<p>Consider a Leontief production function:</p>

<p>$$ Y = \text{min}(aL,bK) $$</p>

<p>Optimal capital-labour ratio is:</p>

<p>$$ \frac{K^*}{L^*}=\frac{a}{b} $$ </p>

<p><strong>Labour-saving</strong> technical change is such that $a$ increases. The optimal capital-labour ratio increases, this is, firms use <strong>less labour per unit of capital</strong>. This is also called <strong>Capital-augmenting</strong> technical change (see reference [2]).</p>

<p><strong>Labour-augmenting</strong> technical change is such that $b$ increases. The optimal capital-labour ratio falls, this is, firms use <strong>more labour per unit of capital</strong>.</p>

<p>Notice that how output per worker changes depend on how $Y$ changes. For example, assume that the above adjustment is such that $Y$ is unchanged after the technical change. Then, output per worker increases in the labour-saving case but falls in the labour-augmenting change. A complete analysis would require a general equilibrium approach, where factor prices are endogenous. All I am showing here is that <strong>it is not necessarily the case that either type of technical change increases output per worker.</strong></p>

<p>Some references: <a href="https://www.brown.edu/academics/economics/sites/brown.edu.academics.economics/files/uploads/Rage%20Against_Joachim%20Voth.pdf" rel="nofollow noreferrer">[1]</a>, <a href="http://web.mit.edu/daron/www/lab-cap5.pdf" rel="nofollow noreferrer">[2]</a>.</p>

<p>PS: I use the Leontief for simplicity. In a Cobb-Douglas, any technical change is Hicks-neutral, as it does not affect the K/L ratio (assuming fixed factor prices). In a CES, the nature of technical change depends on the elasticity of substitution. </p>

CC BY-SA 3.0
2017-08-31T21:15:11.307Z
labour-augmenting technical change makes each worker more productive by augmenting their labour. How would output per unit of labour falls if labour input does not change assuming output does not change in the second case above?
london
CC BY-SA 3.0
2017-09-01T08:44:29.913Z
@london Maybe I was not clear enough, You can imagine a situation where labour-augmenting leads to hire more L and less K, (so K/L falls). Then, for a given Y, Y/L falls.
luchonacho
CC BY-SA 3.0
2017-09-01T22:20:57.913Z
Thanks @luchonacho, I am still puzzled as to why output could be unchanged when labour augmentation increases but more labour is employed relative to capital. Do you know of a textbook or a chapter/paper that documents the theory you outlined above?
london
CC BY-SA 3.0
2017-09-02T20:41:25.297Z
@london That was just a theoretical example, to indicate that such case is technically possible (although might never happen in reality). I will look for an example and let you know.
luchonacho
CC BY-SA 3.0
2017-08-31T07:10:43.977Z
2017-08-31T07:21:28.897Z
2017-08-31T07:21:28.897Z
luchonacho
<p>From what I understand, <strong>labor augmentation</strong> is when the labor productivity is increased when coupled with an amplifier such as <a href="http://www.investopedia.com/terms/h/humancapital.asp" rel="nofollow noreferrer">human capital</a>.</p>

<p>Looking at a sample labor augmented  production function with constant returns to scale we have:
$$F(L,K)=(AL)^\alpha K^{1-\alpha}$$</p>

<p>Where $L$ is labor, $K$ is capital, $A$ is our augmenter and $\alpha$<sup>1</sup> is our output elasticity from labor.</p>

<p>It is through a change in technology by which labor is augmented<sup>2</sup>.</p>

<p><strong>labor saving</strong> from what is where there is a high <a href="http://www.businessdictionary.com/definition/elasticity-of-substitution.html" rel="nofollow noreferrer">elasticity of subsitution</a> in a production function's inputs.</p>

<p>For example if we have a production function of</p>

<p>$$F(L,K)=L+K$$</p>

<p>we have a case where elasticity of subsitution is equal to infinity or $\sigma=\infty $. </p>

<p><strong>Note:It is possible to have a labor augmenting production function which is not labor saving. (i.e the leontif production function)</strong></p>

<hr>

<p><sub>1.where $\alpha&lt;1$</sub>
<br><sub>2. <a href="https://mnmeconomics.wordpress.com/2011/07/18/labour-augmenting-technical-progress/" rel="nofollow noreferrer">https://mnmeconomics.wordpress.com/2011/07/18/labour-augmenting-technical-progress/</a></sub></p>

CC BY-SA 3.0
2017-09-01T19:35:14.467Z
Can you also please elaborate on how factor augmentation vs. saving affects productivity?
london
CC BY-SA 3.0
2017-09-01T22:13:58.860Z
@london the factor augmentation increases the effectiveness of one or more outputs, this increases productivity in when looking at our production function. factor saving is determined by the substitutability of the factors. The practical significance of this is that if input prices differ, we have the option of using a different input thus saving a factor.
EconJohn
CC BY-SA 4.0
2017-09-01T18:24:14.580Z
2018-05-07T17:06:25.640Z
2018-05-07T17:06:25.640Z
EconJohn
<p>It really depends on context and model.</p>

<p>As an example, consider a Real Business Cycle model, with a representative individual that values consumption and leisure. Given a technology shock, adjusted labor will drop and, eventually, return to the stationary state. This could mean that people are laid off because the new technology replaced them, or because there's a shortage of qualified workers, or even that people decided to work less, now that the rest of the (more productive) society gives them unemployment benefits.</p>

<p>I haven't worked much with search&amp;match models of unemployment, but given a set of firms with varying productivity, I guess a model could be constructed to define labor-saving and labor-augmenting in precise terms, based on the effect a shock has on the probability of firing people.</p>

<p>Finally, labor-augmenting technology is necessary for balanced growth. You may not care about it, but many models do.</p>

CC BY-SA 3.0
2017-08-31T04:43:52.313Z
2017-08-31T04:43:52.313Z
one_teach_wonder
<p>Either way, output per unit of labour input increases. You could explain or define this process in any way you could - there is no clear difference between them.</p>

CC BY-SA 3.0
2017-08-30T22:01:53.027Z
2017-08-30T22:01:53.027Z
london
<p>It seems reasonable to say that technology generally increases output per unit of labour.  Therefore in any factory which has installed new technology one can reasonably expect that for the same output one is likely to need less employees than before (or perhaps the firm will retain the same number of employees but output will increase).  Therefore, in either case, the output per employee has increased.  Therefore one could say that labour has been saved by the new technology.  One could also say that labour has been augmented by the new technology as each worker is supported by the new technology and is now more productive.</p>

<p>My question is: do we have clear definitions of these two terms and what is the difference?</p>

CC BY-SA 3.0
2017-08-30T21:59:21.550Z
I guess this doesn't have that much to do with the technology itself, but rather whether the firm wants to increase output in proportion to the increase in productivity or not. If it doesn't then people will lose their jobs (labour saving technology). If the firm is happy with the increase in output, people can keep their jobs (labour augmenting technology). I guess the firm will be asking itself whether there is demand for the increased output.
M3RS
<labor-economics><productivity><technology>
Labour Saving vs. Labour Augmenting - what is the difference?
beastofburden
# Labour Saving vs. Labour Augmenting - what is the difference?

(Asked by: username_0 on 2017-08-30)

It seems reasonable to say that technology generally increases output per unit of labour. Therefore in any factory which has installed new technology one can reasonably expect that for the same output one is likely to need less employees than before (or perhaps the firm will retain the same number of employees but output will increase). Therefore, in either case, the output per employee has increased. Therefore one could say that labour has been saved by the new technology. One could also say that labour has been augmented by the new technology as each worker is supported by the new technology and is now more productive.

My question is: do we have clear definitions of these two terms and what is the difference?

**Tags:** labor-economics, productivity, technology

> **Comments:**
> **username_1**: I guess this doesn't have that much to do with the technology itself, but rather whether the firm wants to increase output in proportion to the increase in productivity or not. If it doesn't then people will lose their jobs (labour saving technology). If the firm is happy with the increase in output, people can keep their jobs (labour augmenting technology). I guess the firm will be asking itself whether there is demand for the increased output.  

---

## 4 answers

### Answer by username_2 on 2017-08-31. Score: 3

Consider a Leontief production function:

$$ Y = \text{min}(aL,bK) $$

Optimal capital-labour ratio is:

$$ \frac{K^\*}{L^\*}=\frac{a}{b} $$

**Labour-saving** technical change is such that $a$ increases. The optimal capital-labour ratio increases, this is, firms use **less labour per unit of capital**. This is also called **Capital-augmenting** technical change (see reference [2]).

**Labour-augmenting** technical change is such that $b$ increases. The optimal capital-labour ratio falls, this is, firms use **more labour per unit of capital**.

Notice that how output per worker changes depend on how $Y$ changes. For example, assume that the above adjustment is such that $Y$ is unchanged after the technical change. Then, output per worker increases in the labour-saving case but falls in the labour-augmenting change. A complete analysis would require a general equilibrium approach, where factor prices are endogenous. All I am showing here is that **it is not necessarily the case that either type of technical change increases output per worker.**

Some references: [[1]](https://www.brown.edu/academics/economics/sites/brown.edu.academics.economics/files/uploads/Rage%20Against_Joachim%20Voth.pdf), [[2]](http://web.mit.edu/daron/www/lab-cap5.pdf).

PS: I use the Leontief for simplicity. In a Cobb-Douglas, any technical change is Hicks-neutral, as it does not affect the K/L ratio (assuming fixed factor prices). In a CES, the nature of technical change depends on the elasticity of substitution.

> **Comments:**
> **username_3**: labour-augmenting technical change makes each worker more productive by augmenting their labour. How would output per unit of labour falls if labour input does not change assuming output does not change in the second case above?  
> **username_2**: @username_3 Maybe I was not clear enough, You can imagine a situation where labour-augmenting leads to hire more L and less K, (so K/L falls). Then, for a given Y, Y/L falls.  
> **username_3**: Thanks @username_2, I am still puzzled as to why output could be unchanged when labour augmentation increases but more labour is employed relative to capital. Do you know of a textbook or a chapter/paper that documents the theory you outlined above?  
> **username_2**: @username_3 That was just a theoretical example, to indicate that such case is technically possible (although might never happen in reality). I will look for an example and let you know.  

---

### Answer by username_4 on 2017-09-01. Score: 2

From what I understand, **labor augmentation** is when the labor productivity is increased when coupled with an amplifier such as [human capital](http://www.investopedia.com/terms/h/humancapital.asp).

Looking at a sample labor augmented production function with constant returns to scale we have:
$$F(L,K)=(AL)^\alpha K^{1-\alpha}$$

Where $L$ is labor, $K$ is capital, $A$ is our augmenter and $\alpha$1 is our output elasticity from labor.

It is through a change in technology by which labor is augmented2.

**labor saving** from what is where there is a high [elasticity of subsitution](http://www.businessdictionary.com/definition/elasticity-of-substitution.html) in a production function's inputs.

For example if we have a production function of

$$F(L,K)=L+K$$

we have a case where elasticity of subsitution is equal to infinity or $\sigma=\infty $.

**Note:It is possible to have a labor augmenting production function which is not labor saving. (i.e the leontif production function)**

---

1.where $\alpha<1$
  
2. <https://mnmeconomics.wordpress.com/2011/07/18/labour-augmenting-technical-progress/>

> **Comments:**
> **username_3**: Can you also please elaborate on how factor augmentation vs. saving affects productivity?  
> **username_4**: @username_3 the factor augmentation increases the effectiveness of one or more outputs, this increases productivity in when looking at our production function. factor saving is determined by the substitutability of the factors. The practical significance of this is that if input prices differ, we have the option of using a different input thus saving a factor.  

---

### Answer by username_5 on 2017-08-31. Score: 0

It really depends on context and model.

As an example, consider a Real Business Cycle model, with a representative individual that values consumption and leisure. Given a technology shock, adjusted labor will drop and, eventually, return to the stationary state. This could mean that people are laid off because the new technology replaced them, or because there's a shortage of qualified workers, or even that people decided to work less, now that the rest of the (more productive) society gives them unemployment benefits.

I haven't worked much with search&match models of unemployment, but given a set of firms with varying productivity, I guess a model could be constructed to define labor-saving and labor-augmenting in precise terms, based on the effect a shock has on the probability of firing people.

Finally, labor-augmenting technology is necessary for balanced growth. You may not care about it, but many models do.


---

### Answer by username_3 on 2017-08-30. Score: 0

Either way, output per unit of labour input increases. You could explain or define this process in any way you could - there is no clear difference between them.


---

