ECON 696: Managerial Economics and Strategy
Lecture Notes 8: The Dynamics of Pricing Rivalry
The previous chapter discussed firms making strategic decisions and then competing
tactically in markets characterized either by Cournot or Bertrand oligopolies. This
chapter goes beyond this analysis to talk about multi-period dynamics in which firms
make tactical decisions, other firms respond, and then the original firms have a chance to
respond to their competitors' responses.
The firms in an industry would ideally like to keep prices high and quantities low, but
these conditions give individual firms incentives to undercut the others, selling a large
quantity of merchandise at slightly lower prices and earning large profits.
Sometimes, high prices in an industry can be maintained while other times they cannot,
and we will discuss what factors help to determine this.
The important difference between this chapter and the previous analysis is that in this
chapter, each firm will have opportunities to change its tactical behavior. It will do this
after considering:
 the solid knowledge it has about its own costs
 somewhat less solid knowledge about the price elasticity of demand for its own
products and cross-price elasticities of demand between its own products and its
competitors' products (that is, the degree to which they are substitutes)
 the likely responses of its competitors who, of course, are also doing this sort of
analysis
The Most Simple Model
For a basic understanding of what we're talking about in this chapter, consider the
diagram from p. 262. It describes the monopoly outcome in a market with constant
marginal costs of $20. The monopolist will produce 40 units and sell them at a price of
$60.
If, instead, there are two firms in this market and each has constant marginal costs equal
to $20, they will maximize their combined profits if they produce a total of 40 units and
sell them at the price determined by the demand curve, $60.
We can't predict how they will divide the market. It might seem reasonable that each
firm would produce 20 units and just keep doing that forever. If representatives of the
firms meet and discuss the matter (which is a crime in much of the world) they may come
up with another division that is mutually beneficial.
If the two firms cannot successfully keep the quantity sold at 40 and the price at $60 the
quantity produced is likely to rise and the price to fall. In the worst case, they may reach
the Bertrand equilibrium where the price is equal to the marginal cost of $20 and neither
firm is making any profit. This might happen because the competitors can't decide how
to divide the market or because, having reached an agreement (either explicitly or tacitly)
one firm starts cheating, either producing more or cutting prices.
The Calculations Involved in Predicting Responses
The book describes points relevant to predicting how a competitor will respond to a
firm's decision to raise prices. They make some assumptions about profits resulting from
each course of action. I'd like to provide a little insight into how you might estimate
relevant numbers if you attempt this type of analysis. For simplicity we'll do the analysis
assuming there are just two firms in the market.
For this example, your firm will be one of two in an industry. Imagine you are
considering changing your price and are wondering whether your competitor will respond
with a corresponding price change. You may be thinking about raising the price and
want to know if your competitor is likely to follow your lead or you may be thinking
about lowering your price and want to know if he will retaliate.
Again, for simplicity, we'll assume that your competitor has the option of maintaining his
price or matching your change, which may mean moving to the same price you will
charge or changing his price by a percentage similar to your percentage change. The
decision about which to do will depend on:
 the quantity he can expect to sell if he maintains his price versus if he matches your
change
 the difference between price and marginal cost (P-MC) or average marginal profit if he
maintains versus if he matches
Estimating these numbers requires some information. What you would like to know, or
at least have some approximate guesses about, is the following:
 The price elasticity of demand for your competitor's good. How much of an increase
in sales can he expect if he cuts prices by, say 1% or if he raises them by a similar
amount.
 Your competitor's marginal cost of production. Roughly, how much would it cost
him to produce one additional unit of output given his current capacity?
An example
Imagine that your firm and another firm are supplying a good or service to a market at
a price of $100/unit. You are considering raising your price to $110, but this will
only be a good move if your competitor does the same. You would like to figure out
how likely they are to match your increase.
The first thing you would like to know is the price elasticity of demand for your
competitor's product. If your competitor matches your price increase of 10%, how
can he expect that the quantity he sells will change. Let's imagine that your
competitor's product has an elasticity of -1.8, so that a price increase of 10% will
bring about a 18% decrease in the quantity sold.1
The second thing you would like to know is your competitor's marginal cost. You're
not likely to have exact figures for this, but if you know a little about his production
process you should be able to make a crude guess, which is probably good enough.
The important question is, will the price increase result in a large enough increase in
1
Note that this is a bit artificial. A price elasticity of demand figure assumes that all things other than the
price of the product in question remain the same. However, if your company changes its price, one
important component of the demand for your competitor's product, the price of a substitute, will have
changed. The analysis will be valid as long as your price change doesn't have too great an effect on how
your competitor's customers respond to a change in the price of his product.
the marginal profit per unit (P-MC) to make up for the 18% reduction in the quantity
sold.
If your competitor's marginal cost is $90, then the increase in price from $100 to $110
will double the profit per unit sold, and profits will rise despite the 18% decrease in
quantity sold. In this case, he is likely to match the price increase.
If your competitor's marginal cost is $20, the increase in price from $100 to $110 will
only be about a 12.5% increase in the profit per unit sold and might not be sufficient
to make up for the 18% decrease in quantity sold. In this case, he is unlikely to match
the price increase.
Incidentally, this example illustrates why it is often the lowest cost providers who are
market leaders. Under the assumption of lower marginal costs the competitor is less
likely to follow the price increase.
The Calculations Involved in Initiating Action
So, once you have determined whether a competitor is likely to respond to an action, how
do you determine whether it is an action you want to take?
The process is similar to the decision your competitor will make about responding to your
action. Your decision about initiating a price change will depend on:
 How much your quantity sold will change as a result of your price change
 How much your quantity sold will change as a result of your competitor's response, if
he will change his price in response.
 How much it will cost you to increase production or how much you will save if you
reduce output slightly.
 How much an increase in future profits is worth to you today
 How quickly your competitor can respond to your price change
Estimating these numbers will require at least approximate values for the following:
 The price elasticity of demand for your firm's product
 The cross-price elasticity between the quantity of your product demanded and your
competitor's price
 Your marginal cost of producing one additional unit of output and the amount, if any,
of your excess production capacity
 Your rate of time preference, or how much you discount future profits
 How long it might take for your competitor to respond to your price change
An example
Imagine that your firm and another firm are supplying a good or service to a market at
a price of $100/unit. You are considering raising your price to $110, but this will
only be a good move if it results in increased profits. You would like to figure out if
this move is likely to increase profits.
The first thing you would like to know is the price elasticity of demand for your
firm's product. That is, holding other things constant, how much of a decrease in
sales can you expect as a result of the 10% increase in price? Let's imagine that your
product has a price elasticity of demand of -2.0, so that the 10% increase you're
considering will result in a 20% decrease in the quantity you sell.
The second thing you would like to know is the cross-price elasticity of demand
between your good and your competitor's price, just in case they decide to match your
price change. Imagine that the cross price elasticity is 0.8, so that a 10% increase in
your competitor's price will result in a 8% increase in the quantity of your product
demanded. If your competitor matches your price increase of 10%, your net
reduction in quantity sold will be approximately 20% - 8% = 12%.2
The third thing you would like to know is what difference this will make to your
profits in each period. As discussed for your competitor above, if your marginal cost
is $90, the increase in price from $100 to $110 will double your marginal profit per
unit and will more than make up for the 16% decrease in quantity sold.
If your marginal cost is $30, the increase in price from $100 to $110 will increase
your marginal profit per unit by about 14.3%. This may be enough to make up for the
decrease in sales if your competitor responds, but not if he doesn't.
Finally, you need to know how long you might have to wait for your competitor to
respond to your price change and, if you will suffer diminished profits in the interim,
how these foregone profits compare to the increased future profits if he responds with
a price increase. The length of time required for a competitor's response depends on
the structure of the industry. The steps required to calculate the present value of a
future stream of profits are laid out in the book.
In this example, if your firm starts out with sales of 1,000 units per period and a
marginal cost of $40 and then increases the price from $100 to $110, the resulting
decrease in quantity sold of 20% (or roughly 200 units) will decrease profits by
1000$100  $40  800$110  $40  $60,000  $56,000  $4,000
So, profits will be diminished by $4,000 until the competitor responds. If and when
your competitor responds by raising his price by 10%, the resulting 8% increase in
the quantity you sell (from 800 to about 800*1.08=864) will change the calculation to
1000$100  $40  864$110  $40  $60,000  $60,480  $480
or a $480 increase in profits.
1.20
 1.1111
1.08
or a decrease of 11.11%. However, as the elasticity estimates are likely to be somewhat inexact, rough
calculations will probably be sufficient.
2
This isn't exactly right. The net result of a 20% decrease and a 4% increase would be
If the competitor matches your change immediately, then your stream of profits
would change from
$60,000 $60,000 $60,000 $60,000 $60,000 $60,000
|-------|-------|-------|-------|-------|-------0
1
2
3
4
5
to
$60,480 $60,480 $60,480 $60,480 $60,480 $60,480
|-------|-------|-------|-------|-------|-------0
1
2
3
4
5
with a change in per period profits of
$480
$480
$480
$480
$480
$480
|-------|-------|-------|-------|-------|-------0
1
2
3
4
5
The increase in profits happens right away and the move is definitely a good idea.
If, however, the competitor matches the move after one period (whether this is a
week, month or year depends on the industry) the stream of profits would change to
$56,000 $60,480 $60,480 $60,480 $60,480 $60,480
|-------|-------|-------|-------|-------|-------0
1
2
3
4
5
for a change in per period profits of
-$4000
$480
$480
$480
$480
$480
|-------|-------|-------|-------|-------|-------0
1
2
3
4
5
The present value of the change in profits is
 $4,000 
480
480
480
480
480
480






3
4
5
1  i 1  i2
1  i 1  i 1  i 1  i6
and if the $480 per period increases are assumed to continue in perpetuity, this is
equal to
 $4,000 
480
i
which will be positive as long as i 
480
 0.12 .
4000
So, as long as the rate at which your firm discounts future profits is less than 12% per
period (where a period is the length of time you expect it will take the competitor to
respond) the price change will increase the present value of your profits if the
competitor responds after one period.
Coordinating Cooperative Pricing
Coordinating pricing decisions is tricky business. Such collusion is illegal in many
countries, so it is a crime to discuss such matters explicitly and is impossible to make
legally binding contracts regarding pricing and output decisions.
Any coordination along these lines must be done without explicit negotiation. If there is
to be some distribution of territory or if one firm is to decide when prices will change, it
must happen in some natural way without an actual decision being made.
Any agreement must be self-enforcing. That is, the parties to the arrangement must find
conforming to the agreement preferable to breaking it. In general, this means that the
present value of the profits from sticking with the agreement must be greater than the
present value of the profits to be had from cutting your price and stealing customers from
other firms.
A further difficulty is that you must be able to tell if other firms in the industry are
sticking with the agreement or not. They're not likely to share that information with you.
With all these problems in mind, let's consider different characteristics of a market which
make it more likely or less likely that a cooperative pricing agreement (keeping prices
relatively high) will endure. The book contains pretty good descriptions of each, so I will
just mention each briefly here.
Market Characteristics That Affect Cooperative Pricing
Market Concentration
The more concentrated the market is, the easier it will be to sustain a cooperative pricing
arrangement. There is, of course, the expected future market structure to consider.
Cooperative pricing will be impossible to sustain if there is significant entry into the
market, and the greater current profits are, the more incentive potential entrants will have
to push their way past any barriers to entry.
Ability to Detect Cheating
If firms have an easier time detecting other firms cheating (cutting prices or increasing
quantities) then cooperative pricing will be easier to sustain because the punishment for
cheating will be sure and swift. For this reason, firms are less likely to ever cheat in the
first place.
Note that, for the most part, the way to punish cheating firms is for the other firms to
increase quantities and cut prices to drive the cheater's profits to zero, or lower. This, of
course, hurts the other firms in the industry as well, but the important thing is to make it
clear that you will punish cheaters in order to reduce the incentives for firms to cheat and,
hopefully, eliminate the incentive to cheat in the first place.
Detection of cheating can be difficult if firms cannot easily observe each other. If you
can't observe another firm's behavior directly, you have no way of knowing if your recent
downturn in sales is due to a poor local economy or cheating by a competitor. This will
be particularly difficult if sales are done on the basis of individual, private contracts. On
the other hand, if, say, gas stations post their prices in numbers four feet high, each
station can easily detect cheating.
Reaction Lags
The more quickly a cheater can be punished the less likely it will be that any firm will
cheat in the first place.
If sales in the industry are more or less continuous and if prices are free to change on a
daily basis, or quicker, a firm which has been observed cheating can be swiftly punished.
If industry sales tend to occur all at once every few months or every few years, it will be
impossible for other firms to punish a cheater quickly. Because any punishment is
delayed, its present value (the present value of the losses associated with the punishment
phase) will be smaller and the punishment will be less effective. Alternatively, the
punishment can be made more severe and will be just as effective as a less severe earlier
punishment, but this will come at a greater cost to the punishing firms. Indeed, it may
hurt them more than it does the cheating firm.
Demand Volatility
If demand in a market goes through cycles of high and low demand, firms have an
incentive to cheat when a market is in decline because punishments are less significant
when the market is in a period of low demand and profits are likely to be low anyway.
Similarly, cooperative agreement can quickly erode when markets are shrinking due to
long run, permanent decreases in demand. Without getting into the mathematics of the
situation, the future benefits of cooperating become smaller and smaller and, at some
point, the immediate incentives to cheat become too great for the agreement to stand.
Asymmetries Among Firms
As the differences between firms become greater, a cooperative agreement becomes
harder to establish. Once established, however, the agreement may be easier to sustain.
Consider the example of two firms trying to decide how to divide the joint profit
maximizing quantity of 40 units of output described at the beginning of the chapter. If
the firms are more or less identical and you asked people how they might divide the
market, most people would give the focal point answer of 50-50. That is, each firm gets
an equal share and produces 20 units.
However, if one firm is initially larger, or is older, or produces a slightly different product
than the other, an initial allocation may not be so easily determined. The cooperative
agreement may never be established.
Once established, as the book describes, firm asymmetries may make the cooperative
agreement more difficult to sustain due to incentives that small firms have to cheat,
knowing that they may be too small to punish.
On the other hand, if a market consists of, say, four different product types and each firm
produces and sells two of these types, it may be relatively easy for the other firms to
punish a cheater by cutting prices in the cheater's lines of business without suffering
losses in their other lines.
Consider the following diagram of four firms serving four different markets or producing
four slightly different products:
Firm 1 produces products A and C, Firm 2 produces products C and D, and so on.
Imagine that Firm 4 is found cheating. Firms 1 and 3 can punish it by cutting their prices
on products A and B without suffering losses on products C and D. The cheating firm 4
is effectively punished at relatively small cost to firms 1 and 3 and at no cost to firm 2.
Actions that affect cooperative pricing
The items listed above are inherent market characteristics which make it more or less
likely that cooperative pricing will persist in a market.
In addition to existing market characteristics, there are a number of actions which firms
can take to make cooperative pricing more successful.
Price Leadership
A price leader is a company which is usually the first to announce price changes, changes
which other firms in the industry usually match. Price leaders generally are the largest or
oldest firms in the market, although the example presented earlier in these notes suggests
that firms with lower costs may have good theoretical claims to price leadership simply
because they have less incentive to follow than do firms with higher costs.
Advance Announcement of Price Changes
This happens in a surprising large number of industries, and airlines are a good example.
A firm will announce future changes in prices, often by declaring a sale with a set
expiration date, and will then wait to see if other firms match their price change. The
change is usually a price increase (which would come at the end of a sale) and, if other
firms give the indication that they won't go along with the cooperative price increase the
firm can always delay or cancel the price change (perhaps by extending the sale).
Most Favored Customer Clauses
A most favored customer (MFC) clause states that if you offer a better price on a certain
product to another customer, you must rebate the price difference to any customer with
whom you have an MFC clause.
While an MFC clause might seem like a good form of protection for a customer, it also
facilitates cooperative pricing because, by offering MFC clauses to its large customers, a
firm is committing to not cutting prices in an attempt to steal customers from other firms
in the industry. This is because an MFC clause increases the cost of selective price
cutting.
MFC clauses are a type of commitment reminiscent of the discussion in the previous
chapter. By granting these clauses, firms force themselves to maintain higher prices than
they might otherwise choose. In a pricing (Bertrand) model, they are committing to a
soft position and inviting their competitors to take a similarly soft position, increasing
profits for both.
Quality Competition
The chapter concludes with a discussion of quality competition.
The most important point here is that competing by offering higher quality at the same
price requires well-informed consumers. Getting information to consumers is difficult,
because any information provided by the firm is suspect. For this reason, the lemons
problem predicts that in some markets poor products will dominate and good products
will be unable to gain a foothold.
Providing information to overcome this problem is not likely to be a profitable line of
business because, once released, information can be fairly easily duplicated and
distributed.
An excellent example of quality competition was the airlines in the United States prior to
deregulation of air travel in the 1970s. Fares for interstate routes were set by regulators
at fairly high levels that should have allowed airlines to be very profitable. Because they
were competing for customers, however, and were constrained to charge high prices,
airlines competed by offering more and more luxurious service on their flights. The
effect was that customers paid high prices for excellent service and airlines, because of
their competitive expenditures, were no more profitable than if they were competing in a
more normal way.
Another example of quality competition came to me when my wife was working at a
public library in Toledo, Ohio. At this time, her favorite fast food chain had centralized
pricing enforced through a large national advertising campaign. There were three
franchises within a ten-minute drive of her library that were all committed (although not
necessarily voluntarily) to these prices. The competed by offering better service. Neither
before nor since have I been in a fast food restaurant which not only offered free drink
refills, but also had people whose job it was to get those refills for you.
Summary
This chapter discusses how firms determine prices, taking into account other firms'
probable reactions. The most important issue is cooperative pricing, which means a
group of firms collectively charge higher prices than they would if they were competing
aggressively. This may occur through actual agreement, which is usually a crime, or
through longstanding traditions.
Various characteristics of a market help to determine how likely cooperative pricing is,
and there are various actions which the firms in that industry can take to enhance their
probability of cooperative success.