Economics 2022 Paper I 50 marks Solve

Q2

(a) Consider a duopoly market, P = 100 – 2Q, MC = 10 and Q = q₁ + q₂ where P : Market price Q : Total output or the sum total of both firms' output q₁ & q₂ : Firm 1 and Firm 2's output respectively MC : Marginal cost Suppose Firm 1 is the market leader and Firm 2 is the follower. Firm 1 decides its output first and then Firm 2 takes its output decision. Find equilibrium output, price and profit of both the firms. 20 (b) Do you think Firm 1 would have had the first mover advantage if it had gone for the price adjustment? Explain your answer. 15 (c) A competitive equilibrium is both Pareto efficient and equitable. Do you agree? Justify your answer. 15

हिंदी में प्रश्न पढ़ें

(a) एक द्व्याधिकारी (डुओपोली) बाजार में, P = 100 – 2Q, MC = 10 और Q = q₁ + q₂ जहाँ P : बाजार मूल्य Q : कुल उत्पादन/दोनों फर्मों के उत्पादन का कुल योग q₁ तथा q₂ : प्रथम फर्म तथा द्वितीय फर्म का क्रमशः उत्पादन MC : सीमांत लागत मान लीजिए प्रथम फर्म बाजार में नेतृत्व करती है तथा द्वितीय फर्म उसका अनुसरण करती है । पहले प्रथम फर्म अपना उत्पादन निर्धारित करती है तत्पश्चात् द्वितीय फर्म अपना उत्पादन निश्चित करती है । दोनों फर्मों का संतुलन उत्पादन, मूल्य तथा लाभ ज्ञात कीजिए । 20 (b) यदि प्रथम फर्म मूल्य समायोजित करती, तो क्या उसे पहले प्रस्तावक का लाभ प्राप्त होता ? अपने उत्तर की व्याख्या कीजिए । 15 (c) प्रतिस्पर्धी संतुलन पैरेटो कुशल और साम्यिक दोनों है । क्या आप सहमत हैं ? अपने उत्तर के औचित्य को स्थापित कीजिए । 15

Evaluate your answer to this question → See all 2022 Economics questions

Directive word: Solve

This question asks you to solve. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Solve the Stackelberg duopoly model in part (a) by deriving Firm 2's reaction function first, then Firm 1's profit maximization, showing all algebraic steps clearly. For part (b), explain why price leadership yields different first-mover advantages compared to quantity leadership, referencing kinked demand curve or Bertrand competition. For part (c), critically evaluate the efficiency-equity trade-off using the First and Second Welfare Theorems. Allocate approximately 40% effort to (a) given its 20 marks, 30% each to (b) and (c). Structure with brief introduction, systematic working for each part, and concluding synthesis on market structure implications.

Key points expected

  • Part (a): Derive Firm 2's reaction function q₂ = (90 - 2q₁)/4 = 22.5 - 0.5q₁ by maximizing π₂ = (100 - 2q₁ - 2q₂)q₂ - 10q₂
  • Part (a): Substitute reaction function into Firm 1's profit π₁ = (100 - 2q₁ - 2q₂)q₁ - 10q₁ to get q₁ = 22.5, q₂ = 11.25, P = 32.5, π₁ = 506.25, π₂ = 253.125
  • Part (b): Explain that under price competition (Bertrand), first-mover advantage disappears or reverses because p = MC = 10 yields zero economic profit, unlike quantity leadership
  • Part (b): Contrast Stackelberg quantity leadership (positive profits, strategic commitment value) with price leadership where undercutting eliminates rents
  • Part (c): State First Welfare Theorem: competitive equilibrium is Pareto efficient (no reallocation can improve one without harming another)
  • Part (c): Distinguish efficiency from equity—competitive equilibrium may be inequitable (unequal endowments, poverty despite efficiency), requiring redistribution or social welfare functions
  • Part (c): Mention Second Welfare Theorem: any Pareto efficient allocation can be achieved via competitive equilibrium with appropriate lump-sum transfers

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness25%12.5Accurately applies Stackelberg model for (a), distinguishes Bertrand vs Cournot/Stackelberg for (b), and correctly states both Welfare Theorems with precise distinction between efficiency and equity for (c); no conceptual confusion between price and quantity competitionCorrectly solves (a) but vague on why price leadership fails in (b); states competitive equilibrium is efficient but conflates efficiency with equity in (c) without clear theoretical groundingConfuses leader-follower with Cournot-Nash equilibrium; fails to recognize that price competition eliminates profits; omits Second Welfare Theorem or claims competitive equilibrium is automatically equitable
Diagram / model15%7.5Draws clear reaction function diagram for (a) showing isoprofit curves, Stackelberg equilibrium vs Cournot-Nash; sketches Edgeworth box or production possibility frontier for (c) illustrating Pareto efficiency and contract curveIncludes basic reaction function diagram for (a) but misses isoprofit tangency; no diagram for (c) or generic supply-demand without welfare contextNo diagrams; or incorrect diagrams showing simultaneous rather than sequential move game; missing axes labels or wrong equilibrium points
Quantitative reasoning25%12.5Complete algebraic derivation with all steps shown for (a): reaction function derivation, substitution, first-order conditions, second-order verification; correct numerical values for q₁, q₂, P, π₁, π₂; profit comparison with Cournot if mentionedCorrect final answers for (a) but skips intermediate steps or shows calculation errors in reaction function; partial credit for correct method with arithmetic errorsIncorrect reaction function derivation; treats as Cournot or collusive monopoly; wrong profit calculations; no quantitative work shown
Indian / empirical examples15%7.5Cites Indian duopoly cases like telecom (Jio-Airtel), aviation (Indigo-Air India), or cement industry for quantity leadership; references NITI Aayog or Economic Survey on inequality vs growth trade-off for (c); mentions MNREGA or progressive taxation as equity instrumentsGeneric mention of Indian markets without specific firms; vague reference to poverty/inequality without policy linkage or empirical dataNo Indian examples; or irrelevant examples (perfect competition in agriculture for duopoly question); no empirical grounding for efficiency-equity debate
Policy implication20%10For (a)-(b): discusses when government should prefer quantity vs price competition, merger regulation in duopolies; for (c): evaluates whether to prioritize efficiency (growth) or equity (redistribution), citing India's experience with liberalization and targeted welfare programs like PM-KISAN or food securityGeneric statement that competition policy matters; mentions need for redistribution without specific policy instruments or trade-off analysisNo policy discussion; or irrelevant policy prescriptions (price controls in Stackelberg model); fails to connect theoretical results to real-world antitrust or welfare policy

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Economics 2022 Paper I