The marginal costs (ci) and marginal benefits (bi) of getting more education can vary across individuals – i.e., heterogeneous costs and benefits. Assume that marginal costs increase with the education level and marginal benefits decline with the education level.
a. Suppose the marginal costs and benefits of getting more education are the same for all individuals (bi = b and ci = c for everyone). Also suppose that omitted ability varies, but there are only two types of people (indexed by j and k) where the k-type has higher ability (ak) than the j-type (aj). Finally, assume that ability has a constant effect on earnings – i.e., the difference in log-earnings between k- and j-types at each education level is ak − aj > 0. Draw a figure (with log-earnings on the y-axis and education on the x-axis) to show the educational choice of the two-types of people. Will they choose different education levels?
b. Suppose that the two-types of people also have different marginal benefits (bj and bk) from an extra year of schooling. The k-type has a higher benefit (bj < bk), but both types face the same marginal cost functions. Use a figure to show the education choice made by the two-types, and what the OLS estimate of the return to education would be in this world. How does the OLS estimate compare to the “true return” to education for each type?