Given a symmetric Cournot oligopoly with n= 3: P = 8-Ex, C(x) = 4x, 0x 1...

 

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Given a symmetric Cournot oligopoly with n= 3: P = 8-Ex₁, C₁(x₁) = 4x₁, 0≤x≤ 1 for i=1, 2, 3, where each firm has a capacity constraint 1. a) Derive the coalitional game, compute its MNBP, and show core Ø; b) Find the upper bound for monopoly merging cost, denoted by mmc*, below which the first merger precondition (profitability) holds. In other words, the profitability precondition holds if and only if mmc S mmc* holds. c) Find the upper bound for monopoly merging cost, denoted by mmc**, below which the the second merger precondition (non-empty core) holds. In other words, the non-empty core precondition holds if and only if mmc ≤ mmc** holds. Hint for MNBP: use symmetry, and use binding constraints for two-member coalitions. Given a symmetric Cournot oligopoly with n= 3: P = 8-Ex₁, C₁(x₁) = 4x₁, 0≤x≤ 1 for i=1, 2, 3, where each firm has a capacity constraint 1. a) Derive the coalitional game, compute its MNBP, and show core Ø; b) Find the upper bound for monopoly merging cost, denoted by mmc*, below which the first merger precondition (profitability) holds. In other words, the profitability precondition holds if and only if mmc S mmc* holds. c) Find the upper bound for monopoly merging cost, denoted by mmc**, below which the the second merger precondition (non-empty core) holds. In other words, the non-empty core precondition holds if and only if mmc ≤ mmc** holds. Hint for MNBP: use symmetry, and use binding constraints for two-member coalitions.

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ANSWER a To derive the coalitional game we need to consider all possible coalitions that can be formed by the three firms Since the game is symmetric we only need to consider two types of coalitions t... View the full answer