b6-diff-price

Differentiated Product Price Competition Location Model

Overview

  • Constrains location choice while allowing price setting.

Cost Structure

  • Firm i sets price (Pi); market determines quantity (qi).

  • Total cost for firm i:

    • TC(qi) = c * qi.

Consumer Value

  • Value from purchasing good i:

    • Consumer value = [V - Pi] - αdi,

    • Where V = maximum consumer value, Pi = price of good, α = sensitivity factor, di = distance to the firm.

  • Value of not consuming:

    • ¯u, sometimes set as -∞; consumers choose to consume either 0 or 1 unit.

Monopoly with Location Choice

Demand Function

  • Any location results in a specific demand function.

  • Monopoly selects location to optimize demand.

  • Graphically represented by:

    • Basic diagrams showing parameters like V, P, ¯u, Q, and ∆P.

Pricing Strategies

  • Benefits of positioning near the middle and the effects of different price strategies:

    • Illustrate scenarios with fixed prices and varying benefits.

    • Examine demand when positioned centrally with different pricing setups.

Demand Definition

  • Demand when in the middle:

    • P¯ = V − ¯u − α/2.

  • Quantity demand based on price thresholds:

    • Q(P) = 1 if P ≤ P¯,

    • Q(P) = 2α[V − ¯u] − 2αP if P ≥ P¯.

Analysis of Two-Firm Competition Without Location Choice

Initial Assumptions

  • Location choice is simplified; firms are positioned at opposite ends of the market.

  • Assumption on utility:

    • Ensure u ≤ V - c - (3/2)α.

Pricing Functions

  • Utility functions per firm:

    • u(1, x) = V - p1 - αx,

    • u(2, x) = V - p2 - α(1 - x).

  • Implications of price setting on marginal revenue:

    • Firms set prices aiming to equalize marginal revenue with marginal costs (MC).

Role of Marginal Revenue in Strategy

  • Define marginal revenue (MR) under price setting:

    • For firm i: MR = pi + (∂pi/∂qi * qi) = c.

Reaction Functions and Equilibrium

Setting Up Reaction Functions

  • Establish equilibria by equating MR1:

    • MR1 = 2p1 - α - p2, set equal to marginal cost (c).

Resolution of Equilibrium Prices

  • Reaction prices:

    • pr1 = (c + α + p2)/2,

    • pr2 = (c + α + p1)/2.

  • Equilibrium established through consistent pricing conditions:

    • p1 = p2 = c + α.

Impact of Increased Differentiation

Decision Dynamics

  • Increased differentiation shifts equilibrium prices and demand.

  • Impacts on marginal cost ranges and symmetry.

Graphing Changes in Reaction Functions

  • As differentiation increases:

    • pr1 and pr2 exhibit slopes that reflect varied competitive dynamics.

Vertical Differentiation Considerations

Effects on Competition

  • Both firms can benefit from one-sided increased differentiation.

  • A differentiation decline impacts share:

    • One firm benefits while the other loses market share.

Example: American Tobacco Industry

Market and Brand Dynamics

  • Presence of three premium brands: Camel, Lucky Strikes, Chesterfield.

  • Competition against lower-quality fringe brands.

Historical Context

  • Price manipulation strategies implemented:

    1. Bidding up prices of low-quality tobacco.

    2. Price leadership established by Reynolds.

Price Leadership Concept

  • Price leadership refers to firms coordinating prices in parallel, but with potential resistance to competitive coordination.