Technical Progress (Production Function)

2 years ago
Atiqur Rahman
9 minutes

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.

π‘Œ = 𝐹 (𝐾, 𝐿) ………. (1)

If we multiply capital and labour by any constant Ξ», then output is also multiplied by the same number, i.e. πœ†π‘Œ = 𝐹(πœ†πΎ, πœ†πΏ).

Let us put Ξ»=1/L, then π‘Œ/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 (π‘˜) = 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(π‘˜) if π‘˜ = 0 π‘‘β„Žπ‘’π‘› 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(π‘˜, 𝑑0). After the technical progress, the curve shifts upward to 𝑓(π‘˜, 𝑑1). 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:

π‘Œ = 𝐹[𝐴(𝑑)𝐾, 𝐢(𝑑)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 Θ¦(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 Θ¦(t) is positive and C(t) is equal to 1, i.e. Θ¦(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(𝑑)/𝑀𝑃𝐿(𝑑) > 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(𝑑) π‘Žπ‘›π‘‘ 𝑀𝑃𝐿(𝑑) are the marginal products before the technical progress and 𝑀𝑃𝐾(0) π‘Žπ‘›π‘‘ 𝑀𝑃𝐿(0) after the technical progress.

● The technical progress is said to be capital saving if 𝑀𝑃𝐾(𝑑)/𝑀𝑃𝐿(𝑑) < 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(𝑑)/𝑀𝑃𝐿(𝑑) = 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. π‘ŸπΎ/𝑀𝐿 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. π‘ŸπΎ/𝑀𝐿 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. π‘ŸπΎ/𝑀𝐿 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. π‘ŸπΎ/𝑀𝐿 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. π‘ŸπΎ/𝑀𝐿 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. π‘ŸπΎ/𝑀𝐿 remains constant.

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