Tutorial 10: Firms With Market Power
The Price-setting Firm
In this Tutorial we alter our model of the revenue earned
by firms from the sale of their output, to account for firms
with "market power". These are firms that can
set their own price for the product they sell rather than
take the market price as given. Then we combine that revenue
model with the cost model developed in Tutorial 8, and use
the new model to see how firms with market power
go 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 in both the short run and the long run.
Marginal revenue for a price-setting
firm 
In Tutorial
9 we learned that the total revenue earned by a firm from
the sale of its product is calculated as
R(Q) = P(Q)·Q,
where
P(Q) represents the inverse market demand function
rather than a constant, market determined price. In that
same Tutorial we learned that marginal revenue, MR(Q), measures
the additional revenue, DR(Q),
from the sale of one more unit of output, DQ,
i.e.,
MR(Q) = DR(Q)/DQ.
There
are two important differences in what we saw in Tutorial
9 in the form of each equation. First, in the total revenue
function, the price charged by the firm varies inversely
with output. A firm that set its own price for what it produces
can do so only when it alone faces the market demand for
that good. In such a case, the firm must lower price to
sell more goods -- by the law of demand the quantity demanded
in the market varies inversely with price. The second difference
is that MR is neither constant nor equal to market price.
Let's work through an example to help see the differences.
Example:
Let the inverse market demand curve be given by P(Q)
= 6 - Q.
Then R(Q) = P(Q)·Q = 6Q - Q2
Using calculus, MR(Q) = 
= 6 - 2Q
\ MR(Q) varies inversely
with quantity, is lower than market price, and has twice
the slope of the inverse demand function.
Figure 1 illustrates the demand and marginal revenue functions
for such a firm, which is the only seller of a product in
the market (hence, D1 is the market demand curve).
Figure 1
MR and Ep
While it may be clearer after the above example
why MR varies inversely with quantity and has twice the
slope as inverse demand, it is not clear at first sight
why MR in this model is less than, let alone not equal to,
price (as measured by inverse demand). Figure 2 might help
you to see why this is so.
Suppose D1 illustrates the (inverse) market demand. At
a price of P1, this firm will sell Q1 units of its product
per time period. To sell more, it must lower the price of
each unit. So at a price of P2 it will sell Q2 units per
time period. When it lowers price it loses the total revenue
(TR) it used to make on those first Q1 units -- see the
rectangle labeled -TR. But
it does sell more at the lower price, so the additional
units sold at a price of P2 add to its revenue -- see the
larger rectangle labeled +TR.
So, in this case, total revenue rises when it sells the
additional output, i.e., MR > 0, but MR < P2 because
the firm loses revenue on the first Q1 units sold.
Figure 2
Similarly, at a price of P3, this firm will
sell Q3 units of its product per time period. To sell more,
it must lower the price of each unit. So at a price of P4
it will sell Q4 units per time period. When it lowers price
in this range, it loses the revenue it used to make on those
first Q3 units -- see the rectangle labeled -TR.
But it does sell more at the lower price, so the additional
units sold at a price of P4 add to its revenue -- see the
smaller rectangle labeled +TR.
So, in this case, total revenue falls when it sells the
additional output, i.e., MR < 0, but MR is still less
than P4 because the firm loses a lot of revenue on the first
Q3 units sold. (Not to mention the trivial fact that price
cannot be negative...)
A mathemagical generalization
of this follows:
DR = -
TR + TR
DR = P2(DQ)
+ (DP)Q1
Dividing through by DQ,
Combining terms by dropping the subscripts, MR = P +  ·Q
Multiplying through by P/P, MR = P + P··
Because Ep =  ,
MR = P + P·
\ MR = P·
...where Ep < 0.
So in the case where Ep = -infinity (i.e., the
firm's demand is perfectly elastic), MR = P (because
= 0 when Ep = infinity). In all other cases,
MR < P because
< 1.
| Now it's time to
"do the thing".
Click on the following link
to download the Price
Elasticity Workbook. Work through Question
10. Add a column measuring MR as a function
of output, MR(Q), and add MR(Q) to the plot
of Pd(Q) in step f. This will help you visualize
the relationships among Pd(Q), MR(Q), and
EP(Q).
Return here when you have finished.
Need help
downloading the Excel file? |
|
Now we've altered our model of a profit-maximizing firm
to account for the differences in total and marginal revenue
when firm's have market power. Firms that set their own
price for their output face a downward sloping inverse market
demand curve. As a result, marginal revenue is also a downward
sloping line with twice the slope of the inverse demand
function. Thus, P > MR for price setting firms.
By reworking the price elasticity question in the PElas.xls
worksheet, you should have discovered that, in addition
to the fact that P > MR, when MR > 0, inverse demand
was price elastic. When demand turned price inelastic, MR
< 0.
In the next part of this Tutorial we look at the profit-maximizing
firm's output and pricing decisions.
Continues...
|
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The price-setting firm