Dominant Firm

• A dominant firm model is a blend of our baseline models of perfect competition and monopoly
• The dominant firm model gives us a more realistic representation of markets
• The dominant firm has power to set a price that maximizes its own profits.
• The market contains many firms but most of them are very small and act as perfect competitors (i.e. price-takers)
• This group of firms is referred to as the competitive fringe
• The dominant firm must take into account the competitive fringe, in addition to demand, when making its price and output decision

Model Assumptions

• The dominant firm has lower production costs than the other firms in the competitive fringe
• The dominant firm knows the market demand and how much output the competitive fringe will produce
• All firms in the competitive fringe are price-takers
• All firms produce homogeneous products

Results

• Lower profits for dominant firm
• Lower price paid by consumers

Examples of markets where a dominant firm (fringe) model is appropriate

1. AT&T (1982): controlled the telecommunication industry through government regulations, vertical integration, and competitive practices.
2. Microsoft (2002): tied its Internet Explorer browser with Windows and restricted the market for competing browsers
3. OPEC: a cartel that operates as a dominant firm
4. Hotels and Airbnbs: hotels set prices and Airbnb hosts act as price-takers (maybe not so much anymore… )

Solving the dominant firm model

• Let $$S_{cf}$$ be the fringe supply curve and $$D$$ be market demand
• The dominant firm must account for the competitive fringe and calculates the residual demand curve: $$d=D-S_{cf}$$
• Once the dominant firm accounts for the presence of fringe firms, the dominant firm acts as a monopolist
• Dominant firm (subscripted as $$df$$) has lower costs and sets the price
• The competitive fringe (subscripted as $$cf$$) is comprised of price-takers
• Dominant firm sets price off of residual demand after choosing the profit maximizing quantity ($$MC = MR$$)
• Competitive fringe dampens the pricing power of the dominant firm
• Note difference between residual demand price ($$d$$) and market demand price ($$D$$) at $$q_{df}$$
• Note that $$q_{total}=q_{cf}+q_{df}$$

Suppose we’re looking at a market with a dominant firm where the marginal cost, market demand, and competitive fringe are given below:

$MC=28\\ D(p)=180-2p\\ S_{cf}(p)=10p-300$

The equilibrium for this model is comprised of an optimal quantity for the dominant firm, competitive fringe quantity, and a price set by the dominant firm

$(q_{df}, q_{cf}, p^{\ast})$

First, find residual demand

\begin{aligned} d &=D-S_{cf}\\ &=(180-2p)-(10p-300)\\ &=480-12p \end{aligned}

Rearrange d to find inverse residual demand then use our trick from earlier to find MR

\begin{aligned} p(q) &=40-\frac{1}{12} q \\ MR(q)&=40-\frac{1}{6} q \end{aligned}

Next, solve for the dominant firm’s profit maximizing quantity and use that to find equilibrium price and competitive fringe

\begin{aligned} MC&=MR\\ 28&=40-\frac{1}{6}q\\ q_{df}&=72\\ p(q_{df})&=40-\frac{1}{12}72 \\ p^{\ast}&=34\\ S_{cf}(p^\ast)&=10(34)-300\\ q_{cf}&=40 \end{aligned}

Last, check our results to ensure we found the correct equilibrium:

$D(p^\ast) = 180-2(34)=112\\ q_{cf}+q_{df}=40+72=112$