CES Production Function
Another popular neo-classical production function is the constant elasticity of substitution (CES) production function. The CES production function was developed by Arrow, Chenery, Minhas and Solow as a generalisation of the Cobb-Douglas production function that allows for non-negative and constant elasticity of substitution.
Functional Form:
The standard CES production function can be written as follows:
Y = A [Ξ΄πΎβπ + (1βΞ΄) πΏβπ]β1/π
Where,
Y is the output,
K and L are capital and labour inputs, and
A, Ξ΄, Ο are the parameters.
- A, technology determines the productivity and Aπ[0, β).
- δ determines the optimal distribution of inputs and δϡ[0,1].
- Ξ‘ determines the elasticity of substitution (Ο) where ΟΟ΅[-1,0) U(0,β) and π = 1/1+π
Special Cases under CES Production Function
- For Οβ0, Ο approaches 1Β» Cobb Douglas Production Function.
- For Οβ+β, Ο approaches 0Β» Leontief Production Function.
- For Οβ-1, Ο approaches βΒ» Perfect Substitutes.
The CES production function is linearly homogeneous and therefore exhibits constant returns to scale. It is non-linear in parameters, so it cannot be estimated using the least squares method.
Properties of CES Production Function
(i). Constant Returns to Scale:
The Cobb-Douglas production function exhibits constant returns to scale.
Y = A [Ξ΄πΎβπ + (1βΞ΄) πΏβπ]β1/π
π(ππΎ, ππΏ, π΄) = A [Ξ΄ (ππΎ)βπ + (1βΞ΄) (ππΏ)βπ]β1/π
= A Ξ»[Ξ΄πΎβπ + (1βΞ΄) πΏβπ]β1/π
=Ξ»Y
(ii). Positive and Diminishing Returns to Inputs:
The marginal products of the input are:
πππΎ = βY/βK = πΏ/π΄π (π/πΎ)π+1
πππΏ = βY/βL = 1βπΏ/π΄π (π/πΏ)π+1
They both are positive for K, L> 0. Any small increase in capital or labour increases the output but at a diminishing rate.
(iii) Inada Conditions
(iv). The Elasticity of Substitution is π = π/π+π
The elasticity of substitution is calculated using the formula:
Read More- Microeconomics
- Microeconomics: Definition, Meaning and Scope
- Methods of Analysis in Economics
- Problem of Choice & Production Possibility Curve
- Concept of Market & Market Mechanism in Economics
- Concept of Demand and Supply in Economics
- Concept of Equilibrium & Dis-equilibrium in Economics
- Cardinal Utility Theory: Concept, Assumptions, Equilibrium & Drawbacks
- Ordinal Utility Theory: Meaning & Assumptions
- Indifference Curve: Concept, Properties & Shapes
- Budget Line: Concept & Explanation
- Consumer Equilibrium: Ordinal Approach, Income & Price Consumption Curve
- Applications of Indifference Curve
- Measuring Effects of Income & Excise Taxes and Income & Excise Subsidies
- Normal Goods: Income & Substitution Effects
- Inferior Goods: Income & Substitution Effects
- Giffen Paradox or Giffen Goods: Income & Substitution Effects
- Concept of Elasticity: Demand & Supply
- Demand Elasticity: Price Elasticity, Income Elasticity & Cross Elasticity
- Determinants of Price Elasticity of Demand
- Measuring Price Elasticity of Demand
- Price Elasticity of Supply and Its Determinants
- Revealed Preference Theory of Samuelson: Concept, Assumptions & Explanation
- Hicks’s Revision of Demand Theory
- Choice Involving Risk and Uncertainty
- Inter Temporal Choice: Budget Constraint & Consumer Preferences
- Theories in Demand Analysis
- Elementary Theory of Price Determination: Demand, Supply & Equilibrium Price
- Cobweb Model: Concept, Theorem and Lagged Adjustments in Interrelated Markets
- Production Function: Concept, Assumptions & Law of Diminishing Return
- Isoquant: Assumptions and Properties
- Isoquant Map and Economic Region of Production
- Elasticity of Technical Substitution
- Law of Returns to Scale
- Production Function and Returns to Scale
- Eulerβs Theorem and Product Exhaustion Theorem
- Technical Progress (Production Function)
- Multi-Product Firm and Production Possibility Curve
- Concept of Production Function
- Cobb Douglas Production Function
- CES Production Function
- VES Production Function
- Translog Production Function
- Concepts of Costs: Private, Social, Explicit, Implicit and Opportunity
- Traditional Theory of Costs: Short Run
- Traditional Theory of Costs: Long Run
- Modern Theory Of Cost: Short-run and Long-run
- Modern Theory Of Cost: Short Run
- Modern Theory Of Cost: Long Run
- Empirical Evidences on the Shape of Cost Curves
- Derivation of Short-Run Average and Marginal Cost Curves From Total Cost Curves
- Cost Curves In The Long-Run: LRAC and LRMC
- Economies of Scope
- The Learning Curve
- Perfect Competition: Meaning and Assumptions
- Perfect Competition: Pricing and Output Decisions
- Perfect Competition: Demand Curve
- Perfect Competition Equilibrium: Short Run and Long Run
- Monopoly: Meaning, Characteristics and Equilibrium (Short-run & Long-run)
- Multi-Plant Monopoly
- Deadweight Loss in Monopoly
- Welfare Aspects of Monopoly
- Price Discrimination under Monopoly: Types, Degree and Equilibrium
- Monopolistic Competition: Concept, Characteristics and Criticism
- Excess Capacity: Concept and Explanation
- Difference Between Perfect Competition and Monopolistic Competition
- Oligopoly Market: Concept, Types and Characteristics
- Difference Between Oligopoly Market and Monopolistic Market
- Oligopoly: Collusive Models- Cartel & Price Leadership
- Oligopoly: Non-Collusive Models- Cournot, Stackelberg, Bertrand, Sweezy or Kinked Demand Curve
- Monopsony Market Structure
- Bilateral Monopoly Market Structure
- Workable Competition in Market: Meaning and Explanation
- Baumolβs Sales Revenue Maximization Model
- Williamsonβs Model of Managerial Discretion
- Robin Marris Model of Managerial Enterprise
- Hall and Hitch Full Cost Pricing Theory
- Andrewβs Full Cost Pricing Theory
- Bainβs Model of Limit Pricing
- Sylos Labiniβs Model of Limit Pricing
- Behavioural Theory of Cyert and March
- Game Theory: Concept, Application, and Example
- Prisonerβs Dilemma: Concept and Example