Suppose that spending more on education of a student increases her productivity/wages. (We assume that wages increase in

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Suppose that spending more on education of a student increases
her productivity/wages. (We assume that wages increase in tandem
with productivity.) Draw the relationship between
productivity/wages (assuming that there are diminishing returns to
education.) Assume that more able students have, for each level of
education, a higher level of productivity/wages.
(a) Assume that you want to maximize total output for a given
level of expenditure. How would you allocate educational
expenditures? Would you necessarily spend more on the more able
students?
(b) Assume that you want to reduce inequalities in income. How
would this affect patterns of educational expenditure?