In a mean-field productivity model, dedicated teachers are optimal only above a critical population size, peak at intermediate sizes, and never exceed half the population.
tion G(x) := x 2 1:x (1 + :x) , x > 1, which can be approximated as G(x) j G 2(1)(x 2 1) = 1 2 (x 2 1) around x = 1, up to first order
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When it pays to teach: a population threshold for dedicated teaching
In a mean-field productivity model, dedicated teachers are optimal only above a critical population size, peak at intermediate sizes, and never exceed half the population.