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Cobb-Douglas Production Function: Explained for UGC NET Commerce and Economics
Tags: Production Function, Economics, UGC NET Commerce, Cobb-Douglas Function, Microeconomics
📘 What is Cobb-Douglas Production Function?
The Cobb-Douglas Production Function is a specific form of production function used to represent the relationship between output and input factors such as labour and capital. It is widely used in economic analysis due to its simplicity and empirical relevance.
The Isoquants of this production function are hyperbolic, asymptotic to both the axis (i.e. it never touches any axis). Refer Fig.
📐 Mathematical Formula
Total Production\((TP_{LK})=Q = A · L^α · K^β\)- Q = Output
- L = Labour input
- K = Capital input
- A = Total Factor Productivity (technology)
- α = Output elasticity of labour
- β = Output elasticity of capital
Averga Production\((TP_K)= A · L^α · K^{β-1}\)
Marginal Production\((MP_L = A α· L^{α-1} · K^β\)
Marginal Production\((MP_K) = Aβ · L^α · K^{β-1}\)
Marginal Rate of Technical Substitutes MRTS = $\frac{MP_L}{MP_K}$ = $\frac{A α· L^{α-1} · K^β}{Aβ · L^α · K^{β-1}}$ $\frac{αK}{βL}$
🧠 Key Characteristics
- Elasticity of substitution is equal to 1
- Can exhibit increasing, decreasing, or constant returns to scale depending on α + β
- Isoquants are smooth, convex to origin, and reflect diminishing MRTS (Marginal Rate of Technical Substitution)
- Used to model economies in both micro and macroeconomic frameworks
📊 Returns to Scale Based on α + β
- α + β = 1 ⇒ Constant returns to scale
- α + β > 1 ⇒ Increasing returns to scale
- α + β < 1 ⇒ Decreasing returns to scale
📈 Isoquants of Cobb-Douglas
The isoquants in Cobb-Douglas are convex and downward sloping. As a firm substitutes one input for another, the output remains constant. This reflects the diminishing MRTS between labour and capital.
📝 UGC NET MCQs Based on Cobb-Douglas
- If α = 0.5 and β = 0.4, what is the return to scale?
Answer: Decreasing returns (α + β = 0.9) - Elasticity of substitution in Cobb-Douglas is:
Answer: 1 - In Cobb-Douglas, isoquants are:
Answer: Convex to origin - Which parameter represents output elasticity of labour?
Answer: α
🎯 Summary
- Cobb-Douglas is realistic for modelling real-world production processes
- Widely used for estimating returns to scale and factor productivity
- Frequently asked in UGC NET Economics and Commerce exams
💡 Important Exam & Study Tips
- Master NCERT Fundamentals: Ensure thorough familiarity with standard textbook definitions, formulas, and in-text examples before solving advanced problems.
- Step-by-Step Presentation: In board examinations, neat presentation, correct formula application, and labeled steps earn maximum step-marking.
- Practice Under Timed Conditions: Regular practice with previous years' question papers (PYQs) builds exam speed and accuracy.
📚 Related Study Materials on StudyMats
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