## Quantitative Problems

 1. In presenting the Oaxaca transformation, it was assumed that the slopes of the male and female wage schedules were the same: . What is the Oaxaca transformation in the more general case, and ? 2. Suppose that the earnings of men and women depend on their (material) productivities, q, as, and , respectively.(a) If the productivities of the average man and women are, respectively, q − m = 15 and q − f = 10 what are their average earnings and what is the gap between them?(b) Use the Oaxaca transformation to characterize the extent of wage discrimination. 3. The fraction of men and women employed in occupations i = 1, 2, 3 are, respectively, . Calculate the Duncan index of dissimilarity. 4. What is self-selection bias, and why might it compromise the efforts to accurately gauge the extent of Black economic progress? 5. Suppose that men and women face the same costs of acquiring human capital, h, given by . Furthermore, suppose that, because of discrimination, their earnings depend upon their human capital levels, h, according to and .(a) If each worker's utility, u, is simply u = \$(w − c), then how much human capital do men and women accumulate? (Hint: The marginal cost of h equals for both men and women.)(b) What are their resulting earnings? How much of any gap that emerges is attributable to discrimination? 6. Why do White men systematically earn more than Black men? 7. What is meant by premarket discrimination, and why are its effects so insidious? 8. The employment to population ratio (ep) of Black women has moved in apparent lockstep with that of White women over the past 40 years or so. (Figure 12.5). Moreover, the wage gap between White and Black women has narrowed over time (in 2004 it was only 12%). Does this evidence establish that Black women have caught up with White women? 9. "Equal pay has been the law since 1963. But today, 37 years later, women are still paid less than men— even when we have similar education, skills and experience. In 1999, women were paid 72 cents for every dollar men received." [AFL-CIO] Does this evidence provide unequivocal proof of discrimination? 10. Explain why controlling for actual work experience is critical in explaining the observed gender wage gap. 11. Discuss the effects of affirmative action programs on labor-market outcomes. 12. Have the antidiscrimination policies promulgated over the last 40 years or so been successful in combating discrimination against Blacks?