Suppose two firms produce a homogeneous good for a given market. Firm 1 is a domestic...

  

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Suppose two firms produce a homogeneous good for a given market. Firm 1 is a domestic firm and determines their quantity supply q₁ of the good which is produced at cost c₁(91) (91)2. Firm 2 produces internationally and determines their quantity supply 12 of the good which is produced at cost c2(92) = 392. The price of the good depends on supplied quantity in the following way: p(q) = 60 - q where q = 9₁ +92 is total quantity supply. (a) First, assume that both firms determine their quantities simulta- neously. Write down the game in strategic form and determine the Nash equilibrium of the game. What is the price of the good in the Nash equilibrium of this game? [6] (b) Now, assume that firm 2 determines its quantity first, and firm 1 chooses its quantity after observing the choice by firm 2. Deter- mine the subgame perfect Nash equilibrium. What is the price of the good in the subgame perfect Nash equilibrium of this game? [6] (c) Suppose both firms collude and determine the quantities that maximise the industry profits defined by the sum of both firms' profits. Determine these quantities and the resulting price in this collusion scenario. Explain the relation to (a) and (b). [6] Suppose two firms produce a homogeneous good for a given market. Firm 1 is a domestic firm and determines their quantity supply q₁ of the good which is produced at cost c₁(91) (91)2. Firm 2 produces internationally and determines their quantity supply 12 of the good which is produced at cost c2(92) = 392. The price of the good depends on supplied quantity in the following way: p(q) = 60 - q where q = 9₁ +92 is total quantity supply. (a) First, assume that both firms determine their quantities simulta- neously. Write down the game in strategic form and determine the Nash equilibrium of the game. What is the price of the good in the Nash equilibrium of this game? [6] (b) Now, assume that firm 2 determines its quantity first, and firm 1 chooses its quantity after observing the choice by firm 2. Deter- mine the subgame perfect Nash equilibrium. What is the price of the good in the subgame perfect Nash equilibrium of this game? [6] (c) Suppose both firms collude and determine the quantities that maximise the industry profits defined by the sum of both firms' profits. Determine these quantities and the resulting price in this collusion scenario. Explain the relation to (a) and (b). [6]

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The problem youve presented is a classic example of a Cournot duopoly where two firms compete on the quantity of output to determine the market price They are also examples of game theory in economics ... View the full answer