Solow's Growth Model

Solow’s Model | Exogenous G.M. | Neo-classical G.M. | S-S model (1956)

Why Exogenous?

Essentially, he added $A$ (technical productivity) to the growth model $Y=Af(k,L)$¹. He believed that this $A$ is not decided or derived inside the model.

Why do we call it the extension of HD model?

• Added Labor to the equation
• Diminishing Returns of $K$ and $L$ separately
• Constant Returns to Scale²
• Technical Progress
• capital output and capital labor ratio is not fixeddoubt

Technical Productivity

$$Y=AF(K,L)$$

$A$ captures the state of technical knowledge and overall efficiency.³

Transclude of Growth-Theories--and--Models-2024-09-20-11.29.05.excalidraw

Per man Labor
$y=\frac{Y}{L}$	output per labor
$k=\frac{K}{L}$	capital per labor

Due to technical progress, $A$ will increase and the production function shifts upwards (RED) leading to higher levels of output $y_3$ for a given level of factor inputs (i.e. $K$ and $L$). Thus, shift in the production function $⟹$ increase in the productivity of factors.

Before technical progress, rise in $k$ from $k_1\to k_2$ leads to an increase in the level of income $y$ from $y_1\to y_2$

But, due to technical progress which is captured by increase in capital, $A$ shifts the production function upwards so that $y$ rises from $y_1\to y_3$ even if $k$ stays at $k_1$

Footnotes

1. generally left hand variables are exogenous, and right hand ones are endogenous ↩

2. Constant Returns to Scale ↩

3. for the same amount of capital and labor I get more productivity ↩