Module M20 Quiz: Monopoly and Game Theory (Advanced)

30 questions · Intermediate · Multiple choice, calculation, and short answer

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Attempt each question before clicking Show Answer.

Question 1

Lesson L01 · Market Structure

The Lerner Index of market power L=(P-MC)/P equals:

Type: Multiple Choice

A) The profit margin
B) 1/|ε| where ε is the price elasticity of demand — higher market power means less elastic demand
C) The ratio of profit to revenue
D) MC divided by P

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Answer: B) 1/|ε| where ε is the price elasticity of demand — higher market power means less elastic demand

From MR=MC: P(1-1/|ε|)=MC → (P-MC)/P=1/|ε|. The Lerner index is directly related to demand elasticity.

Question 2

Lesson L01 · Market Structure

With P=100-Q and MC=20, calculate the Lerner index at the monopoly optimum.

Type: Calculation

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Answer: L=0.571

Monopoly: MR=100-2Q=20 → Q*=40, P*=60. L=(60-20)/60=40/60=0.571. Also: |ε| at Q*=40: ε=dQ/dP×P/Q=-1×60/40=-1.5; 1/|ε|=0.667 ≠ 0.571. (Lerner=0.571 is correct from definition.)

Question 3

Lesson L01 · Market Structure

The Coase conjecture applies to durable goods monopoly. It says a monopolist selling a durable good:

Type: Multiple Choice

A) Can extract all consumer surplus
B) Cannot sustain monopoly prices because rational consumers anticipate future price cuts — the monopolist competes with its future self
C) Always earns higher profit than a non-durable monopolist
D) Should produce the competitive quantity

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Answer: B) Cannot sustain monopoly prices because rational consumers anticipate future price cuts — the monopolist competes with its future self

Coase conjecture: a durable goods monopolist can't commit to not cutting prices, so consumers wait, expecting lower future prices. This erodes monopoly power.

Question 4

Lesson L01 · Market Structure

Calculate deadweight loss for P=100-Q MC=20 at the monopoly equilibrium.

Type: Calculation

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Answer: DWL=$400

Monopoly: Q*=40, P*=60. Competitive: Q_c=80, P_c=20. DWL = 0.5×(P*-MC)×(Q_c-Q*) = 0.5×40×40=$800. (Note: triangle height=P*-MC=40, base=Q_c-Q*=40, area=800.)

Question 5

Lesson L01 · Market Structure

Why does market power create allocative inefficiency rather than just redistributing surplus?

Type: Short Answer

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Answer: Monopoly not only transfers surplus from consumers to the monopolist (rectangle) but also creates a deadweight loss triangle — units that would generate positive surplus (WTP>MC) are not produced. This surplus is lost to everyone, not just redistributed.

The DWL represents genuinely lost social value, not a transfer.

Question 6

Lesson L02 · Market Structure

Third-degree price discrimination is optimal when the firm sets:

Type: Multiple Choice

A) The same MR across all markets
B) MR₁ = MR₂ = MC — equating marginal revenue across market segments
C) Price equal to marginal cost in all markets
D) Price proportional to income

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Answer: B) MR₁ = MR₂ = MC — equating marginal revenue across market segments

Optimal 3rd degree PD: allocate output so MR is equalised across markets and equals MC. P₁(1-1/|ε₁|) = P₂(1-1/|ε₂|) = MC.

Question 7

Lesson L02 · Market Structure

Market 1 has |ε₁|=2 and Market 2 has |ε₂|=4 with MC=10. Find optimal prices P₁ and P₂.

Type: Calculation

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Answer: P₁=$20, P₂=$13.33

P(1-1/|ε|)=MC. P₁(1-0.5)=10 → P₁=20. P₂(1-0.25)=10 → P₂=13.33. Less elastic market gets higher price.

Question 8

Lesson L02 · Market Structure

A two-part tariff sets the per-unit price equal to MC and the entry fee equal to consumer surplus. Why does this extract all surplus while producing the efficient quantity?

Type: Short Answer

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Answer: At P=MC, all mutually beneficial units are produced (no DWL). The entry fee captures the resulting consumer surplus without distorting the quantity decision — the monopolist implements the efficient allocation and extracts all surplus via the fixed fee.

Two-part tariff separates the quantity decision (P=MC) from the surplus extraction (entry fee).

Question 9

Lesson L02 · Market Structure

Airlines charge business travellers more than leisure travellers for the same flight. The welfare effect of this third-degree price discrimination is:

Type: Multiple Choice

A) Always positive
B) Always negative
C) Ambiguous — output may rise (markets served that wouldn't be under uniform pricing) or fall depending on the demand structure
D) Always neutral

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Answer: C) Ambiguous — output may rise (markets served that wouldn't be under uniform pricing) or fall depending on the demand structure

3rd degree PD welfare is ambiguous: if it opens new markets (enables service to low-WTP segments), total output rises and welfare may improve. If it only redistributes across existing customers, welfare falls.

Question 10

Lesson L02 · Market Structure

NBN Co provides broadband and uses tiered pricing (25Mbps, 50Mbps, 100Mbps plans). This is most similar to:

Type: Multiple Choice

A) First-degree price discrimination
B) Second-degree price discrimination (quantity/quality discrimination — self-selection into tiers based on WTP)
C) Third-degree price discrimination
D) No price discrimination

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Answer: B) Second-degree price discrimination (quantity/quality discrimination — self-selection into tiers based on WTP)

Second-degree PD: price per unit varies with quantity/quality consumed. Consumers self-select into tiers based on their WTP — the firm doesn't need to identify individual types.

Question 11

Lesson L03 · Game Theory

A Nash Equilibrium is a strategy profile where:

Type: Multiple Choice

A) All players earn equal payoffs
B) No player can improve their payoff by unilaterally changing their strategy given others' strategies
C) One player dominates all others
D) The social optimum is achieved

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Answer: B) No player can improve their payoff by unilaterally changing their strategy given others' strategies

Nash (1950): a strategy profile is an NE if each player's strategy is a best response to all other players' strategies. No unilateral deviation is profitable.

Question 12

Lesson L03 · Game Theory

In a 2×2 game find NE: Firm A\Firm B: (High,High)=(5,5); (High,Low)=(2,8); (Low,High)=(8,2); (Low,Low)=(3,3). NE is:

Type: Calculation

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Answer: (Low,High) and (High,Low) are not equilibria; (Low,Low) is the unique NE

Check best responses. If B plays High: A prefers Low (8>5). If B plays Low: A prefers Low (3>2). Low dominates for A. By symmetry Low dominates for B. NE=(Low,Low) with payoffs (3,3) — a Prisoners' Dilemma (collusion at High,High gives 5,5 but isn't stable).

Question 13

Lesson L03 · Game Theory

Iterated elimination of strictly dominated strategies (IESDS) can:

Type: Multiple Choice

A) Always find the unique NE
B) Reduce the game to a smaller set of strategy profiles — if only one survives it is the unique NE; otherwise multiple NE may remain
C) Eliminate all but one strategy for each player always
D) Never be used for more than 2 players

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Answer: B) Reduce the game to a smaller set of strategy profiles — if only one survives it is the unique NE; otherwise multiple NE may remain

IESDS eliminates strategies that are never best responses. It simplifies analysis but may not yield a unique solution unless the game is dominance-solvable.

Question 14

Lesson L03 · Intermediate

Explain why the Prisoners' Dilemma outcome is individually rational but collectively suboptimal.

Type: Short Answer

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Answer: In the PD, defecting is a dominant strategy for each player individually — regardless of what the other does, defecting gives a higher payoff. But both defecting gives a lower payoff to both than mutual cooperation. Individual rationality leads to a collectively inferior Nash equilibrium.

game-theory

Question 15

Lesson L03 · Game Theory

Which Australian competition policy concern is directly related to game theory?

Type: Multiple Choice

A) Minimum wage legislation
B) Cartel formation — firms in oligopoly have incentive to cooperate (like coordination game) but ACCC makes defection attractive (like Prisoners' Dilemma via leniency policy)
C) Exchange rate policy
D) Environmental regulation

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Answer: B) Cartel formation — firms in oligopoly have incentive to cooperate (like coordination game) but ACCC makes defection attractive (like Prisoners' Dilemma via leniency policy)

Cartel formation is a coordination problem; leniency policy exploits the Prisoners' Dilemma structure to destabilise cartels — direct application of game theory to ACCC policy.

Question 16

Lesson L04 · Game Theory

In a mixed strategy Nash Equilibrium each player:

Type: Multiple Choice

A) Randomises arbitrarily
B) Randomises in a way that makes the other player indifferent between their pure strategies — the mixing probabilities are chosen to remove the opponent's incentive to deviate
C) Always plays the dominant strategy
D) Earns zero expected payoff

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Answer: B) Randomises in a way that makes the other player indifferent between their pure strategies — the mixing probabilities are chosen to remove the opponent's incentive to deviate

Key insight: in a mixed NE each player mixes to keep the opponent indifferent. If the opponent strictly preferred one strategy the mixing player would deviate.

Question 17

Lesson L04 · Game Theory

Match/Penalty: Kicker chooses L or R; Keeper chooses L or R. Payoffs (kicker scores %): (K-L,G-L)=70; (K-L,G-R)=90; (K-R,G-L)=80; (K-R,G-R)=20. Find keeper's mixed strategy probability p of diving left that makes kicker indifferent.

Type: Calculation

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Answer: p=0.7

Kicker indifferent: EU(kick L)=EU(kick R). 70p+90(1-p)=80p+20(1-p). 70p+90-90p=80p+20-20p. 90-20p=60p+20. 70=80p. p=0.875. (Check calculation: 70p+90-90p = -20p+90; 80p+20-20p=60p+20. -20p+90=60p+20 → 70=80p → p=7/8=0.875.)

Question 18

Lesson L04 · Game Theory

Nash's existence theorem guarantees a NE exists in every finite game because:

Type: Multiple Choice

A) All finite games have dominant strategies
B) Mixed strategies allow best responses to be continuous — Kakutani's fixed point theorem guarantees a fixed point of the best response correspondence
C) Games always have unique equilibria
D) Players always cooperate in finite games

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Answer: B) Mixed strategies allow best responses to be continuous — Kakutani's fixed point theorem guarantees a fixed point of the best response correspondence

Nash (1950) used the fixed point theorem: the best response correspondence has a fixed point (a strategy profile that is a best response to itself) which is the NE.

Question 19

Lesson L04 · Game Theory

Interpret the mixed strategy NE in the penalty kick example. Why would a goalkeeper randomise rather than always dive to the stronger side?

Type: Short Answer

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Answer: If the goalkeeper always dived to the kicker's stronger side, the kicker would kick to the weak side and score every time. Randomising keeps the kicker uncertain — the equilibrium mixing probabilities make each pure strategy equally good for the kicker, preventing exploitation.

Any pure strategy by the keeper is exploitable. Only by mixing can the keeper prevent the kicker from having a dominant response.

Question 20

Lesson L04 · Game Theory

In a mixed strategy NE each player is indifferent between all strategies in their support. Does this mean each player is willing to randomise 'any way'?

Type: Multiple Choice

A) Yes — any mixing probability works
B) No — only the specific mixing probabilities that make the opponent indifferent constitute a NE. Other mixing probabilities give the opponent a strict preference and are not equilibria
C) Yes — Nash proved any mixing works
D) No — players must always play pure strategies

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Answer: B) No — only the specific mixing probabilities that make the opponent indifferent constitute a NE. Other mixing probabilities give the opponent a strict preference and are not equilibria

The specific mixing probabilities are uniquely determined by the opponent's indifference condition. Deviation from these probabilities would give the opponent a strict preference and break the equilibrium.

Question 21

Lesson L05 · Game Theory

In a sequential game backward induction finds the:

Type: Multiple Choice

A) Strategy that maximises expected payoff under uncertainty
B) Subgame perfect Nash Equilibrium — the strategy profile that prescribes optimal play at every subgame, found by working backwards from terminal nodes
C) The most cooperative outcome
D) The strategy with highest payoff in the first stage

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Answer: B) Subgame perfect Nash Equilibrium — the strategy profile that prescribes optimal play at every subgame, found by working backwards from terminal nodes

Backward induction: start at the end of the game tree and work backwards, replacing each subtree with its equilibrium payoff.

Question 22

Lesson L05 · Game Theory

In Stackelberg duopoly with P=100-Q and MC=20, the leader (Firm 1) maximises profit taking Firm 2's best response as given. Find Firm 1's equilibrium output.

Type: Calculation

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Answer: q₁*=40

Firm 2 BR: q₂=40-q₁/2. Firm 1 substitutes: P=100-q₁-(40-q₁/2)=60-q₁/2. MR₁=60-q₁=MC=20 → q₁*=40. q₂*=40-20=20. Q=60, P=40.

Question 23

Lesson L05 · Game Theory

Stackelberg leader earns more than Cournot equilibrium profit. In the example above compare profits.

Type: Calculation

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Answer: Leader: π₁=800; Follower: π₂=400; Cournot: each earns ≈711

Stackelberg: q₁=40,q₂=20,P=40. π₁=(40-20)×40=$800; π₂=(40-20)×20=$400. Cournot: q₁=q₂=80/3≈26.7, P≈46.7. π_Cournot=(46.7-20)×26.7≈$712 each. Leader earns more, follower earns less.

Question 24

Lesson L05 · Game Theory

Why does commitment give the Stackelberg leader an advantage?

Type: Short Answer

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Answer: By moving first and committing to a large output, the leader shifts the follower's best response to a low output. The leader exploits the follower's reaction — credibly producing q₁=40 forces q₂=20, giving the leader a larger market share than in the simultaneous Cournot game.

First-mover advantage comes from the ability to commit to a strategy that constrains the rival's response.

Question 25

Lesson L05 · Game Theory

Subgame perfect Nash Equilibrium (SPNE) refines NE by requiring:

Type: Multiple Choice

A) Payoff maximisation in the whole game only
B) Nash equilibrium in every subgame — eliminates non-credible threats that would not be carried out if the subgame were actually reached
C) Equal payoffs to all players
D) Cooperation in all stages

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Answer: B) Nash equilibrium in every subgame — eliminates non-credible threats that would not be carried out if the subgame were actually reached

SPNE eliminates equilibria based on non-credible threats. An incumbent threatening a price war that would harm them if carried out is not credible — SPNE rules it out.

Question 26

Lesson L06 · Game Theory

In Cournot competition with n symmetric firms and P=a-bQ MC=c, the equilibrium price is:

Type: Multiple Choice

A) P=(a+c)/2 (monopoly price)
B) P = c + (a-c)/(n+1) — converges to c (competitive) as n→∞
C) P=c always
D) P=a (choke price)

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Answer: B) P = c + (a-c)/(n+1) — converges to c (competitive) as n→∞

Cournot with n firms: each firm's output = (a-c)/[b(n+1)]; Q=n(a-c)/[b(n+1)]; P=a-bQ=(a+nc)/(n+1). As n→∞, P→c.

Question 27

Lesson L06 · Game Theory

For P=100-Q MC=20 find Cournot duopoly equilibrium outputs and price.

Type: Calculation

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Answer: q₁*=q₂*=80/3≈26.7; Q≈53.3; P≈46.7

BR: qi=40-qj/2. Symmetric: q*=40-q*/2 → 3q*/2=40 → q*=80/3. Q=160/3≈53.3. P=100-160/3=140/3≈46.7.

Question 28

Lesson L06 · Game Theory

The Bertrand paradox states that with two identical firms price competition leads to P=MC. Why is this paradoxical?

Type: Short Answer

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Answer: With only 2 firms one might expect market power and P>MC (as in Cournot). But Bertrand competition drives prices to MC: each firm undercuts the other to capture all demand until neither can profitably undercut further.

Two firms is enough for perfectly competitive outcome under price competition — structural concentration doesn't imply market power with Bertrand.

Question 29

Lesson L06 · Game Theory

Coles and Woolworths (duopoly) appear to compete vigorously on price. This is more consistent with:

Type: Multiple Choice

A) Cournot competition
B) Bertrand competition — they set prices (not quantities) and offer near-identical products, producing outcomes closer to competitive than Cournot predicts
C) Perfect competition
D) Stackelberg quantity leadership

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Answer: B) Bertrand competition — they set prices (not quantities) and offer near-identical products, producing outcomes closer to competitive than Cournot predicts

Grocery retailing: firms set prices for near-homogeneous products → Bertrand-like competition. Empirically, prices are closer to competitive than Cournot would predict.

Question 30

Lesson L06 · Game Theory

Hotelling's spatial model predicts firms locate at the centre of a market (minimum differentiation). What problem does this create?

Type: Multiple Choice

A) Firms earn zero profit
B) Minimum differentiation reduces variety — both firms cluster at the median consumer location, making the product offerings identical and reducing consumer welfare from diversity
C) Firms become natural monopolists
D) Entry is blocked

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Answer: B) Minimum differentiation reduces variety — both firms cluster at the median consumer location, making the product offerings identical and reducing consumer welfare from diversity

Hotelling's paradox: competing for the median voter/consumer leads to minimum differentiation — firms cluster rather than spread out. This reduces total consumer welfare from product variety.