Any good diagnosis of the much concerned epidemic, “the diploma disease”, would need a clear criterion of the healthy condition of educational institutions. Social optimality as maximization of economic production may be one, though obviously not the only one, such criterion.There are two different formal models about the relationship between education and economic productivity. The Human Capital Theory asserts that an individual's marginal productivity increases as he receives more education. The Screening Theory, on the other hand, hypothesizes that of the higher marginal productivity is in fact observed to be correlated to the more education, it is not because of the latter's direct causation, but because of the screening function of education through which individuals blessed with innate higher productive ability eventually receive more education.This paper analyses these two models these two models and inquires (a) the conditions of social optimality and (b) the logical relationships between optimality and equilibrium in the models. Consequently the analysis shows (1) that the conditions of social optimality differs between the two models, and (2) that in the Screening Model equilibrium does not imply social optimality, whereas it does in the Human Capital Theory Model.