# The link between market concentration and economic welfare

The HHI may be able to measure the 'competitiveness' of a market, but is it an appropriate measure of welfare?

To isolate the consequences of using concentration indices as a guide to policy, let us consider two markets, *X* and Y, with identical demand curves and an identical number of firms. The only difference between these markets is the cost structure of the firms. This difference in cost structure drives differences in market concentration. If industry *Y* has a higher measure of market concentration than industry X, is welfare lower in market *Y*?

To illustrate the main issues, consider the following constant elasticity of demand function:

where *? >* 0 is the absolute value of price elasticity of demand. There are *n* non-identical firms, indexed by *i* = 1,...,n. Suppose that each firm has constant marginal costs of *c**.* The marginal revenue of firm *i* is:

where *s _{i} *

*=*

*—*— is the equilibrium market share of firm i. In a Cournot

? i=1 *qi*

equilibrium, firms set marginal revenue equal to marginal cost, so that:

Summing over all *n* firms gives the equilibrium market price:

- X'=1 c

where *c =* — is the average marginal cost across all firms. Each

*n*

firm's output, *q _{t}* is equal to:

Firm *i's* profits are: and consumer welfare is:

The expression in equation (10.33) reveals an important result in this particular example: with constant marginal costs, and if the number of firms is also constant, then consumer welfare depends only on the *average *marginal cost, *c*, and not on the *spread* of the marginal costs among these firms. Consumers are indifferent between a situation in which firm 1 was a low-cost firm and the remaining firms were high cost, or a situation in which firm 1 was a high-cost firm and the remaining firms had low costs, as long as ^ =_{1} *c _{i}* remained unchanged. This is just a special case of the more general problem analysed in Bergstrom and Varian (1985) who show that in certain cases equilibrium outcomes (that is, market price and quantity, private provision of public goods, and so on) in various strategic situations may be independent of the distribution of the characteristics across the participants.

On the other hand, industry profits *will* depend on the distribution of characteristics across firms. Note that firm i's market share is:

and that total industry profits are:

where *HHI **=* ^ ” *s*^{2} is the Herfindahl-Hirschman concentration index defined earlier. Aggregate profits depend on the distribution of market shares, which (from the expression for *s** _{i}*) themselves depend on the distribution of costs. Low- (high-)cost firms will have high (low) market share. Aggregate welfare is the sum of the consumer surplus and producer profits: