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An Elementary Theory of Directed Technical Change and Wage Inequality

This paper generalizes central results from the theory of (endogenously) directed technical change to settings where technology does not take a labor-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 labor-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 takes the form of machines that perfectly substitute for labor in the production of tasks, any increase in the relative supply of skilled workers stimulates both automation and investment into improving the productivity of machines, potentially leading skill premia to increase in relative skill supply. Relatedly, trade with a skill-scarce country discourages automation and machine improvements, potentially reversing the standard Heckscher-Ohlin effects. JEL: J24, J31, O33,