Technical Progress (Production Function)

Technical progress is defined as improvement in technology. In other words, technical progress means:

  • More output can be produced from the same amount of factor inputs, or the same output can be produced by a smaller amount of one or more of the factor inputs. Or
  • Any qualitative improvement in the existing product Or
  • Production of entirely new products.

Technical progress is the most important factor in determining the rate of growth of the economy.

Technical Progress and Production Function:

The technical progress can be represented with the help of the production function. Here we are making use of per worker production function. The assumption of constant returns to scale permits us to write an aggregate production function into a per-worker form.

𝑌 = 𝐹 (𝐾, 𝐿) ………. (1)

If we multiply capital and labour by any constant λ, then output is also multiplied by the same number, i.e. 𝜆𝑌 = 𝐹(𝜆𝐾, 𝜆𝐿).

Let us put λ=1/L, then 𝑌/𝐿 = 𝐹 (𝐾/𝐿, 1) ………. (2)

Where,

Y/L is output per worker, and

K/L is capital-labour ratio.

Let y = Y/L and k = K/L, then equation (2) can be written as

𝑦 = 𝑓 (𝑘) = 𝐹 (𝐾/𝐿, 1) ………. (3)

This is the per-worker form of the production function where output per worker depends upon capital per worker.

If there is no usage of inputs, the output would be zero, i.e. 𝑦 = 𝑓(𝑘) if 𝑘 = 0 𝑡ℎ𝑒𝑛 𝑦 = 0. It ensures that the per-worker production function starts from the origin.

Diagrammatic Representation of Per Worker Production Function:

In Fig. 1, The K/L ratio is measured on the x-axis and the Y/L ratio on the y-axis. The curve starts from the origin, as output is zero when no factor is employed. The Output per worker is increasing but at a diminishing rate as the ratio K/L ratio rises.

Per worker Production Function: The output per worker depends upon capital per worker
Figure 1: Per worker Production Function: The output per worker depends upon capital per worker

Technical Progress Shifts the Production Function Upward:

The technical progress shifts the production function upward. It is shown in Figure 2. The production function without any technical progress is shown by curve 𝑓(𝑘, 𝑡0). After the technical progress, the curve shifts upward to 𝑓(𝑘, 𝑡1). At any level of the K/L ratio on the new production function except zero, more output per worker is produced.

Shift in Production Function
Figure 2: Shift in Production Function

Factor Augmenting Representation of Technical Change:

Technical progress shifts the production function upward such that more output is produced with the same quantity of factors, i.e. without any increase in the usage of capital and labour. If the factors of production had been augmented, then the production function can be written as:

𝑌 = 𝐹[𝐴(𝑡)𝐾, 𝐶(𝑡)𝐿]

Where,

Y is output

K is Capital

L is Labor

t is Time

A and C are Factors

A(t) K is Effective Capital

C(t) L is Effective Labor

Here the capital and labour force are multiplied by factors A and C, which are functions of time.

  • If Ȧ(t)>0, i.e. the rate of change is positive, then effective capital stock increases as time goes on even though the actual capital stock remains constant.
  • If Ċ(t)>0, i.e. the rate of change is positive, then effective labour stock increases as time goes on even though the actual labour stock remains constant.

The technical change can be characterized as:

(i) Purely Capital Augmenting

The technical change is said to be purely capital augmented if Ȧ(t) is positive and C(t) is equal to 1, i.e. Ȧ(t) > 0 and C(t) = 1.

(ii) Purely Labor Augmenting

The technical change is said to be purely labour augmented if Ċ(t) is positive and A(t) is equal to 1, i.e. Ċ(t) > 0 and A(t) = 1.

(iii) Equally Capital and Labor Augmenting

The technical change is said to be equally capital and labour augmented if Ȧ (t) and Ċ (t) both are positive.

Classification of Technical Progress

The classification of technical progress as labour saving, capital saving or neutral was originally the work of Harrod (1948) & Hicks (1932), and there exist differences in the criteria of classification. Harrod employs the concept of capital-output ratio to explain technical progress classification, whereas Hicks used the concept of Marginal rate of Substitution between factors leaving output unchanged. Let us study them in detail.

(1). Hicks Classification of Technical Progress

a). Classification in terms of Marginal Product Ratio

● The technical progress is said to be labour saving if 𝑀𝑃𝐾(𝑡)/𝑀𝑃𝐿(𝑡) > 𝑀𝑃𝐿(0)/𝑀𝑃𝐾(0) Or Any technical progress resulting in an upward shift in the production function is said to be labour saving if any constant value of the capital-labour ratio, the ratio of 𝑀𝑃𝐾 to 𝑀𝑃𝐿 has increased.

● Here, 𝑀𝑃𝐾(𝑡) 𝑎𝑛𝑑 𝑀𝑃𝐿(𝑡) are the marginal products before the technical progress and 𝑀𝑃𝐾(0) 𝑎𝑛𝑑 𝑀𝑃𝐿(0) after the technical progress.

● The technical progress is said to be capital saving if 𝑀𝑃𝐾(𝑡)/𝑀𝑃𝐿(𝑡) < 𝑀𝑃𝐿(0)/𝑀𝑃𝐾(0) Or Any technical progress resulting in an upward shift in the production function is said to be labour-saving if any constant value of the capital-labour ratio, the ratio of 𝑀𝑃𝐾 to 𝑀𝑃𝐿 has decreased.

● The technical progress is said to be Hicks Neutral if 𝑀𝑃𝐾(𝑡)/𝑀𝑃𝐿(𝑡) = 𝑀𝑃𝐿(0)/𝑀𝑃𝐾(0) Or Any technical progress resulting in an upward shift in the production function is said to be labour-saving if any constant value of the capital-labour ratio, the ratio of 𝑀𝑃𝐾 to 𝑀𝑃𝐿 has remains constant.

Classification in terms of Ratio of Relative Shares

● The technical progress is said to be labour saving if, at any constant value of the capital-labour ratio, the ratio of relative shares, i.e. 𝑟𝐾/𝑤𝐿 is increasing.

● The technical progress is said to be capital saving if, at any constant value of the capital-labour ratio, the ratio of relative shares, i.e. 𝑟𝐾/𝑤𝐿 is decreasing.

● The technical progress is said to be Hicks Neutral if, at any constant value of the capital-labour ratio, the ratio of relative shares, i.e. 𝑟𝐾/𝑤𝐿 remains constant.

(2). Hicks Classification of Technical Progress

● Any technical progress resulting in an upward shift in the production function is said to be labour-saving; if any constant value of the capital-output ratio, the 𝑀𝑃𝐾 is increasing. In other words, technical progress is said to be labour saving if, at any constant value of the capital-output ratio, the ratio of relative shares, i.e. 𝑟𝐾/𝑤𝐿 is increasing.

● Any technical progress resulting in an upward shift in the production function is said to be capital saving; if any constant value of the capital-output ratio, the 𝑀𝑃𝐾 is decreasing. In other words, technical progress is said to be capital saving if, at any constant value of the capital-output ratio, the ratio of relative shares, i.e. 𝑟𝐾/𝑤𝐿 is decreasing.

● Any technical progress resulting in an upward shift in the production function is said to be Harrod neutral; if any constant value of the capital-output ratio, the 𝑀𝑃𝐾 remains unchanged. In other words, technical progress is said to be Harrod neutral if, at any constant value of the capital-output ratio, the ratio of relative shares, i.e. 𝑟𝐾/𝑤𝐿 remains constant.

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

Similar Posts

Share Your Thoughts