## Market Power

Monopolies derive their market power from their ability to set prices while remaining profitable

• The market power of a monopoly is contingent on its ability to profitably raise prices above the competitive level

• There’s no way for a monopoly to coerce a consumer to buy their good

• Market power isn’t binary → We need a way to measure a firm’s relative market power

• Before we get to our measure of market power, we need to review two important concepts:

• Recall that own-price elasticity of demand measures the responsiveness of consumers to price changes

$\eta = \frac{\% \Delta Q}{\% \Delta P} < 0$

• It can also be shown that the marginal revenue function for a non-competitive firm is given by the following equation

$MR=P \left(1-\frac{1}{|\eta|}\right)$

### Measuring market power: the Lerner index

• The Lerner index allows us to measure market power:

$\lambda = \frac{P-P_c}{P}$

• Perfect competition and profit maximization implies $$P_c=MC=MR$$
• Substituting into our equation will give us:

\begin{aligned} \lambda &= \frac{P-MC}{P} \\ &= \frac{P-MR}{P} \end{aligned}

• Using our equation for MR from the previous slide, the Lerner index simplies to

$\lambda = \frac{1}{|\eta|}$

### Lerner Index: Dominant Firm Extension

• While true monopolies are quite rare, we often observe markets that can be modelled as a dominant firm
• Recall that the dominant firm acts as a monopolist, after accounting for the competitive fringe
• The Lerner index for a dominant firm:

$\lambda = \frac{S}{|\eta|+\varepsilon(1-S)}$

where S denotes the dominant firm’s market share ($$S = \frac{q_{df}}{D} = \frac{q_{df}}{q_{df}+q_{cf}}$$) , $$\eta$$ denotes the own-price elasticity of market demand, $$\varepsilon$$ is the price elasticity of supply for the competitive fringe

#### What happens to $$\lambda$$ as the dominant firm’s market share (S) rises?

• $$\lambda$$ is a measure of the dominant firm’s market power, hence, the higher the portion of output they supply (the higher their market share) the more market power they will control.

• Suppose S = 0 and the firm has a market share of zero:

• Then $$\lambda$$ = 0 and the firm will have no market power because they don’t even supply to that market.
• Now suppose S = 1 so the firm is the sole supplier of output to the market:

$\lambda = \frac{1}{|\eta| + \varepsilon(1-1)} = \frac{1}{|\eta|}$

• Then we will end up with the Lerner index we had previously in the case of a pure monopoly

#### What happens to $$\lambda$$ as the fringe supply becomes more elastic?

• As $$\varepsilon$$ increases, the competitive fringe’s output decisions will be more responsive to price increases by the dominant firm.
• Hence, the competitive fringe will capture more of the market leaving a smaller residual demand.

#### What happens to $$\lambda$$ as the own-price elasticity of demand becomes more elastic?

• More elastic demand can be interpreted as a good or service being more easily substituted.
• If a product has a lot of substitutes, consumers will have stronger reactions to price changes.
• Hence, the more elastic demand is for a product, the less market power a dominant firm will have in that market.