# Nash Equilibrium: producing tennis balls

Suppose you are one of two producers of tennis balls. Both you and your competitor have zero marginal costs. Total demand for tennis balls is

P = 60 - Q

Where Q = the sum of the outputs of you and your competitor.

a) Suppose you are in this situation only once. You and your competitor have to announce your individual outputs at the same time. You expect your competitor to choose the Nash equilibrium strategy. How much will you choose to produce and what is your expected profit?

b) Now suppose that you have to announce your output before your competitor does. How much will you choose to produce? What is your expected profit? Is it an advantage or a disadvantage to move first? Explain.

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#### Solution Preview

a) P = 60 - (Q1 + Q2)

TR1 = PQ1 = {60 - (Q1 + Q2)} Q1 = 60Q1 - Q1^2 - Q2Q1

MR1 = 60 - 2Q1 - Q2

Reaction curve for firm 1 is Q1 = 30 - Q2/2 --- (1)

Similarly, reaction curve for firm 2 is Q2 = 30 - Q1/2

As the product is homogenous and both firms announce their ...

#### Solution Summary

The expert examines the Nash equilibrium for producing tennis balls.