If training is costly or takes many years to obtain this will lead to supply inelasticity. If, as is the case in some occupations, further barriers exists this will make supply even more inelastic. For example, in the US many talented students aren't able to find entry to medical school. The profession keeps the number of admissions low to assure higher earnings for practicing physicians. Other unions also keep membership artificually low and induce an inelasticity on labor supply, though none more effectively than the medical profession.
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