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Week4_Day4_Consumer_Theory_Part4

🎓 Week 4 Day🎓 Week 4 Day 4: Consumer Theory Part 4 - Demand Functions, Lagrangian Method & Tangency Condition | UGC NET Economics Paper-II Welcome to Day 4 of our Consumer Theory series! This lecture covers the derivation of Marshallian demand functions using the Lagrangian method, with special focus on Cobb-Douglas demand functions and tangency conditions. 📚 TOPICS COVERED: ✅ Marshallian Demand Function Derivation ✅ Lagrangian Method for Constrained Optimization ✅ Setting up the Lagrangian Function ✅ First-Order Conditions (FOC) ✅ Tangency Condition: MRS = Price Ratio ✅ Cobb-Douglas Demand Function Derivation ✅ Properties of Demand Functions ✅ Step-by-Step Problem Solving ✅ UGC NET Previous Year Questions 🎯 WHAT YOU'LL LEARN: Derive demand functions from utility maximization Master the Lagrangian method for optimization Understand and apply tangency conditions Derive Cobb-Douglas demand functions: x₁* = αm/p₁ Calculate optimal consumption bundles Interpret λ (Lagrange multiplier) as marginal utility of income Solve constrained optimization problems systematically Master key concepts for UGC NET exam 👩‍🏫 INSTRUCTOR: Mrs. Bhaktilata Tripathy Assistant Professor, Department of Economics Government Women's College, Jeypore Vikram Deb University, Odisha 📖 COURSE DETAILS: Paper: Paper-II (Economics) Unit: Unit-I Microeconomics Topic: Consumer Theory - Part 4 Week: 4, Day: 4 Level: NTA UGC NET June 2026 Preparation Duration: Complete coverage of demand function derivation Language: English with clear mathematical explanations 🔗 CONSUMER THEORY SERIES: ✓ Part 1: Introduction to Consumer Theory ✓ Part 2: Indifference Curves & Utility Functions ✓ Part 3: Advanced Utility & Optimization ✓ Part 4: Demand Functions & Lagrangian Method (This Video) ✓ Part 5: Income & Substitution Effects (Coming Next) 💯 FREE DAILY ZOOM CLASSES: Subscribe to this channel and join our free daily live Zoom classes for: ✓ Interactive learning & doubt clearing ✓ Step-by-step mathematical derivations ✓ Exam strategy and preparation tips ✓ Previous year question analysis ✓ Direct interaction with experienced faculty 📌 KEY CONCEPTS & FORMULAS: Lagrangian: ℒ = U(x₁, x₂) + λ(m - p₁x₁ - p₂x₂) FOC: ∂ℒ/∂x₁ = 0, ∂ℒ/∂x₂ = 0, ∂ℒ/∂λ = 0 Tangency: MU₁/MU₂ = p₁/p₂ Cobb-Douglas U = x₁ᵃx₂ᵇ Demand: x₁* = αm/p₁, x₂* = βm/p₂ (where α+β=1) Budget Constraint: p₁x₁ + p₂x₂ = m λ* = marginal utility of income 🎯 WHO SHOULD WATCH: UGC NET Economics aspirants Students preparing for competitive exams Economics postgraduate students Anyone learning advanced microeconomics Students continuing from Part 3 Learners wanting to master demand theory 📢 SUBSCRIBE for: ✓ Complete UGC NET Economics preparation (Paper-I & Paper-II) ✓ Unit-I Microeconomics full coverage ✓ Free daily Zoom classes with expert faculty ✓ Consumer theory complete series ✓ Mathematical economics step-by-step ✓ Lagrangian optimization techniques ✓ Previous year question detailed solutions 🏛️ INITIATIVE BY: Career Counselling Cell Government Women's College, Jeypore 👍 Like | 💬 Comment | 📤 Share | 🔔 Subscribe #DemandFunction #LagrangianMethod #TangencyCondition #CobbDouglas #ConsumerTheory #Microeconomics #UGCNETEconomics #PaperII #Unit1 #MarshallianDemand #ConstrainedOptimization #UGCNETJune2026 #EconomicsLectures #FreeCoaching #NTAUGCNet #CompetitiveExams #MathematicalEconomics --- 📧 Contact: upananda.pani@gmail.com 🌐 Channel:    / @ugcneteconomicswithupananda   © Career Counselling Cell, GWC, Jeypore #UGCNET2026 #Economics #FreeEducation #ConsumerTheory 4: Consumer Theory Part 4 - Demand Functions, Lagrangian Method & Tangency Condition | UGC NET Economics Paper-II Welcome to Day 4 of our Consumer Theory series! This lecture covers the derivation of Marshallian demand functions using the Lagrangian method, with special focus on Cobb-Douglas demand functions and tangency conditions. 📚 TOPICS COVERED: ✅ Marshallian Demand Function Derivation ✅ Lagrangian Method for Constrained Optimization ✅ Setting up the Lagrangian Function ✅ First-Order Conditions (FOC) ✅ Tangency Condition: MRS = Price Ratio ✅ Cobb-Douglas Demand Function Derivation ✅ Properties of Demand Functions ✅ Step-by-Step Problem Solving ✅ UGC NET Previous Year Questions 🎯 WHAT YOU'LL LEARN: Derive demand functions from utility maximization Master the Lagrangian method for optimization Understand and apply tangency conditions 👩‍🏫 INSTRUCTOR: Mrs. Bhaktilata Tripathy Assistant Professor, Department of Economics Government Women's College, Jeypore 📖 COURSE DETAILS: Paper: Paper-II (Economics) Unit: Unit-I Microeconomics Topic: Consumer Theory - Part 4 Week: 4, Day: 4 📌 KEY CONCEPTS & FORMULAS: Lagrangian: ℒ = U(x₁, x₂) + λ(m - p₁x₁ - p₂x₂) FOC: ∂ℒ/∂x₁ = 0, ∂ℒ/∂x₂ = 0, ∂ℒ/∂λ = 0 Tangency: MU₁/MU₂ = p₁/p₂ Cobb-Douglas U = x₁ᵃx₂ᵇ Demand: x₁* = αm/p₁, x₂* = βm/p₂ (where α+β=1) Budget Constraint: p₁x₁ + p₂x₂ = m