Part 2 / Section 7: Automation and New Tasks Section 7.4

Output expansion and employment at adopting firms

Less labor per unit of output need not mean fewer workers in total. We return to the same demand curve used in Sections~Section 2: The Cobb--Douglas technology and~Section 4: Examples and Applications of the CES Production Function:

\[\begin{equation} Y=BP^{-\varepsilon},\qquad B>0,\quad\varepsilon>0. \tag{7.16} \end{equation}\]

In a competitive industry the price reflects the unit cost, \(P=c\). So, the cost reduction \(\Gamma\) raises output by \(\Delta\log Y=\varepsilon\Gamma\). Combining this with (7.13) gives

\[\begin{equation} \Delta\log L \;=\;\underbrace{\varepsilon\Gamma}_{\text{scale}} \;-\;\overbrace{\eta\Gamma}^{\text{task substitution}} \;+\;\underbrace{\log(1-D)}_{\text{displacement}} \;\approx\;(\varepsilon-\eta)\Gamma-D. \tag{7.17} \end{equation}\]

The increase in the scale of production coming from additional demand for the firm's output introduces a force in favor of more labor. If demand is sufficiently elastic labor demand can increase. The exact condition is

\[\begin{equation} (\varepsilon-\eta)\Gamma>-\log(1-D). \tag{7.18} \end{equation}\]

Here we see that \(\varepsilon>\eta\) is necessary but no longer sufficient for employment to rise because labor is lost not just to substitution but also to direct displacement \(D\).