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Economics 2024 Paper I 50 marks Derive

Paper I — Q2

(a) Derive Pareto optimality conditions in production in a two commodities-two factors-two producers framework. Show that Pareto…

(a)

Derive Pareto optimality conditions in production in a two commodities-two factors-two producers framework. Show that Pareto optimality does not necessarily guarantee for equity. (10+10=20 marks)

(b)

Write down the behavioural assumptions used in Marshallian and Walrasian approaches of market stability. Show that these two approaches become conflicting when both the demand and supply curves are positively sloped. (8+7=15 marks)

(c)

Describe the short-run and long-run equilibrium of a firm under monopolistic competition. 15 marks

हिंदी में प्रश्न पढ़ें

(क) उत्पादन में दो वस्तु-दो साधन-दो उत्पादकों के ढाँचे के अंतर्गत पैरेटो इष्टतमता की शर्तों को व्युत्पन्न कीजिए। सिद्ध कीजिए कि पैरेटो इष्टतमता आवश्यक रूप से समानता का आश्वासन नहीं देती है। (10+10=20 अंक)

(ख) मार्शल और वालरस के बाजार की स्थिरता के दृष्टिकोण में प्रयुक्त व्यवहार-संबंधी मान्यताओं को लिखिए। स्पष्ट कीजिए कि ये दोनों दृष्टिकोण उस समय परस्पर विरोधी हो जाते हैं जब माँग व पूर्ति दोनों वक्रों का ढाल सकारात्मक होता है। (8+7=15 अंक)

(ग) एकाधिकारात्मक प्रतियोगिता के अंतर्गत एक फर्म के अल्पकालीन व दीर्घकालीन संतुलन का वर्णन कीजिए। (15 अंक)

Q2 of the 2024 UPSC Mains Economics Paper I, as printed
The question as printed in the 2024 Economics paper
Evaluate your answer to this question → See all 2024 Economics questions

Model answer

Drafted with AI by UPSC Answer Check against this question's marking rubric, to the expected length. UPSC does not publish answers for Mains — this is one way to score well, not an official key. How we build rubrics and answers.

(a)(i) In a two-commodity X,Y, two-factor L,K, two-producer framework, let X=f(L₁,K₁), Y=g(L₂,K₂), with L₁+L₂=L̄ and K₁+K₂=K̄. Pareto optimality in production requires that no reallocation of factors can raise one commodity without lowering the other. Equivalently, the X- and Y-isoquants must be tangent in the Edgeworth box. For cost minimisation by each producer, minimise wL₁+rK₁ subject to f(L₁,K₁)=X̄; the first-order condition is ∂f/∂L₁ ÷ ∂f/∂K₁ = w/r. Similarly, ∂g/∂L₂ ÷ ∂g/∂K₂ = w/r. Hence MRTS(LK) in X = MRTS(LK) in Y = w/r. The same condition follows without prices: maximise X = f(L₁,K₁) subject to g(L̄ − L₁, K̄ − K₁) = Ȳ. With ℒ = f(L₁,K₁) + λ[g(L̄ − L₁, K̄ − K₁) − Ȳ], the first-order conditions are f_L = λg_L and f_K = λg_K, so f_L/f_K = g_L/g_K. The locus of all such tangencies in the Edgeworth box is the production contract curve; mapping each point to its (X, Y) outputs gives the production possibility curve.

Diagram: Edgeworth production box: isoquant tangencies trace the production contract curve

How this answer will be evaluated

Framework: Microeconomic Theory: Welfare Economics and Market Structures

What earns full marks: Rigorous derivations, precise diagrams, clear distinction between concepts, named economists referenced

Evaluation rubric

Each sub-part is marked on its own, against the marks and word limit printed on the paper.

  1. (a) Derive the Pareto optimality conditions in production in a 2×2×2 framework and show that Pareto optimality does not guarantee equity. 20 marks

    derive— given → assumptions → stepwise derivation → result → check

    Must cover

    • Set-up: X = f(L₁,K₁), Y = g(L₂,K₂), L₁ + L₂ = L̄, K₁ + K₂ = K̄; maximise X for given Y with a Lagrangian
    • Condition: MRTS_LK in X = MRTS_LK in Y (f_L/f_K = g_L/g_K); tangency of isoquants on the production contract curve in the Edgeworth box, which maps into the production possibility curve
    • Edgeworth box diagram showing tangency points and an inefficient point with a lens
    • Equity: every point on the contract curve is efficient but distributions differ widely; efficiency depends on initial endowments; choosing among efficient points needs a social welfare function (Bergson–Samuelson)

    Loses marks

    • Deriving only the exchange condition
    • Claiming Pareto optimality implies fairness

    Earns more

    • Competitive markets achieve the condition through a common w/r
    • Extension to exchange (MRS equality) and top-level MRS = MRT

    Extra mark

    • Second welfare theorem: any efficient point attainable with lump-sum redistribution
  2. (b) State the behavioural assumptions of Marshallian and Walrasian stability and show they conflict when both curves slope upward. 15 marks

    explain— definition/context → points in order → small example → short close

    Must cover

    • Marshallian: quantity adjusts to the gap between demand price and supply price (producers respond to price gap); stability if demand price falls faster than supply price, Pᵈ′(Q) < Pˢ′(Q)
    • Walrasian: price adjusts to excess demand (tâtonnement, buyers and sellers respond to quantity gap); stability if D′(P) < S′(P)
    • Positive slopes: with Pᵈ = a + bQ and Pˢ = c + dQ, Marshall needs b < d while Walras needs 1/b < 1/d, i.e. d < b, so one is stable when the other is unstable
    • Diagram or clear interpretation of which curve cuts from which side

    Loses marks

    • Mixing up the adjustment variable in the two approaches
    • No proof of the conflict

    Earns more

    • Same conflict when both slope downward (backward-bending or decreasing-cost supply)
    • Short-run vs long-run context of each approach

    Extra mark

    • Note that with normally sloped curves both criteria agree
  3. (c) Describe the short-run and long-run equilibrium of a firm under monopolistic competition. 15 marks

    describe— define → structure or process in order → labelled diagram → significance

    Must cover

    • Assumptions: many sellers, product differentiation, free entry and exit, downward-sloping demand, selling costs
    • Short run: MR = MC with MC cutting MR from below; price from the demand curve; supernormal profit, normal profit or loss possible
    • Long run: entry/exit shifts demand until it is tangent to LAC; MR = MC and P = AC, zero economic profit
    • Diagrams for both runs; excess capacity (output below minimum-LAC output) and P > MC

    Loses marks

    • Long-run tangency at minimum LAC
    • No diagram

    Earns more

    • Chamberlin's dd/DD group equilibrium
    • Welfare comment: variety versus inefficiency

    Extra mark

    • Criticism of the excess capacity theorem (Demsetz, selling costs)
What "Derive" is asking you to do

Reach the stated expression from a starting relation, justifying every step. The destination is printed in the question, so only the route earns marks, and the assumptions you work under are part of that route.

Structure that answers it

Assumptions and notation defined → starting relation or governing equation → each step with its justification → the required expression → limiting case or boundary check

Where marks are lost

Writing the standard result first and fitting three lines to it, which an examiner reads at a glance. Marks also go on assumptions left unstated — lossless medium, small amplitude, errors independent with zero mean — and on symbols used before they are defined, even when the question says usual notations.

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