# Economies of scale v.s. technological change

In Greene's Econometric Analysis, 7th edition, page 355, it is written that:

A long-standing problem in the analysis of production functions has been the inability to separate economies of scale and technological change.

I know what the boldfaced terms refer to but it's not clear to me what is the source of the described "inability to separate." Can you please illustrate via a simple model, preferably one (adopted) from an article / a book that studies this very issue.

The problem is to distinguish between changes along the production function, from $f(K_1, L_1)$ to $f(K_2, L_2)$, and changes of the production function, from $f(K_1, L_1)$ to $g(K_1, L_1)$.

A very simple example/model. Imagine that the only input is labor and that this input doubles between t and t+1, but output more than doubles : $L_{t+1} = 2 L_t$, $Y_{t+1} > 2 Y_t$.

To interpret this observation you have two alternatives :

• Assume that there is a production function with increasing returns to scale, i.e. $1/Y dY/dL > 1$, so that $Y_t = f(L_t)$ and $Y_{t+1} = f(L_{t+1})$.

• Assume that the production function has constant returns to scale, i.e. $Y_t = \alpha L_t$ and $Y_{t+1} = \beta L_{t+1}$, but technical progress has occurred between periods $t$ and $t+1$, so that $\beta > \alpha$.

• Of course any combination of the two explanations above is admissible.

During the 'Cambridge controversies on capital', this was one the arguments which led the English Keynesians to reject the notion of production function. One famous paper building a growth model without a production function is Kaldor-Mirrles (1962), A New Model of economic growth

• Thank you. I will most likely accept your answer later today. Cheers. Mar 18 '17 at 18:47