Question

Distinguish between labour-augmenting technical change and neutral technical change. Explain, using a Solow-model diagram, how the technological progress affects the steady state levels of capital-labour ratio and output per person.

Answer 1

Difference between labour-augmenting technical change and neutral technical change

Consider a standard Cobb-Douglas production function without technical change first:

$Y=K^{\alpha}L^{1-\alpha}$

Labour Augmenting Technology

Now, modify this production function to include a labour-augmenting technical change. Let it be given by . Then the production function is:

$Y=K^{\alpha}(EL)^{1-\alpha},\; 0<\alpha<1$

Typically,
E 1
. What does the production function imply? 1 unit of labour is now more productive. The increase in his productivity increases with the value of . So, in this production function, improvement in technology makes labour more productive.

Neutral Technology

Consider again the first production function (without technical change). Now add a neutral technical change. Let it be given by . The labour-augmenting technical change makes only labour more productive. However, the neutral technical change increases the productivity of both capital and labour. to capture this effect, we mathematically express it as follows:

$Y=AK^{\alpha}L^{1-\alpha},\; 0<\alpha<1$

Notice, here has been multiplied to the whole production function, as opposed to , in the previous function, that had just been multiplied to .

Technical Change in the Solow diagram

To draw the diagram, I'm going to consider the model with neutral technical change. The model is:

$Y=AK^{\alpha}L^{1-\alpha},\; 0<\alpha<1$

Now, let denote output per worker and denote capital per worker. Formally,

$y=\frac{Y}{L},\; k=\frac{K}{L}$

Then the above production function becomes:

$y=Ak^{\alpha}$

In the steady state, we have the following condition:

$sy=(n+\delta )k$

Where shows the savings rate, shows the growth rate of population and $\delta$ shows the rate of depreciation of capital stock.

Graphically we have the following:

nt Sead Sねた 2*

Growth of technology will shift the curve outward. And the final effect will be as follows. You'll see that the steady state level of output- given by in $y^{*}$ the diagram, and the steady state level of capital- given by the $k^{*}$ in the diagram, both increase.

ol Notes: