178 307 Markets Firms and Consumers Lecture 11

178. 307 Markets, Firms and Consumers Lecture 11: Competition

Overview l l Firms interact with other firms. This is often in various forms of competition. l Keywords – – – Cournot Model Stackleberg Model Betrand Model Hotelling Model Salop Model Predatory Pricing

Neoclassical Models l l Both Cournot and Betrand Models can be solved by Game Theory. Cournot Model has firms competing on output. l l Bertrand Market has firms competing on price. Collusion is much less stable in a Betrand market.

Cournot Model l See tutorial exercises

Betrand Duopoly

Reaction Functions Note: this implies a firm will increase (decrease) its price if its competitors increase (decrease) theirs. l Solve (simultaneously) for all firms and find that all optimal prices are: (a+c)/(2 -b)

Stackelberg Model l Game is similar to Cournot Outputs are no longer selected simultaneously. We make one firm the leader. l l l The solution is by ‘backward induction’. We use the terminal point of the game to determine the follower’s output. This used to derive the leader’s output.

Stackelberg Game

Solutions l l Leader obtains larger share of market (first-mover advantage) In Cournot model the share is (a-c)/3 b each.

Simple Spatial Competition l Hotelling Model (1929) – See tutorial

Salop Model- Introduction l l l Depositors are uniformly located along a circle. There are n banks, indexed by i= 1, . . , n. Banks invest cash in a riskless technology with a return of r. Depositors don’t have access to technology. Transport costs of αx are incurred by each depositor, where x is ‘distance’. • Each depositor has 1 unit of cash. • The Total Length of the circle = 1 • Total mass of depositors =D

Optimal Organisation l l The most distance any consumer will travel to a bank is 1/2 n (halfway round the circle). The sum of all transport costs are Note: you don’t need to prove this.

Optimal number of banks l l Let the unit cost of setting up a bank is F. Optimal number is found by minimising setup and transport costs:

Solution

Define the marginal depositor

Volume of Deposits l Total volume of deposits are ‘doubled’ to take account of banks both sides of the bank i.

Profit of Bank i The solution here requires the use of the product rule

Simplify l Only one solution is possible, if all banks charge the same interest rates…

Profit of Bank

Free Competition Output l l l Free competition leads to too many banks This provides scope for regulation Note that decreasing ‘r’ (e. g. by reserve requirement) has no effect.

Predatory Pricing l A firm sets prices below cost, in an attempt to drive competitors out of the market. – – It hopes to recoup losses after the competitors have been driven out. It does so by exploiting market power after the exit of these other firms. l l It is difficult to distinguish aggressive pricing in a competitive market from predatory pricing. Predatory pricing is usually regarded as illegal.

Theoretical Work l l l Selten (1978) began with a chain-store game. Accomodating Firm 2 weakly dominates Fighting for Firm 1. Firm 2’s type is unknown. If W, it leaves, if T, it stays. Firm 2 T W Firm Fight -1, -1 1 a, 0 Acc. a, 0 0, b

Hence l l Firm 1 may wish to adopt predatory in an infinite length game. The per-period payoff (-1)q +(1 -q)a > 0 l The Firm has to be patient (does not discount future too much). l l l In a finite length game, Firm 1 always accomodates in the last period. Backward induction then implies it will always accommodate. Predatory pricing requires games of infinite length.

Conclusion l l l Predatory Pricing is not as common as some people believe. Conditions depend on asymmetry of information. Predatory firm has to have better information on each firm’s costs. l Experiments on theory (Issac and Smith) confirm these aspects. – – Predatory pricing does not occur with complete information. With incomplete information, some players do slash prices to signal toughness (reputation effect).