Translog Production Function

The translog production function can be expressed as:

𝑌 = 𝑓(𝑥₁, 𝑥₂ ….. , 𝑥_𝑛)

Where,

Y: Output

𝛼₀: Efficiency Parameter

𝛼_𝑖 𝑎𝑛𝑑 𝛽_𝑖𝑗: 𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠 (𝑈𝑛𝑘𝑛𝑜𝑤𝑛)

𝑥_𝑗: 𝐼𝑛𝑝𝑢𝑡 𝑗

Logarithm Form:

Taking log both sides, we obtain:

The translog production function is a generalisation of the Cobb-Douglas production function. For 𝛽𝑖𝑗 = 0, the log form of the translog function reduces to a Cobb-Douglas production function. It is linear in parameters, so it can be estimated using the least squares method.

Monotonicity and Translog Production Function:

The marginal product, i.e. addition to the total product due to the addition of one more factor, is-

𝑀𝑃_𝑖 = ∂Y/∂x_i = ∂lnY/∂lnx_i . 𝑌/𝑥_𝑖

Where ∂lnY/∂lnx_i is the production elasticity which can be calculated from log form.

∂lnY/∂lnx_i =

• MP of x_i can be positive for a range in values of x_j but can be negative if 𝛽_𝑖𝑗 > 0
• (all i,j) and x_j → 0. If there exists at least one 𝛽𝑖𝑗 < 0, then 𝑀𝑃_𝑖 < 0 𝑎𝑠 x_j → ∞. Thus, the translog function is not monotonic.

Are Isoquants under Translog Function Convex?

The isoquants are strictly quasi-convex if the Bordered Hessian matrix is negative definite. In order to construct a Bordered Hessian matrix, we need to derive second direct and cross-partial derivatives using the chain rule.

Here the values of the first and second partial derivatives vary with input levels, and there is no guarantee that the isoquants are globally convex.

Read More- Microeconomics

1. Microeconomics: Definition, Meaning and Scope
2. Methods of Analysis in Economics
3. Problem of Choice & Production Possibility Curve
4. Concept of Market & Market Mechanism in Economics
5. Concept of Demand and Supply in Economics
6. Concept of Equilibrium & Dis-equilibrium in Economics
7. Cardinal Utility Theory: Concept, Assumptions, Equilibrium & Drawbacks
8. Ordinal Utility Theory: Meaning & Assumptions
9. Indifference Curve: Concept, Properties & Shapes
10. Budget Line: Concept & Explanation
11. Consumer Equilibrium: Ordinal Approach, Income & Price Consumption Curve
12. Applications of Indifference Curve
13. Measuring Effects of Income & Excise Taxes and Income & Excise Subsidies
14. Normal Goods: Income & Substitution Effects
15. Inferior Goods: Income & Substitution Effects
16. Giffen Paradox or Giffen Goods: Income & Substitution Effects
17. Concept of Elasticity: Demand & Supply
18. Demand Elasticity: Price Elasticity, Income Elasticity & Cross Elasticity
19. Determinants of Price Elasticity of Demand
20. Measuring Price Elasticity of Demand
21. Price Elasticity of Supply and Its Determinants
22. Revealed Preference Theory of Samuelson: Concept, Assumptions & Explanation
23. Hicks’s Revision of Demand Theory
24. Choice Involving Risk and Uncertainty
25. Inter Temporal Choice: Budget Constraint & Consumer Preferences
26. Theories in Demand Analysis
27. Elementary Theory of Price Determination: Demand, Supply & Equilibrium Price
28. Cobweb Model: Concept, Theorem and Lagged Adjustments in Interrelated Markets
29. Production Function: Concept, Assumptions & Law of Diminishing Return
30. Isoquant: Assumptions and Properties
31. Isoquant Map and Economic Region of Production
32. Elasticity of Technical Substitution
33. Law of Returns to Scale
34. Production Function and Returns to Scale
35. Euler’s Theorem and Product Exhaustion Theorem
36. Technical Progress (Production Function)
37. Multi-Product Firm and Production Possibility Curve
38. Concept of Production Function
39. Cobb Douglas Production Function
40. CES Production Function
41. VES Production Function
42. Translog Production Function
43. Concepts of Costs: Private, Social, Explicit, Implicit and Opportunity
44. Traditional Theory of Costs: Short Run
45. Traditional Theory of Costs: Long Run
46. Modern Theory Of Cost: Short-run and Long-run
47. Modern Theory Of Cost: Short Run
48. Modern Theory Of Cost: Long Run
49. Empirical Evidences on the Shape of Cost Curves
50. Derivation of Short-Run Average and Marginal Cost Curves From Total Cost Curves
51. Cost Curves In The Long-Run: LRAC and LRMC
52. Economies of Scope
53. The Learning Curve
54. Perfect Competition: Meaning and Assumptions
55. Perfect Competition: Pricing and Output Decisions
56. Perfect Competition: Demand Curve
57. Perfect Competition Equilibrium: Short Run and Long Run
58. Monopoly: Meaning, Characteristics and Equilibrium (Short-run & Long-run)
59. Multi-Plant Monopoly
60. Deadweight Loss in Monopoly
61. Welfare Aspects of Monopoly
62. Price Discrimination under Monopoly: Types, Degree and Equilibrium
63. Monopolistic Competition: Concept, Characteristics and Criticism
64. Excess Capacity: Concept and Explanation
65. Difference Between Perfect Competition and Monopolistic Competition
66. Oligopoly Market: Concept, Types and Characteristics
67. Difference Between Oligopoly Market and Monopolistic Market
68. Oligopoly: Collusive Models- Cartel & Price Leadership
69. Oligopoly: Non-Collusive Models- Cournot, Stackelberg, Bertrand, Sweezy or Kinked Demand Curve
70. Monopsony Market Structure
71. Bilateral Monopoly Market Structure
72. Workable Competition in Market: Meaning and Explanation
73. Baumol’s Sales Revenue Maximization Model
74. Williamson’s Model of Managerial Discretion
75. Robin Marris Model of Managerial Enterprise
76. Hall and Hitch Full Cost Pricing Theory
77. Andrew’s Full Cost Pricing Theory
78. Bain’s Model of Limit Pricing
79. Sylos Labini’s Model of Limit Pricing
80. Behavioural Theory of Cyert and March
81. Game Theory: Concept, Application, and Example
82. Prisoner’s Dilemma: Concept and Example