set its output level such that the
marginal cost of the last unit produced equals the marginal
revenue from the sale of that unit.
In the next part of this Tutorial we will explore this
latter point further.