Market Structures: Cheat Sheet
Monopoly & Oligopoly Guide (Varian)
1. Monopoly Reaction Function (R1 )
A single seller faces the market demand curve. Firm 1’s best response to Firm 2’s output.
Profit Maximization max[P (y1 + ȳ2 )y1 − c(y1 )]
y1
The monopolist sets output where Marginal Revenue Equilibrium: Intersection of reaction curves.
equals Marginal Cost.
y1 = R1 (y2 ) and y2 = R2 (y1 )
M R(y) = M C(y) Output is higher than Monopoly, lower than Perfect Com-
petition.
Since demand slopes down, P > M R, so P > M C.
4. Oligopoly: Stackelberg (Sequential)
Inverse Elasticity Rule
Leader moves first; Follower moves second.
Pricing rule based on demand elasticity ϵ.
MC Backward Induction
P = 1
1 − |ϵ|
1. **Follower:** Maximizes profit taking Leader’s output
as given (yF = RF (yL )). 2. **Leader:** Maximizes profit
Logic: The less elastic the demand (lower |ϵ|), the higher
knowing the Follower’s reaction.
the markup. A monopolist never operates where |ϵ| < 1.
πL = P (yL + RF (yL )) · yL − c(yL )
Efficiency
Result: Leader produces more and earns more than in
Monopolies create Deadweight Loss (DWL) because Cournot.
they produce less than the socially optimal level (P =
M C).
5. Oligopoly: Bertrand (Price)
2. Price Discrimination Firms choose Price simultaneously.
Selling the same good at different prices. • Homogeneous Goods: If firms have same MC, they
undercut until P = M C. (Zero profit).
1st Degree (Perfect) • Differentiated Goods: Prices will be above MC.
Charge everyone their max willingness to pay.
6. Cartel (Collusion)
• Outcome: P = M C for the last unit. Zero consumer
surplus. Pareto Efficient. Firms act together as a single Monopolist.
max π = P (y1 + y2 )(y1 + y2 ) − c(y1 ) − c(y2 )
2nd Degree (Self-Selection) y1 ,y2
Result: Highest industry profit, lowest quantity. Sta-
Volume discounts (block pricing). Consumers sort them-
bility: Unstable. M R > M C for the individual firm,
selves into groups.
creating an incentive to cheat.
3rd Degree (Segmentation)
7. Monopolistic Competition
Charging different groups different prices based on elastic-
ity. Many firms, free entry, differentiated products.
P1 (1 − 1/|ϵ1 |) = M C = P2 (1 − 1/|ϵ2 |)
• Short Run: Acts like a mini-monopoly (π > 0).
Rule: Charge higher price to the group with inelastic
demand. • Long Run: Entry drives demand down/flat until
profits are zero.
3. Oligopoly: Cournot (Simultaneous) P = AC and P > MC
Firms choose Quantity simultaneously. Tangent demand curve to AC curve.
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Monopoly & Oligopoly Guide (Varian)
1. Monopoly Reaction Function (R1 )
A single seller faces the market demand curve. Firm 1’s best response to Firm 2’s output.
Profit Maximization max[P (y1 + ȳ2 )y1 − c(y1 )]
y1
The monopolist sets output where Marginal Revenue Equilibrium: Intersection of reaction curves.
equals Marginal Cost.
y1 = R1 (y2 ) and y2 = R2 (y1 )
M R(y) = M C(y) Output is higher than Monopoly, lower than Perfect Com-
petition.
Since demand slopes down, P > M R, so P > M C.
4. Oligopoly: Stackelberg (Sequential)
Inverse Elasticity Rule
Leader moves first; Follower moves second.
Pricing rule based on demand elasticity ϵ.
MC Backward Induction
P = 1
1 − |ϵ|
1. **Follower:** Maximizes profit taking Leader’s output
as given (yF = RF (yL )). 2. **Leader:** Maximizes profit
Logic: The less elastic the demand (lower |ϵ|), the higher
knowing the Follower’s reaction.
the markup. A monopolist never operates where |ϵ| < 1.
πL = P (yL + RF (yL )) · yL − c(yL )
Efficiency
Result: Leader produces more and earns more than in
Monopolies create Deadweight Loss (DWL) because Cournot.
they produce less than the socially optimal level (P =
M C).
5. Oligopoly: Bertrand (Price)
2. Price Discrimination Firms choose Price simultaneously.
Selling the same good at different prices. • Homogeneous Goods: If firms have same MC, they
undercut until P = M C. (Zero profit).
1st Degree (Perfect) • Differentiated Goods: Prices will be above MC.
Charge everyone their max willingness to pay.
6. Cartel (Collusion)
• Outcome: P = M C for the last unit. Zero consumer
surplus. Pareto Efficient. Firms act together as a single Monopolist.
max π = P (y1 + y2 )(y1 + y2 ) − c(y1 ) − c(y2 )
2nd Degree (Self-Selection) y1 ,y2
Result: Highest industry profit, lowest quantity. Sta-
Volume discounts (block pricing). Consumers sort them-
bility: Unstable. M R > M C for the individual firm,
selves into groups.
creating an incentive to cheat.
3rd Degree (Segmentation)
7. Monopolistic Competition
Charging different groups different prices based on elastic-
ity. Many firms, free entry, differentiated products.
P1 (1 − 1/|ϵ1 |) = M C = P2 (1 − 1/|ϵ2 |)
• Short Run: Acts like a mini-monopoly (π > 0).
Rule: Charge higher price to the group with inelastic
demand. • Long Run: Entry drives demand down/flat until
profits are zero.
3. Oligopoly: Cournot (Simultaneous) P = AC and P > MC
Firms choose Quantity simultaneously. Tangent demand curve to AC curve.
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