This paper presents a general equilibrium assignment model of workers to tasks with endogenous supply of skills. In the model, skills are endogenous and multidimensional, and two types of assignment occur: workers self‐select the type of skills to supply, and firms assign workers to tasks. The model shows that the impact of any skill‐biased technical change on wage inequality is tightly related to the distribution of skills in the population. When the supply of skills is endogenous, productivity effects can be overestimated or underestimated by wage data, and Johnson's () distinction between intensive and extensive technical change is impossible.