(a) Derive Marshallian demand curve for an inferior good in a two-commodity framework by using income and substitution effects. Is this demand curve always negatively sloped ? Explain. 15+5=20

(b) Consider a firm in a Duopoly market with product dif

Question

(a) Derive Marshallian demand curve for an inferior good in a two-commodity framework by using income and substitution effects. Is this demand curve always negatively sloped ? Explain. 15+5=20

(b) Consider a firm in a Duopoly market with product differentiation in which, Duopolist I faces a demand function given by :

p₁ = 200 - 4q₁ - 2q₂

The cost function of Duopolist I is :

c₁ = 5q₁²

Assume that Duopolist II has 1/3 rd share of the whole market.

Find out optimal price, output and profit for Duopolist I. Also find out the output of Duopolist II. 15

(c) What is Scitovsky Paradox ? Explain it in the context of Kaldor-Hicks compensation test. 5+10=15

UPSC Answer Check · Accepted Answer

Derive the Marshallian demand curve for part (a) using Hicksian decomposition with clear income and substitution effects, then solve the duopoly problem in (b) by setting up profit maximization with conjectural variation, and finally explain the Scitovsky Paradox for (c). Allocate approximately 40% time to part (a), 35% to part (b), and 25% to part (c) based on mark distribution. Structure with brief introductions for each sub-part, rigorous derivation/solution in the body, and concluding insights on theoretical significance.
- Part (a): Derive Marshallian demand using Slutsky equation; decompose price effect into substitution effect (Hicksian: utility constant) and income effect (negative for inferior goods); show demand curve may be positively sloped if income effect > substitution effect (Giffen case)
- Part (a): Diagram with price consumption curve, budget lines, and indifference curves showing SE and IE movements in opposite directions for inferior goods
- Part (b): Set up profit function π₁ = p₁q₁ - c₁ = (200 - 4q₁ - 2q₂)q₁ - 5q₁²; use market share condition q₂/(q₁+q₂) = 1/3 to express q₂ = 0.5q₁; derive first-order condition and solve for q₁, q₂, p₁, π₁
- Part (c): Define Scitovsky Paradox as potential inconsistency where Kaldor-Hicks improvement in one direction can be reversed by compensation in opposite direction, making criterion non-transitive
- Part (c): Explain how double compensation test (Kaldor + Scitovsky) attempts to resolve paradox but still leaves value judgments unresolved; contrast with Bergson-Samuelson social welfare function

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	22%	11	Precise distinction between ordinary (Marshallian) and compensated (Hicksian) demand; correctly identifies Giffen goods as subset of inferior goods; accurate profit maximization setup with correct conjectural variation; explains why Scitovsky reversal occurs due to income distribution effects	Basic understanding of income-substitution decomposition but confuses Hicksian and Slutsky approaches; attempts duopoly solution but errors in market share interpretation; states paradox without explaining mechanism	Confuses normal/inferior/Giffen goods; fundamental errors in profit maximization FOC; describes paradox incorrectly or conflates with other welfare criteria
Diagram / model	18%	9	Clear Hicksian decomposition diagram for part (a) with initial and final equilibrium, compensated budget line, SE and IE arrows labeled; may include Edgeworth box for part (c) showing potential Pareto improvement and reversal	Basic diagram for part (a) but missing compensated budget line or incorrect arrow directions; no diagrams for other parts	No diagram for part (a) or completely incorrect diagram; diagram contradicts verbal explanation
Quantitative reasoning	22%	11	Correct algebraic derivation: q₁ = 15, q₂ = 7.5, p₁ = 125, π₁ = 1125; shows all steps including substitution of market share constraint, FOC, and SOC verification; may discuss reaction function interpretation	Correct setup but arithmetic errors in final values; or correct final answers with missing intermediate steps	Incorrect profit function setup; ignores market share condition; major calculation errors or no quantitative work for part (b)
Indian / empirical examples	18%	9	Cites empirical studies on Giffen behavior (e.g., Jensen & Miller 2008 on rice in China, or Indian context: coarse cereals as inferior goods); references Indian duopoly cases like telecom (Jio-Airtel) or aviation; mentions Indian welfare policy debates (MGNREGA compensation principles)	Generic examples without specific empirical reference; or only one part has relevant example	No empirical examples; or factually incorrect examples (e.g., calling luxury goods Giffen)
Policy implication	20%	10	For (a): discusses why Giffen goods justify targeted subsidies over price controls; for (b): collusion risks in duopoly and need for competition policy; for (c): limitations of cost-benefit analysis in project evaluation and need for distributional considerations in Indian infrastructure projects	Brief mention of policy relevance without depth; or covers only one sub-part	No policy discussion; or irrelevant policy statements disconnected from theory

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