Bertrand Model

Identical Products

• compete through price rather than quantities
• oligopolistic industry
• equilibrium price depends on homogeneity of products
• applicable when changes in capacities are easy to make

Bertrand Paradox

• homogenous products
• one firm undercuts the others
  • takes most customers
• other firms have to adjust (or undercut others themselves)
• strong incentive to undercut everyone
• strong incentive to keep decreasing until p = MC
  • equilibrium: p = MC
• just 2 firms are enough to reach equilibrium
• shows importance of strategic variables (price vs quantity)
• is a form of Nash Equilibrium
• criticism:
  • seems unnatural for firms (gentlemen’s agreement)
  • even at equal prices the firms do not share the market 50/50 necessarily
    • Tie Breaking Rules important with modelling

Different Products

• small differences (still same market)
• each firm sets it’s own price and takes price of competition as given
• oligopolistic industry
• profit maximization:
  • best price to choose

$$P_1^{\ast }=\frac{a+b_2+P_2+c_1{b}_1}{2b_1}$$

- afterwards same thing for $P_{2}^{*}$ 
- then solve for both unknowns $P_{1}$ and $P_2$

• result:
  • when firm 2 increases prices, firm 1 should increase prices as well

Graphically

• Collusion … Cartel price setting
• related to Dilemma Games
  • it would be best (highest profit) for both companies to collude
  • but competing is always the dominant strategy