Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x₁, x₂) = a x₁- x2, where x₁ is the quantity chosen by firm 1, x₂ the quantity chosen by firm 2, and a > 0. The cost functions are C₁ (x₁) = x² and C₂(x₂) = x2. Firm 1 is a Stackelberg leader and firm 2 a Stackelberg follower. Q.2.a Find the subgame-perfect quantities. Q.2.b Calculate each firm's equilibrium profit.

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Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x₁, x₂) = a - X₁ -
x2, where x₁ is the quantity chosen by firm 1, x₂ the quantity chosen by firm 2, and a > 0. The cost
functions are C₁ (x₁) = x² and C₂(x₂) = x2. Firm 1 is a Stackelberg leader and firm 2 a Stackelberg
follower.
Q.2.a Find the subgame-perfect quantities.
Q.2.b Calculate each firm's equilibrium profit.
Transcribed Image Text:Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x₁, x₂) = a - X₁ - x2, where x₁ is the quantity chosen by firm 1, x₂ the quantity chosen by firm 2, and a > 0. The cost functions are C₁ (x₁) = x² and C₂(x₂) = x2. Firm 1 is a Stackelberg leader and firm 2 a Stackelberg follower. Q.2.a Find the subgame-perfect quantities. Q.2.b Calculate each firm's equilibrium profit.
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