Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Consider the following three firm version of Bertrand pricing game that we discussed in class. Four firms each simultaneously choose a price p1, p2, p3

Consider the following three firm version of Bertrand pricing game that we discussed in class. Four firms each simultaneously choose a price p1, p2, p3 0. There is one consumer whose demand function is given by: q(p) = 120 p.

Since all four firms produce the same product, the consumer buys goods only from the lowest price firm. If the lowest price is offered by more than one firm, then these firms equally share the quantity demanded. Suppose that firms 1 and 2 have marginal cost of production equal to 10 while firm 3 has marginal cost of production equal to 20.

Part a: Write down the best response functions of each firm.

Part b: Find one Nash equilibrium of this game. Justify why it is a Nash equilibrium.

Part c: What are all of the Nash equilibria of this game?

Part d: Is there a Nash equilibrium that is Pareto efficient (from the perspective of just the firms) in this game?

Part e: Consider the 10 firm version of the above game where firms 1 5 have marginal cost of 10 and firms 6 10 have marginal cost of 20. In this case, what are all of the Nash equilibria?

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

More Books

Students also viewed these Economics questions

Question

14. Now reconcile what you answered to problem 15 with problem 13.

Answered: 1 week ago