Assume that a firm commits to paying a high wage in a difficult job and a low wage in an easy job. Assume further that the worker (agent) believes that investing in skills will result in promotion to the high job and will make the investment if the opportunity cost of training is less than the wage increase. The firm will choose to promote the trained worker if the profitability of the trained worker in the difficult job is greater than leaving her the easy job (productivity in difficult job must exceed that in easy job by more than the wage difference). The investment will pay off if:

Training is efficient in the sense that its cost is less than the wage differential between the easy and difficult jobs.

The profitability of the trained worker in the difficult job is greater than leaving her the easy job (wage difference in the difficult job smaller than the productivity increase)

Both conditions must be met