Consider a simple Bertrand market in which N=3 firms compete by setting prices. As long as they can purchase for less than 20, 10 million consumers select to buy the good from the cheapest firm, and break indifferences at random with equal probabilities if more than one firm set the lowest price. a- The three firms have equal marginal costs c1 =c2 =c3 =5. Derive the demand and payoff function of each firm i as a function of the prices in the market. b- What is the set of non-dominated strategies (or prices) for each firm? c- Derive the Nash Equilibrium of this game. d- How do total consumer surplus, welfare, and profits in the market change relatively to a- above if firm 1 becomes more efficient, and specifically if c1 =2
Consider a simple Bertrand market in which N=3 firms compete by setting prices. As long as they can purchase for less than 20, 10 million consumers select to buy the good from the cheapest firm, and break indifferences at random with equal probabilities if more than one firm set the lowest price. a- The three firms have equal marginal costs c1 =c2 =c3 =5. Derive the demand and payoff function of each firm i as a function of the prices in the market. b- What is the set of non-dominated strategies (or prices) for each firm? c- Derive the Nash Equilibrium of this game. d- How do total
How does total consumer surplus, welfare, and profits in the market change if
relatively to d- above, while firm 1 becomes more efficient, firms 2 and 3 experience a
cost-increase (e.g. inputs become harder to procure) so that c1 =2<c2 =c3 =7?
f- In parts a,d,e, is there any
deadweight loss due to market power? Is there any decrease in consumer surplus due
to market power? Discuss
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