The reactions of competitors influence price decisions, in particular in an oligop- oly market where each provider is aware of the decisions of the others and react accordingly.
1.8.1 Reactions of Competitors
In addition to the demand curve, which describes the purchasing behavior of cus- tomers with respect to prices, price definition requires estimation of competitors’
reactions, which is very difficult due to the unpredictability of their behavior fac- ing a decrease or increase of prices. Competitors’ reactions also depend on the size of the firm, the production capacity, conjuncture and psychology of the managers.
An effective way to forecast the competitors’ reaction is to organize brain- storming with the employees who have some connections with competitors at the technical, commercial, training, scientific, etc., levels.
1.8.2 Decreasing Prices
To illustrate the notion of a price war, let us consider two providers A and B. We assume that A and B are the only providers for the items under consideration (du- opoly market).
If both providers keep their prices constant, then the revenue of both will re- main constant too. If A decreases his/her prices, some clients will migrate from B to A. As a consequence, the revenue of B will decrease while the revenue of A may increase (see example below). If B decreases his/her prices in reaction, then both will lose a part of their revenues.
A similar remark applies if we replace A by B and B by A. This example is summarized in Table 1.10.
Obviously, this strategy is inadequate since if one of the providers decreases his/her prices, the other one cannot do anything but decrease his/her own prices, and the revenues of both providers decrease. Decreasing the prices can be justified if a provider, A for instance, wants to expel B from the market, but this strategy may backfire if B is able to follow the price decrease.
Table 1.10 Prices decrease
Provider B
Keeps the prices constant Decreases the prices Keeps the prices constant The revenues of A and B
remain constant
The revenue of B may increase. The revenue of
A decreases Provider A Decreases the prices The revenue of A may
increase. The revenue of B decreases
Both revenues decrease
34 1 Introduction to Pricing Example
Let mA (respectively, mB) be the number of items sold initially by A (respec- tively, B), and by bA (respectively, bB) the benefit made by A (respectively, B) for each item sold. Only one type of item is considered.
Assume that A reduces his/her price by α , which results in reducing the bene- fit by α for each item sold. Indeed, α <bA otherwise A loses money. As a con- sequence, x clients migrate from B to A.
We denote by RA0 the initial benefit made by A and by R1A the benefit made af- ter reducing the price:
x x b m R b
x m
R1A =( A+ )( A−α)= A0 − Aα+ A −α
The benefit of A increases by reducing the price if and only if
>0
− +
−mAα bAx αx , which leads to:
α α
> −
A A
b x m
For a given value of α∈[0,bA ), any x such that point (x,α) is above the curve of Figure 1.5 representing x as a function of α leads to an increase of the benefit of A, and this increase is equal to −mAα+bAx−αx. If point (x,α) is below the curve, the benefit of A decreases. For any value of α the benefit of B decreases by xbB.
α bA
x
Figure 1.5 The frontier curve when A decreases his/her price
To conclude, cutting prices in duopoly or oligopoly market is often a mistake:
customers are reluctant to switch to the provider who reduces his/her prices since they know that their provider will follow the move and reduce his/her prices.
Thus, the best strategy of all the providers is to maintain their prices, except if a company is strong enough to expel the other competitors from the market.
Nevertheless, a price war has often happened in the past 20 years, particularly in the food and computer industries, or among Internet access companies or the airlines to quote just a few. A price war originates usually in:
• Surplus production capacity, which incites companies to reduce their inventory level at “any” price.
• Production of basic products easy to manufacture, which encourages an aggres- sive competition.
• Persistence of a low-growth market, which incites some providers to try gain- ing market shares at the expense of competitors.
• Management style.
This list is not exhaustive.
An important question is: how to avoid price wars? Or, in other words, how to avoid aggressiveness of competitors when cutting prices? One of the strategies is to differentiate the products (market segmentation) and to reduce the prices in segments that are not important to competitors. Another strategy is to target prod- ucts that do not attract competitors.
1.8.3 Increasing Prices
A similar evolution may be observed if one of the providers increases his/her prices. The results of such a strategy are summarized in Table 1.11.
Table 1.11 Prices increase
Provider B
Keeps prices constant Increases prices Keeps prices constant The revenues of A and B
remain constant The revenue of A increases. The revenue of
B may decrease.
Provider A
Increases prices The revenue of A may decrease. The revenue of
B increases.
Both revenues increase
Thus, the provider who increases his/her prices is not certain to increase the benefit, but the benefit of the competitor will certainly increase. If the competitor does not change his/her prices, the move may be dangerous, but if the competitor increases his/her prices, then both providers increase their benefits.
36 1 Introduction to Pricing Example
We consider only one type of item. We use the same notation as in the previous example, except that α represents the increase of cost decided by provider A and x is the number of clients that migrate from A to B. Provider B keeps his/her price unchanged.
In this situation:
α α
α R m b x x
b x m
R1A =( A− )( A + )= A0 + A − A − and
B B B B
B m x b R xb
R1 =( + ) = 0+
The benefit of B increases, but the benefit of A decreases only if
<0
−
− α
α b x x
mA A , which can be rewritten as:
α α
> +
A A
b x m
For a given value of α∈[0,+∞), any x such that point (x,α ) is above the curve of Figure 1.6 representing
α α
= +
A A
b
x m leads to a cut of the benefit of A, and this cut is equal to mAα−bAx−αx. If point (x,α ) is below the curve, the benefit of A increases.
mA
x
α Figure 1.6 The frontier curve when A increases his/her price
To conclude, if a provider increases their prices, the result will be a global in- crease of benefits if all competitors increase their prices accordingly. But some competitors may decide to keep their prices unchanged, which would result in a cut of benefits for the providers who increased their prices. A quite common strat-
egy to avoid this problem is to apply the well-known signal theory. In this ap- proach, one of the competitors gives notice, a long time in advance, of their will- ingness to increase a price (justified by some novelty or technical improvement).
This strategy also applies when the goal is to reduce a price. In doing so, competi- tors have time to let it be known if they are ready to follow the move or not.