Tutorial 10: Firms With Market Power (cont.)
The Monopolist's Output Decision
A firm's goal is to maximize economic profit. As we learned
in Tutorial 9, economic profit is at its highest when the
marginal cost of the last unit produced equals the marginal
revenue of the last unit sold. That is, given
P(Q) = R(Q) - C(Q)
P(Q) is maximized when MR(Q*) - MC(Q*) = 0.
In Figure 3, the profit-maximizing level of output for
this price-setting firm is shown at Q* = 3000 units/t, where
MR1 = MC1. Remember that this price-setting firm does not
take the market price as given. Thus, after it sets a target
level of output, it must decide what price to charge. Recall
from Tutorial 2 that market demand shows the maximum willingness
to pay for a given quantity. That means the firm should
look to the demand line at its desired level of output to
see the maximum price that someone will pay for that last
unit. Draw a vertical line up from the x-axis at Q* = 3000
units/t until the line hits the demand curve. Then continue
that line horizontally to the left until it reaches the
vertical axis. That marks the highest price, P* = $70 per
unit, the firm can charge and still sell the last of the
3000 units. For all previous units, some buyers are willing
to pay more, but this firm sets just one price for all the
units it sells.
We know this output and price will generate the highest
economic profit possible for the firm, but how high is it?
Just because economic profit is at a maximum does not mean
it is large -- or even positive!
In Tutorial 9b
we learned that total profit can be calculated as the difference
between price and average cost times the level of output
sold. Graphically, we can find the ATC(Q*) by drawing a
vertical line up from the profit-maximizing output level,
Q*, until it reaches the ATC curve. Then continue that line
horizontally to the left until it reaches the vertical axis.
The point at which that line hits the vertical axis tells
us the average total cost of producing all Q* units per
period. The rectangle (P* - ATC*) · Q* shows the
size of the economic profit earned by this firm from the
sale of Q* units of output at a market price of P*. According
to the Excel workbook for this Tutorial, that economic profit
amounts to just over $55,000.
Example [from MonopQ.xls]
Before turning our attention to the Excel workbook accompanying
this Tutorial, let's work through a numerical example.
Let total cost be written as C(Q) = 75000 + 10·Q
FC = 75000, VC = 10·Q + 0.005·Q
AC = 75000/Q + 10 + 0.005·Q
MC = 10 + 0.01·Q
Let inverse demand be written as P(Q) = 100 - 0.1·Q
TR = 100·Q - 0.1·Q2
MR = 100 - 0.2·Q
Plot just the marginal product curve. [Plotting
cells in nonadjacent columns.]
Remember the steps a profit-maximizing
firm must follow when deciding output and price?
Step 1: To maximize P, set Q* such that set MR
- MC = 0:
(100 - 0.2·Q) - (10 + 0.01·Q)
90 = 0.03·Q
Q* = 3,000 units/t.
Step 2: Set the highest price buyers are willing
From inverse demand, P* = $70 per unit.
Step 3: Calculate P:
P(Q*) = (P* -
where AC* = 75000/3000 + 10 + 0.005 · 3,000
= (70 - 50) · 3,000
P(Q*) = $60,000.
Step 4: Because economic profit is positive,
Step 4 does not apply...
A Rule of Thumb for Pricing
Many economics students find all this talk of how a price-setting
firm chooses price and output to be a bit removed from the
reality of decision making by a real firm. While there is
no doubt that firm's often price just to get close to as
high a profit as possible, there is a relatively simple
way to apply these concepts to finding the P-max price and
output in the real world.
• Recall that MR = P + P·.
• Then, note that MR = MC at P max, so P + P·
Rearranging terms, we get
This gives us a rule of thumb for pricing:
is the markup over marginal cost as a % of P,
which says that the markup should equal to -.
If we rearrange the equation we can write
P as a function of MC and Ed:
...if Ep = -2.33 and MC = $40,
then P = =
$70 / unit.
This is approximately a 43% markup over marginal
cost (at the firm's P-maximizing level of output).
This result of all this mathemagics tells
the firm that the size of the markup they may set (as a
percent of price) depends on price elasticity of demand
for their product. That is, the more responsive buyers are
to an increase in price (i.e., the more price elastic demand
is), the smaller the markup. But the less responsive they
are to a price increase, the larger the markup possible.
Recall from Tutorial 4
that one of the four determinants of buyer responsiveness
is the availability of close substitutes. Thus, demand that
is price elastic can indicate the availability of many substitutes
for this firm's product. So raising the price just chases
the firm's customers to a firm producing a similar product.
When demand is price inelastic, raising the price may leave
customers grumbling, but with few, or no, substitutes available
they have few, if any, choices...
Now it's time to
"do the thing".
Click on the following link
to download the Price-setting
Firm Workbook. Work through Question
1. This will let you practice with the model
of how a price-setting firm chooses the profit-maximizing
level of output and sets the price for the
Return here when you have finished.
downloading the Excel file?
In this part of Tutorial 10 we have discovered that even
firm's with market power, able to set their own product
price, must set output such that MR - MC = 0 in order to
maximize profit. They can then set a price for that output
(rather than have the market set it for them), but that
price cannot be higher than the maximum willingness to pay
of the buyer who purchases the last unit of the firm's output.
So we can discard one street myth about firm's with market
power -- that they can set any price they please!
The law of demand constrains their greed regardless the
magnitude of their market power
In part c of this Tutorial we will look more closely at
the sources of a firm's market power as well as the limitations
of that market power in the long run.