Download Nonexistence of Competitive Equilibrium

Nonexistence of Competitive Equilibrium
A requirement of a competitive equilibrium is that no buyers or sellers have an incentive to
leave the market and strike their own deal. Indeed, it can be shown that the competitive
equilibrium is the only price-quantity pair such that no coalition of buyers and sellers can
benefit by avoiding the market and striking a separate deal. The study of the incentives to
form coalitions is referred to as the theory of the core (Telser 1978).
Figure Long-Run Supply
Consider Figure where all firms have the U-shaped average cost curve, there is free entry, and
the long-run market supply curve is bumpy. Suppose, as shown, that the demand curve cuts
the supply curve where price equals $12 and output equals 25. Because a firm can only
produce at the minimum average cost of $10 if it produces 10 units, it is not possible to
produce profitably the demanded output for $10.
Is the price of $12 and quantity of 25 really a competitive equilibrium? Suppose that some
buyers form a group that collectively buys 10 units and that the group negotiates a separate
deal with one of many potential supplying firms. The group is able to obtain their 10 units at
the minimum average cost of $10 apiece. They have an incentive to contract separately with a
potential supplier, because they can do better than if they rely on the market, and their
incentive is greater for bumpier supply curves (which occur when fixed costs are larger). If
this incentive induces buyers to split off and negotiate separately with a supplier, the
competitive equilibrium does not exist.
To demonstrate this point, we first suppose that the intersection in Figure represents a
competitive equilibrium. In this equilibrium, long-run profits are positive. But we cannot have
a competitive equilibrium in which long-run profits are positive if entry is free. Firms will want
to enter the market, so the proposed equilibrium is not an equilibrium.
The example below discusses how the ocean shipping market coped with the nonexistence of a
competitive equilibrium. When there is only room for a few firms (with sunk costs) in a
market, the price-taking assumption of perfect competition is likely to fail, and other models of
market behavior (those we study in later chapters) are appropriate.
The nonexistence of competitive equilibrium cannot occur if the market supply curve is
perfectly flat at finite output levels rather than only in the limit. If each average cost curve has
a flat bottom for some range of output, then the long-run supply curve is perfectly flat at
some finite output level.
For example, if an individual firm's average cost curve in Figure is flat and equal to $10 for
outputs between 9 and 11 units, then the long-run supply curve for the market is perfectly flat
for outputs equal to or greater than 45 units. If there are five firms in the market, they can
produce outputs of 45 through 55 at the minimum average cost. Six firms can produce outputs
between 54 and 66 at minimum average cost. As long as the demand curve intersects the
market supply curve in the perfectly flat portion, equilibrium exists.
EXAMPLE What Happens When Equilibrium Does Not
Exist?
In some markets, a competitive equilibrium is impossible. That is, there is no coalition of
buyers and sellers who can reach agreement with each other. For any given price, buyers and
sellers leave the market and strike side deals. Chaos results. Some economists (Clark 1923)
have described such situations as destructive competition. A market that is prone to such
instability is likely to foster rules, laws, institutions, or associations that are designed to create
stability.
Pirrong (1987, 1992) shows that ocean shipping for small cargo (less than a boat-load) is
characterized by destructive competition, whereas ocean shipping for boat-sized cargo is not.
The supply curve for small cargo is bumpy and that for large loads is smooth. Pirrong identifies
several instances of destructive competition for small cargo. As a result, numerous
international regulations and cartels (a group of shipping firms) have been formed to control
ocean shipping for small cargo. The cartels have often controlled price and allocated demand
among suppliers. Buyers often sign loyalty agreements under which they agree to use only
one cartel's ships. In contrast, the shipping of large, boat-sized cargo has behaved as a
typically competitive industry.
SOURCES: Clark, James M. 1923. Studies in the Economics of Overhead Costs. Chicago: University of
Chicago Press. Pirrong, Stephen C. 1987. "An Application of Core Theory to the Study of Ocean Shipping
Markets." Ph.D. diss., University of Chicago. Telser, Lester G. 1978. Economic Theory and the
Core. Chicago: University of Chicago Press.