Q2
(a) Explain the Cournot model of duopoly using reaction functions and interpret it as a Nash equilibrium. (20 marks) (b) "Perfect competition is incompatible with increasing returns to scale." Examine the statement. (15 marks) (c) Describe a model of oligopoly that explains price stickiness. (15 marks)
हिंदी में प्रश्न पढ़ें
(a) प्रतिक्रिया फलनों का प्रयोग करते हुए कुर्नों के द्वयधिकार मॉडल की व्याख्या कीजिए तथा इसका नैश-संतुलन के रूप में निर्वचन कीजिए। (20 अंक) (b) "पूर्ण-प्रतियोगिता, पैमाने के बढ़ते प्रतिफल के साथ असंगत है।" इस कथन का परीक्षण कीजिए। (15 अंक) (c) अल्पाधिकार के एक ऐसे मॉडल की व्याख्या कीजिए जो निश्चल-कीमत की व्याख्या करता है। (15 अंक)
Directive word: Explain
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How this answer will be evaluated
Approach
The directive 'explain' demands clear exposition with logical reasoning and causal mechanisms. Spend approximately 40% of word budget on part (a) given its 20 marks, 30% each on (b) and (c). Structure: brief introduction on market structures → part (a) with reaction function derivation and Nash equilibrium interpretation → part (b) examining the incompatibility thesis with graphical analysis → part (c) detailing kinked demand curve or menu cost model → conclusion synthesizing implications for competition policy.
Key points expected
- Part (a): Derivation of Cournot reaction functions for two firms with linear demand and cost functions; intersection as Nash equilibrium where neither firm has incentive to deviate
- Part (a): Mathematical derivation showing equilibrium output q1 = q2 = (a-c)/3b, total output 2/3 of monopoly output, price between monopoly and competitive levels
- Part (b): Explanation of why increasing returns (falling LAC) leads to natural monopoly; incompatibility with P=MC condition under perfect competition
- Part (b): Chamberlin's large group case vs. sustainable industry configuration; role of contestable markets as resolution
- Part (c): Kinked demand curve model (Sweezy) with asymmetric price elasticity; price rigidity despite cost changes
- Part (c): Alternative: Menu cost model (Mankiw) or implicit collusion/tacit coordination models explaining sticky prices
- Integration: Comparison of Cournot equilibrium with competitive and collusive outcomes; welfare implications
- Contemporary relevance: Digital platforms, network effects, and renewed debate on competition-innovation tradeoff
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Concept correctness | 25% | 12.5 | Precise definition of Cournot-Nash equilibrium as mutual best responses; correct exposition of why IRS creates market failure under perfect competition; accurate distinction between price stickiness mechanisms (kinked demand vs. menu costs vs. coordination failure) | Basic understanding of duopoly equilibrium and IRS incompatibility but conflates Cournot with Bertrand or Stackelberg; vague explanation of price rigidity without specifying mechanism | Confuses Nash equilibrium with Pareto optimality; states IRS compatible with perfect competition; describes price stickiness without oligopoly model |
| Diagram / model | 20% | 10 | Clear reaction function diagrams with labeled axes, 45° line reference, and stable equilibrium; downward-sloping LAC curve showing natural monopoly problem; kinked demand diagram with discontinuous MR and price rigidity range | Attempted diagrams with correct general shapes but missing labels or incorrect intersection points; partial representation of models | Missing diagrams for quantitative parts; incorrect slope of reaction functions (upward sloping); no graphical analysis of IRS incompatibility |
| Quantitative reasoning | 20% | 10 | Complete algebraic derivation of Cournot equilibrium quantities, price, and profits; comparison with monopoly (a-c)/2b and competitive (a-c)/b outputs; numerical illustration of welfare loss from IRS under competition | States final Cournot formulas without derivation; mentions quantities are between monopoly and competition without showing mathematically | No mathematical working; purely verbal treatment of quantitative relationships; incorrect formulas |
| Indian / empirical examples | 15% | 7.5 | Specific Indian examples: telecom duopoly (Jio-Airtel) for Cournot analysis; natural monopoly cases like Indian Railways or power distribution; OPEC+ or domestic cement/steel price rigidity; references to CCI cases on tacit collusion | Generic references to 'Indian markets' without specificity; international examples only (OPEC, airline cartels) | No empirical examples; purely theoretical treatment; irrelevant examples from non-oligopoly contexts |
| Policy implication | 20% | 10 | Critical evaluation of competition policy: when to regulate natural monopolies vs. promote competition; limitations of Cournot in dynamic industries; implications of price stickiness for monetary policy transmission; reference to Competition Commission of India jurisprudence | Mentions antitrust policy generally without specific instruments; states government should intervene without specifying how | No policy discussion; ignores welfare and regulatory implications; concludes with description rather than evaluation |
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