Suppose an industry with four firms 1) having the same constant marginal cost c₁=c₂=c₃=c₄ =2 incurring no fixed cost of production; 3) producing a homogeneous good and choosing output simultaneously (i.e., being Cournot competitors ); and 4) facing the linear inverse demand P=10-Q with Q=q₁+q₂+q₃+q₄.

A) Determine each firm's quantity at the pre-merger equilibrium. Assume firm 1 merges with firm 4 and retains the name firm 1 leaving in the market firms 1, 2, and 3. The merger leads to synergies with the marginal cost of the merged firm becoming c₁

B) Determine each firm's quantity at the post-merger equilibrium (each firm quantity will be a function of c₁)

C) Determine the value for c₁ such that the merger becomes profitable.

D) Determine the value for c₁ such that the price decreases post-merger.

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