Why is technical change purely labor-augmenting and skill biased in the 20th century?

The history of modern economic growth indicates that technical change is not only purely labor-augmenting, but also skill biased the 20th century. Although there are papers that have separately analyzed why technical change be purely labor-augmenting or skill biased, there is no paper analyzing why it may be both labor-augmenting and skill biased. This article develops a growth model with endogenous direction and bias of technical change, in which capital accumulation process considers investment adjustment costs, and firms can undertake capital-, skill labor- and unskilled labor-augmenting technological improvements. In the steady-state equilibrium, technical change can include all of them. However, according to the results of the model, when there is no investment adjustment cost (implying capital supply with infinite elasticity), in steady state, technical change will be purely labor-augmenting. If market size effect dominated prices effect in innovation and the relative supply of skilled labor increase continuously, then technological progress will be purely labor-augmenting and skill biased, which result that the skill premium continue to rise, while the economic growth first increases and then decreases in an inverted U-shaped change, and the labor share of income first decreases and then increases in a U-shaped change.