This paper presents a general equilibrium assignment model of workers to tasks with endogenous supply of skills. The model has 2 key features. First, skills are endogenous and multidimensional. Second, two types of assignment occur; workers self-select the type of skills to supply and firms assign workers to tasks/machines. Equilibrium is characterized by two functions mapping skills of each type to tasks and two wage functions, one for each type of skills, so that the wage distributions generally overlap. The model shows that the impact of any given skill-biased technical change on wage inequality is tightly related to the distribution of skills in the population. Productivity effects can be over or under estimated by wage data when the supply of skills is endogenous. The model also shows that Johnson's (1997) distinction between intensive and extensive technical change is impossible when supply is endogenous.