# Assume the same market demand and cost functions as Problem 1, the two firms are duopoly but Firm...

## Question:

Assume the same market demand and cost functions as Problem 1, the two firms are duopoly but Firm 1 enters the market first and sets its output first, firm 2 determines its output decisions after Firm 1. In this case, Firm 1 is the Stackelberg leader and the two firms make their output decisions independently.

The market demand function is {eq}P = 50 - Q {/eq};

Firm's total costs are {eq}TC_1 = 10q_1 \\ TC_2 = 10q_2 {/eq}

where {eq}Q = q_1 + q_2 {/eq}

1. Solve for Firm 1's profit maximizing output decision?

2. Solve for Firm 2's profit maximizing output decision?

3. What is Firm 1's profit? Firm 2's profit? Total profit?

## Reaction Functions:

Reaction functions are schedules that tells a firm exactly how to response to a competitors decisions. For example, If Firm B does *a*, produce *x* units of the good, if Firm B does *b*, then do *y*.

## Answer and Explanation: 1

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View this answerWe start by calculating the followers reaction function, which is solved by maximizing firm 2's profit function.

{eq}\pi_{2}=q_{2}P-TC =...

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Chapter 3 / Lesson 54Explore market power. Learn the definition of market power and understand how it is impacted by different market structures. Discover market power examples.

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