b7-merger

Horizontal Mergers in Cournot

Cournot Model Overview

  • Analysis of Cournot with n ≥ 3 firms.

  • Each firm i sets output: qi.

  • Total cost function: TCi = Fi + c * qi

  • Market price function: P = a - bQ, where Q = q1 + q2 + ... + qn

  • Each firm's output when excluding its own is: Q−i = Q - qi.

Marginal Revenue Calculation

  • Marginal Revenue for firm i:

    MRi = P - (∂P/∂Q) * qi


    • Substituting price function:MRi = a - bQ - bqi


    • Further simplified to:MRi = a - bQ−i - 2bqi

Symmetry and Outputs

  • Using symmetry in output:

    q = (a - c) / (n + 1)b*


    • Total output across firms:Q = n / (n + 1) * (a - c) / b*

Implications of Firm Count (n)

  • As n → ∞, competitive output approaches:

    • Q(n) = n / (n + 1) (a - c) b*

  • At n = 1, output resembles monopoly conditions.

  • Profit for each firm derived from: π i = [P - c]qi - Fi

    • Expanding further: P = a - bQ**

Free Entry in Market Context

  • If there is free entry, new firms enter until profits equal zero.

  • Long-run equilibrium number of firms determined by: n = (a - c) √bF - 1*

    • Largest integer that is less than or equal to n*

Mergers in Cournot

Analysis of Mergers Without Entry

  • Consider a market with 3 firms where firms 1 and 2 merge into a new firm m.

    • Assume that Fi = 0.

    • Branches of firm m:

      • Firms 1 and 2 become branches of firm m.

  • Marginal Revenue for the merged firm relating to branch i’s output: MRi = P + (∂P/∂qi) * (q1 + q2)

Marginal Revenue Comparison

  • Comparison with the marginal revenue of the third firm (firm 3): MR3 = P + (∂P/∂q3) * q3

  • The merged firm m treats the combined outputs of branches in the same way as firm 3 treats its output.

Post-Merger Market Dynamics

  • After the merger, a symmetric Cournot duopoly forms between firm m and firm 3.

    • This leads to a situation where firm 3 may gain significant advantages from the merger.

Market Power and Mergers

Conditions for Profitability of Mergers

  • In a situation with Fi = 0, analyzing the market where n − 1 firms merge:

  • Reference Profit Calculation: πni = 1 / (n + 1)² * (a - c)² / b

Profitability Conditions

  • To determine merger profitability: (n - 1) * (1 / (n + 1)²) * (a - c)² / b < 1 / (2 + 1)² * (a - c)² / b.

    • Rearranging and solving gives conditions for n to be worthwhile.

Stability of Equilibrium Numbers

  • It is indicated that mergers are beneficial for firms only if they can achieve overwhelming market share due to high n.

Reasons for Mergers in Markets with No Intrinsic Power

Motivation Behind Mergers

  • If mergers do not result in overwhelming market shares, they are often motivated by:

    • Cost reductions

    • Quality improvements

  • Empirical implication for mergers:

    • Effects productivity efficiency due robust technological complementarity between merging firms.

Differentiation and Mergers

Consumer Demand Model Approach

  • Consideration of a model with firms at opposite ends of a unit distance (1 KM) beach.

  • Demand function for consumers based on their respective choices: u(i, x) = V - Pi - αdi

    • Where di denotes the distance to firm i.

  • Resulting market pricing and equilibrium calculations inform merger dynamics and impact on consumer surplus.