The Unprofitable Merger
Three identical firms with zero marginal cost compete in Cournot fashion with inverse demand P = 100 − Q. Two of them merge into a single firm that is otherwise identical (still zero cost, and it chooses one quantity), leaving a duopoly. By how much does the combined profit of the two merging firms fall as a result of the merger? Give the size of the fall as a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Firm That Stays Out 3.0/10
- Bertrand Competition 3.0/10
- Cournot Duopoly 3.0/10
Source: Salant, Switzer and Reynolds, 'Losses from Horizontal Merger' (1983). Statement written for AxiomIQ.