# Chapter 12: Monopolistic Competition, Game Theory, Dominant Strategies, IESDS

Latest Version

Published 2 years ago

Latest Version

Published 2 years ago

### 12.1 Monopolistic Competition

**Preface**

**Monopolistic Competition –**many firms with differentiated products.- Market power depends on success in differentiating the product.

#### The Makings of Monopolistic Competition

- Two Key Characteristics:
- Firms compete by selling differentiated products that are highly substitutable for one another but not perfect substitutes.
- Cross-price elasticities of demand are large but not infinite.
**Example**- Toothpaste market- There is free entry and exit – it is relatively easy for new firms to enter the market with their own brands and for existing firms to leave.

#### Equilibrium in the Short Run and the Long Run

- Monopolistic Competition Firms face downward-sloping demand curves – they have some monopoly power.
- Potential to attract new firms drives economic profits to zero.
- Graphically:
- Price > MC and firm has monopoly power.
- SR: Price > AC and firm earns profits.
- LR: Profits attract new firms – demand curve shifts downward. Price = AC so firm earns zero profit despite its power.
- Profit Maximized at LR Demand tangent to firm’s AC curve.

#### Monopolistic Competition and Economic Efficiency

- Monopolistic Competition has two major sources of inefficiency.
**Equilibrium Price > Marginal Cost**- Value to consumers of additional units of output > cost of production.
- Thanks to monopoly power, there is deadweight loss.
**Output is Below that which Minimized Average Cost**- Zero-profit point occurs to the left of min AC because the demand curve is downward sloping.

(PC vs. Monopolistic Competition)

- Monopolistic Competition should not be regulated.
- Monopoly power is small – so DWL is small overall. Because firm’s demand curves are fairly elastic, AC is close to minimum.
**Product Diversity –**consumers value the ability to choose among a wide variety of competing products and brands.

### Chapter 12.2 Oligopoly

- Products may or may not be differentiated – a few firms account for most or all of total production due to barriers to entry.
**Example**- automobiles, steel, aluminum, etc.- Barriers to Entry may be caused by scale economies, patents or access to technology, and the need to spend money for name recognition and reputation.

#### Equilibrium in an Oligopolistic Market

- A firm sets price or output based partly on strategic considerations regarding the behaviour of its competitors.
- Competitors’ decisions depend on the first firm’s decision…
**Equilibrium - Marginal Revenue = Marginal Cost**which maximizes profit.

**Nash Equilibrium**

**Nash Equilibrium –**set of strategies or actions in which each firm does the best it can given its competitors’ actions.**Duopoly –**market in which two firms compete with each other.

#### The Cournot Model

- Oligopoly where firms produce a homogenous good, each firm treats the output of its competitors as
**fixed**, and all firms decide simultaneously how much to produce. **Firm 1’s Output Decision**graphically:- Firm 1’s profit maximizing output depends on how much it
**thinks**that Firm 2 produces. - If it thinks Firm 2 produces nothing, Firm 1’s Demand Curve D
_{1}(0) is the same as the Market Demand Curve. - If it thinks Firm 2 produces 50 units, Firm 1’s Demand Curve D
_{1}(50) is shifted to the left by 50, causing an output of 25 units. - If it thinks Firm 2 produces 75 units, Firm 1’s Demand Curve D
_{1}(75) is shifted to the left by 50, causing an output of 12.5 units. - If it thinks Firm 2 produces 100+ units, Firm 1 will produce nothing.

**Reaction Curves**

**Reaction Curve –**relationship between a firm’s profit maximizing output and the amount it thinks its competitor will produce.- The Firm’s output is a decreasing schedule of how much it thinks its competitor will produce.
**Reaction Curves and Cournot Equilibrium**- The Reaction Curve Schedule relates the firm’s output to how much it thinks its competitor will produce: Q
_{1}*(Q_{2}) and Q_{2}*(Q_{1}) - In Cournot Equilibrium, each firm correctly assumes the amount its competitor produces to thereby maximize its own profits. Neither firm moves from this equilibrium.
**(Intersection between Reaction Curves)**

**Cournot Equilibrium**

**Cournot Equilibrium –**equilibrium in the Cournot Model in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly.- Found at the intersection of two reaction curves, and is an example of a Nash Equilibrium.
**Adjustment:**Cournot Model says nothing about the firms’ adjustment dynamics as neither output is fixed.- It is rational to assume fixed output if 2 firms choose their outputs
**only once**.

#### The Linear Demand Curve (Example)

- Two identical firms face a linear market demand curve:
**P = 30 – Q** - Where Q = total production of both firms and MC = 0.
*Firm’s Total Revenue Curve:*- R
_{1}= PQ_{1}= (30 – Q)Q_{1} - Rearranged: R
_{1}= 30Q_{1}– Q1^{2}– Q_{2}Q_{1} *Firm’s Marginal Revenue*- MR
_{1}= ΔR_{1}/ ΔQ_{1}= 30 – 2Q_{1}– Q_{2} *Firm’s Reaction Curve*- Derived from
**setting MR**_{1}**= 0 (MR) and solving for Q**_{1} - Firm 1’s reaction curve: Q
_{1}= 15 – ½Q_{2} - Firm 2’s reaction curve: Q
_{2}= 15 – ½Q_{1} *Cournot Equilibrium*- Values of Q for each firm at the intersection of the two reaction curves.
- Q
_{1}= Q_{2}= 10 - Total Quantity = 20.
- Market Price: P = 30 - Q, or 10.
*Collusive Equilibrium*- Both firms collude and set outputs to max total profit, split evenly.
- R = PQ = (30 – Q)Q = 30Q – Q
^{2} - MR = ΔR/ ΔQ = 30 – 2Q
- If MR = 0, Q = 15.
- Each firm produces half of total output, Q
_{1}= Q_{2}= 7.5 - Cournot Equilibrium is better than perfect competition but not as good as collusion.
**Duopoly Graphically:**- Collusion curve shows combinations of Q
_{1}and Q_{2}that maximize*total*profits. - If profits are shared equally, each produces 7.5.
- Competitive Equilibrium: Price = MC and Profit = 0.

#### First Mover Advantage – The Stackelberg Model

**Stackelberg Model –**Oligopoly model in which one firm sets its output before other firms do.*Firm 1 sets its output first and then Firm 2, after observing Firm 1’s output, makes its output decision.*- Firm 2’s Profit Maximizing Output
- Profit max at Cournot Reaction Curve Q
_{2}= ½Q_{1} - Firm 1’s Profit Maximizing Output
- Profit max at MR = MC = 0, Firm 1 anticipates how much Firm 2 produces and knows they will choose Q
_{2}according to the reaction curve. - Sub Reaction Curve for Firm 2 Q
_{2}: - R
_{1}= 30Q_{1}– Q_{1}^{2}– Q_{1}(15 – ½Q_{1}) - MR
_{1}= ΔR_{1}/ ΔQ_{1}= 15 – Q_{1} - Set MR = 0 to get
**Q**_{1}**= 15**. **Fait Accompli -**Going first gives Firm 1 an advantage because no matter what the competitor does, the firm will always produce a large output.- Competitor
**must**take the large output level as given and set a low level of output for itself.

Oligopoly (cont’d), Factor Markets (Types of Labour Markets, Labour Demand Functions)

### 12.3 Price Competition

- Competition occurs along price dimensions – use Nash Equilibrium to study price competition.

#### Price Competition with Homogenous Products – the Bertrand Model

**Bertrand Model –**oligopoly in which firms produce a homogenous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge.- Duopoly Example: P = 30 - Q
- Q = Q
_{1}+ Q_{2}is total production of the homogenous good. - MC
_{1}= MC_{2 }= $3 **Cournot Equilibrium:**Q_{1}= Q_{2}= 9, with P = $12, so each firm makes a profit of $81.- Simultaneously choose a
**price**instead of quantity – consumers purchase from the lowest price seller only. - Nash Equilibrium at Price = Marginal Cost: P = $3 for both firms due to zero profit.
- If either firm lowers price just a little, it captures the entire market and doubles its profit.
- Criticism
- It is more natural to compete by setting quantities rather than prices.
- We assume that sales are divided equally among the firms but there is no reason for this.
- Useful to show how the equilibrium outcome in an oligopoly can depend crucially on the firm’s choice of
**strategic variable.**

#### Price Competition with Differentiated Products

- Market shares are determined by prices, as well as differences in design, performance, and durability of products.
- Example: Choosing Prices:
- Two Duopolists with Fixed Costs $20 and Variable Cost = $0
- Demand Curves: Q = 12 – 2P + P
- Both firms set prices at the same time and each firm takes its competitor’s price as fixed.
- Firm1:
- Profit = Revenue less Fixed Costs
- π = P
_{1}Q_{1}– 20 - Sub in Q
_{1}from Demand Curve: π = 12P_{1}– 2P_{1}^{2}+ P_{1}P_{2}- 20 - Profit Maximized depending on P
_{2}, or when incremental profit from a very small increase in its own price is zero. - Δ π
_{1}/ Δ P_{1}= 12 – 4P_{1}+ P_{2}= 0 **Reaction Curve**found by rewriting the profit maximizing price.- P
_{1}= 3 + ¼P_{2} - Firm2: P
_{2}= 3 + ¼P_{1} - Equilibrium
- Point of Intersection of the two reaction curves, with a price of $4 and profit of $12.
- Because each firm is doing the best it can given the price its competitor has set, neither firm has an incentive to change its price.

**Collusion**– If both firms decide to charge the same price to maximize both of their profits, for a higher*collusive equilibrium*of P = $6 and profit of $16.- If Firm 1 sets prices first, there is a
**first mover disadvantage**because it gives the firm that moves second an opportunity to undercut and capture a larger market share.

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