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This article generalizes central results from the theory of (endogenously) directed technical change to settings where technology does not take a labour-augmenting form and with arbitrarily many levels of skill. Building on simple notions of complementarity, the results remain intuitive despite their generality. The developed theory allows to study the endogenous determination of labour-replacing, that is, automation technology through the lens of directed technical change theory. In an assignment model with a continuum of differentially skilled workers and capital, where capital perfectly substitutes for labour in the production of tasks, any increase in the relative supply of skilled workers stimulates investment into improving the productivity of capital, potentially leading skill premia to increase in relative skill supply. Relatedly, trade with a skill-scarce country discourages improvements in capital productivity, potentially reversing the standard Heckscher–Ohlin effects.

An Elementary Theory of Directed Technical Change and Wage Inequality