how to maximize profit when there are two production plants, long-run equilibrium
In a monopolistic market, there is only one firm in the market and the other firms
are immaterial. However, more realistically, companies operate within a market with
multiple competitors. An example of this situation would be an oligopoly, a market in
which there are only a few firms that have substantial influence on the industry as a
whole. Within this type of industry, managers must analyze and take into account the
impact of their decision not only on their firm, but on the other firms in the industry. On
the other hand, managers must also be aware that the actions of the other players in the
industry have a significant impact on the manager’s optimal decisions.
The most basic form of an oligopoly is a duopoly, where there are only two chief
firms in the market. An analysis of the interaction between these two firms allows us to
see the most simplistic form of an oligopoly. To gain a better understanding of how the
interaction between two firms impacts a manager’s decision, Figure 1 presents a
graphical representation of how demand changes depending on the reaction of a rival
firm to a price change.
As may be seen in the graph, assuming one firm is originally at point A with a
price of P0, selling a quantity of Q0, demand changes depending on whether the rival
price matches. Indeed, firms can, in general only control price or quantity in this model
(Singh and Vives, 1984). In this case, the demand curve (D1) assumes that rivals price
match any changes implemented by the firm, whereas demand curve (D2) assumes rivals
do not price match. It is assumed that the firms do not cooperate (Nash, 1950).
Figure 1. Demand Depending on Rivals Actions.
Price
(D1) Demand if rivals
match price changes
2
1
A
P0
(D2) Demand if rivals do
not match price changes
Q
0
Q0
Given the changes in demand depending on whether a firm price matches or not, a
more detailed analysis can see how a change in price effects the quantity demanded of
firm. Figure 2 presents the effect of a price decrease both when the rival firm price
matches and when it does not.
Figure 2. Effect of Price Decrease on Quantity
Demanded Depending on Rival Response.
Price
P0
PL
D2
D1
0
Q0
QL1
Q
QL2
As seen in the graph, when a price decrease occurs, if the rival firm does not
respond and holds its price constant, the price reducing firm sells more. However, if the
firm price matches, the potential increase in units sold is reduced by the price match. On
the other hand, as seen in Figure 3, the opposite happens when a price increase is
implemented.
Figure 3. Effect of Price Increase on Quantity
Demanded Depending on Rival Response.
Price
PH
P0
D2
D1
Q
0 QD2 QD1 Q0
As seen in the graph, when a price increase occurs, if the competing firm does not
respond and holds its price constant, the price increasing firm looses a greater number of
sales than if the rival firm matches the increase.
A well-known example of a duopoly is in the soft drink industry, Coca-Cola vs.
Pepsi (Kopalle et al., 1996). Within the soft drink industry, these two companies are the
most dominant producers and their decisions directly impact each other. Managers at
each firm must constantly determine how they will respond to price changes by the rival
soft drink maker. To show how the previously discussed fundamentals could work in a
real-world setting, assume that you are manager at Coca-Cola and have heard that Pepsi
recently received damaging news from a supplier (the supplier is experiencing a shortage
of a key ingredient in Pepsi), and in response, Pepsi is price-locking its products in order
to keep its supply constant until the supplier can recover. As a manager, how do you
respond? As a manager, you have three options: 1) Increase your prices, 2) Decrease
your prices, or 3) do nothing. If you increase your prices, and Pepsi does not price
match, Coca-Cola will loose a great deal of sales. If you do nothing, nothing will occur.
There should be no change in the quantity demanded. However, if you decrease prices,
the number of units of Coca-Cola products should increase dramatically because Pepsi
cannot price match.
In the long-run, if a rival with match any price change, a manager maximizes
profits when marginal revenue equals marginal cost associated for demand curve D1 (see
Figure 1). If rivals do not price match, the manager will maximize profits when the
marginal revenue equals marginal cost for demand curve D2 (see Figure 1).
References
Henderson, A. (1954). The theory of duopoly. Quarterly Journal of Economics, 64(4),
565-584.
Kopalle, P. K., Rao, A. G., and J. L. Assuncao. (1996). Asymmetric Reference Price
Effects and Dynamic Pricing Policies. Marketing Science, 15(1), 60-85.
Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National
Academy of Sciences, 36(1), 48-49.
Singh, N. and X. Vives (1984). Price and quantity competition in a differentiated
duopoly. Rand Journal of Economics, 15(4) 546-554.
Questions:
1). A market with only two firms present is called a:
A).
B).
C).
D).
E).
Triopoly
Monopoly
Duopoly
Biopoly
None of the above
Answer: C. A duopoly is a form of a oligopoly comprised of only two firms.
2). When a rival matches any price change, demand becomes _____________ elastic
than if they do not.
A).
B).
C).
D).
More
Less
No change
Unable to determine
Answer: B. For any price reduction, a firm will sell more if their rivals do not price
match than if they do. A price decrease will only increase the demanded quantity by a
small amount when rivals price match and vice versa, if they do not price match, a firm
will sell more.
3). The most important element in calculating the benefit of a price change in a duopoly
is:
A).
B).
C).
D).
The number of firms
Calculating when MC=TR
Determining demand
Calculating risk
E). Predicting the interaction between the firms
Answer: E. Predicting the interaction between the two firms is the most important
element in determining how to best optimize profits. Depending on whether a rival firms
will price match in response to a price change determines the benefit level of any
managerial decision.
4). Which of the following would be considered a duopoly:
A).
B).
C).
D).
E).
Pepsi and Coca-Cola
Home Depot and Lowes
DishNetwork and DirecTV
Sirius and XM
All of the above
Answer: E. All of the above would be considered a duopoly within their respective
industries. Each pairing are major competitors and the dominant players in their
industries.
5). Profit maximization is accomplished in a duopoly when:
A).
B).
C).
D).
E).
ATC=MR
MC=AVC
E=MC2
MR=MC
MC=TC
Answer: D. Regardless of whether a firm price matches in a duopoly, a manager’s profit
is maximized when marginal revenue is equal to marginal cost associated with the
respective demand curve.