## 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 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.