c2-VI

Vertical Integration

  • Definition:

    • Merger between two firms:

      • Upstream firm: Makes an intermediate product.

      • Downstream firm: Uses the intermediate product to produce the final product.

  • Challenges of Vertical Integration:

    • Reduced expertise in multiple sectors.

    • Increased layers of management leading to reduced efficiency.

    • Potential loss of market discipline, exemplified by General Motors.

Double Marginalization

  • Market Dynamics:

    • Downstream market model represented as: P = a − bQ.

    • Upstream firm, U: Has marginal cost c, sets price Pu.

    • Downstream firm, D: Observes Pu, then sets quantity qd.

  • Profit Calculation:

    • Downstream firm price: P = a − b * qd.

    • Upstream profit: πu = (Pu - c) * qd.

    • Downstream profit: πd = (P - Pu) * qd.

    • Combined profits: πu + πd = (P - c) * qD.

  • Comparison: Integrated vs. Unintegrated case shown.

Integrated Double Marginalization Case

  • Monopoly Situation:

    • Price and quantity under integration:

      • QM = (a − c) / (2b)

      • PM = (a + c) / 2

      • Maximum profits: πm = (a − c)² / (4b)

  • Price Setting: For D,

    • Quantity offered by D: qD(Pu) = a − Pu / (2b).

    • Upstream firm U chooses Pu to maximize: (Pu − c) * qd.

  • Results:

    • Under integration, firm a maximizes utility, leading to potential for high profits.

    • Profit sharing scenarios addressed in terms of power distributions (sa, sb).

Incomplete Contracts

  • Nature of Contracts:

    • Contracts are often incomplete; covering all contingencies can be impractical.

    • Complete contracts would be costless to enforce but are rarely achievable.

  • Consequences:

    • Difficulty in legally verifying contracted actions/outcomes.

    • Costs associated with punishing breaches and unavoidable renegotiation threats.

    • Efficiency concerns surrounding options for renegotiation.

  • Negotiation Dynamics: If possible, contracts may allow renegotiation, which indicates incompleteness.

Bargaining Process in Incomplete Contracts

  • Large Agents Dynamics:

    • When two large agents trade, price determination typically occurs through bargaining.

    • Gross surplus: V; individual payoffs: πi for agents i = a,b.

  • Surplus Distribution:

    • Agreements with πa + πb ≤ V are possible; failure to agree yields pre-determined payoffs.

  • Bargaining Solution:

    • Agents possess bargaining power si, where sa + sb = 1.

    • Resulting payoffs: πi = si * N + di, showing the mechanism of bargaining divides the surplus.

Hold Up Problem in Games

  • Scenario Overview:

    • Upstream firm (a) creates specialized products for a downstream firm (b).

  • Investment Dynamics:

    1. Initial negotiations on price P0 and quality V¯ between a and b.

    2. Firm a invests I, impacting the quality level, V (I).

    3. Quality verification leads to price renegotiation (P1).

  • Renegotiation Outcomes:

    • Upstream profit: πa = P1 − I.

    • Downstream profit assessment: πb = V (I) − P1.

  • Dependence on Parameters: Outcomes deeply reliant on sa, sb, da, db during renegotiation stages.

    • If V(I) cannot be verified, negative outcomes result for the upstream party.

Efficiency and Surplus Allocation in Hold Up

  • Joint Surplus and Efficiency:

    • Joint surplus formula: πa + πb = V (I) − I.

    • Efficiency condition: ∂V/∂I = 1 should hold.

  • Equilibrium: N = V(I), results in significant implications for profit determination.

    • Underinvestment occur unless bargaining power aligns conveniently (sa = 1).

  • Resolution: Vertical integration as a solution; upstream firm a acquires b, establishing full property rights to avoid hold-up scenarios.