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Industrial Organization

Price Elasticity

  • industrial-organization-1.png
  • \(\Delta R = (p+\Delta p)(q+\Delta q)-pq\)
  • \(MR=\dfrac{\Delta R}{\Delta q}=p(1-\dfrac{1}{|e|})\)
  • e = elasticity
  • MR = MC
  • \(\dfrac{p-MC}{p}=\dfrac{1}{|e|}\)
  • elasticity of demand
    • Products with close substitutes have elastic demand.
    • Demand for an individual brand is more elastic than industry aggregate demand.
    • Products with less complements have more elastic demand.
    • Demand becomes more elastic in the long run.
    • As price increases, demand curves become more price elastic.
  • markup = \(\dfrac{P-C}{P}\)
  • market segmentation limit
    • cost of getting everyone's preference profile
    • hard to stop resale

Oligopoly

see Oligopoly

Bertrand Model

  • Bertrand Model
  • firms set price simultaneosly
  • Nash equilibrium of duopoly is both setting competition price -> Bertrand paradox

Cournot Model

  • Cournot Model
  • firms set output simultaneosly
  • Nash equilibrium of duopoly
    • given \(MC=c, P(Q)=a-bQ, a>c\)
    • \(q_1=q_2=\dfrac{a-c}{3b}, P=\dfrac{a+2c}{3}\)
    • P & Q between monopoly & competition
  • Nash equilibrium of n firms
    • given \(MC=c, P(Q)=a-bQ, a>c\)
    • \(q_1=q_2=\dfrac{a-c}{(n+1)b}, P=\dfrac{a+nc}{n+1}\)
    • \(n \rightarrow \infty\) -> competition

example: linear city with differentiation

  • a 1-unit long linear street with evenly distributed customers, and 2 firms at each end
  • transportation cost per unit distance = t
  • equilibrium price = MC+t
  • transportation cost can be translated to product differentiation
  • with product differentiation, products can sell above competition price even in Bertran model

collusion

  • market power = \(\dfrac{p-MC}{p}\)
    • how much is the firm able to sell above MC
  • system profit in Bertrand competition < system profit of monopoly
  • repeated game
    • infinite period
    • discount factor \(\delta\)
      • 1 in this period -> \(\delta\) in next period

Grim Trigger Strategy

  • algo
    • initially both firms set p = monopoly price
    • if history price was always the monopoly price, set p = monopoly price
    • else set p = MC
  • analysis
    • don't deviate -> share monopoly profit
    • deviate -> get all the profit this period
    • to deviate
      • industrial-organization-2.png
      • industrial-organization-3.png
      • \(\delta \geq \dfrac{1}{2}\)

final

https://hackmd.io/lgE6h18aSzyV4I7PrE0zzg

miscellaneous