Answers To Chapter 12 Review Questions 1. Answer b. Although Answer a is a true statement, the wage gap could be the result of differences in productive characteristics (premarket differences). Labor market discrimination focuses on differences in labor market payoffs to productive characteristics. Answer c is also a true statement but such segregation could be voluntary (i.e., represent premarket choices). 2. Answer d. Differences in any of the factors might justify differing wages between male and female employees. 3. Answer a. Holding occupation constant takes away its affect on wages, making it impossible to see the impact that restricting employment opportunities has on women s relative wages. 4. Answer b. Note that some of these differences may not be measurable or observable, making it impossible to hold them constant. Also, the current values of these productive characteristics may have been influenced by past discrimination. Answer d describes the goal in measuring wage discrimination. 5. Answer a. The observed wages are represented by Points a and b. 6. Answer b. Since some current labor market discrimination may take the form of occupational segregation, it is important not to control the occupation. Given the occupational differences, women would earn $10 (point d ) if they had the same experience as men. That leaves a gap between men s and women s wages of $10 (the difference between points b and d ). 7. Answer c. hen measuring wage discrimination, all premarket factors, including occupation, must be held constant. This leaves the gap between points b and c ($6) unexplained. 8. Answer d. Assuming women s employment options are limited to the low-paying sector because of discrimination, this leads to a reduction in wages of $4, even if women had the same experience as men. Occupational segregation can be represented by the gap between points c and d. 9. Answer d. Note that if women experienced wage discrimination in the past, some of the premarket differences could be attributable to discrimination. Hence, holding them constant would understate the effect of discrimination on wages. 10. Answer c. S = ½ ( 75 10 + 25 90 ) = 65.
326 Ehrenberg/Smith odern Labor Economics: Theory and Public Policy, Tenth Edition 11. Answer d. Prejudiced employers will act as if the marginal product of blacks has been shifted down. If black and white wages are equal this will lead to a reduction in employment for blacks. If blacks and whites are hired in the same numbers, blacks will be paid less since their marginal product will be subjectively devalued. 12. Answer a. If the employer s prejudice causes a reduction in employment, this reduces the area under the marginal product curve. Recall that this area represents output (real income) to the firm. If the firm reduces wages paid to blacks instead of black employment, note that the lower wage would lead a nondiscriminating firm to an even higher employment and output level. See Problem 26 for numerical examples of these points. 13. Answer d. By segregating blacks away from customer contact positions, the firm can avoid losing prejudiced customers. On the other hand, allowing blacks in such positions may be worth it if they are more qualified, and hence more productive, than whites. This higher productivity presumably makes up for the lost customers. Since self-employment takes away the possibility of employment prejudice, an earnings gap between equally productive black and white entrepreneurs points to customer prejudice. 14. Answer d. Prejudiced white employees would have to be paid a compensating differential to work in an integrated group. This creates a window of opportunity for a firm to lower costs and increase profits by substituting less expensive black workers for whites. 15. Answer c. irms use statistical discrimination as a way to identify the most productive workers while avoiding the cost associated with a careful investigation of each worker. The more diverse a group becomes in their productive characteristics, the less reliable is group affiliation as an indicator of productivity. Statistical discrimination does not stem from prejudice or monopoly power. 16. Answer b. The notion of noncompeting groups is a plausible one if firms exercise monopsony power over women and minorities. The problem is that theories do not give any reason for the lack of competition. The theories fit the facts, but are based on assumptions and premises that seem difficult to support. 17. Answer b. irms do not necessarily create prejudice in the monopoly power models, but they are assumed to profit from its existence. However, such scenarios are unlikely to persist since there will be strong incentives for individual firms to cheat on the agreement. 18. Answer c. Disparate treatment occurs if individual workers are intentionally treated differently with respect to wages and employment opportunities because of the demographic group to which they belong. 19. Answer d. Although word-of-mouth recruiting may not intentionally disadvantage any group, it can have a disparate impact over time since it can carry forward the effects of past discrimination. The same is true of seniority systems, but such systems are explicitly allowed under Title VII. 20. Answer c. One shortcoming of standards used in calculating the pool of available applicants is the interest people in the targeted groups have in working at the firm. Because of commuting distance or the mix of compensation offered at a particular firm, all workers in a particular area may not be equally interested in working for the firm. By ignoring worker interest, affirmative action goals may be set beyond the firm s immediate reach.
Answers To Chapter 12 327 21. Answer d. Comparable worth pay systems attempt to make pay a function of the job that is performed, rather than a function of a worker s personal characteristics. 22. Answer b. A job score of 100 would lead to $1,500 in earnings for a man. A salary of $1,200 represents only 80% of what a man earns. Therefore, the women s pay represents a 20% comparable worth earnings gap. Problems 23a. Substituting the appropriate values into the wage formulas yields = 3 + 0.5(4) + 0.6(10) + 1 = 12, = 3 + 0.4(3) + 0.5(6) = 7.2 7.2 = = 0.6 40% earnings gap 12 23b. Substituting ED = 4, EXP = 10, and OC = 1 into the women s wage equation yields = 3 + 0.4(4) + 0.5(10) + 1 = 10.6 10.6 = = 0.883 12 23c. After controlling for all premarket characteristics, women still earn 11.7% less. 23d. Substituting ED = 4, EXP = 10 into the women s wage equation yields 9.6 = 3 + 0.4(4) + 0.5(10) = 9.6 = = 0.8 12 23e. After adjusting for all productive characteristics except occupation, women earn 20% less than men in this example. This gap can be attributed to current labor market discrimination because it reflects different employment opportunities and different labor market payoffs to the various productive characteristics. The occupational segregation costs women an extra $1 in wages and so widens the wage gap by 8.3%. 23f. If the premarket differences in education or experience are the result of past discrimination, the estimate of current labor market discrimination understates the influence of discrimination on labor market outcomes. On the other hand, if unmeasurable or unobservable differences exist in the productive characteristics of men and women, the estimate of current labor market discrimination overstates the problem. 23g. Substituting ED = 3, EXP = 6, and OC = 0 into the men s wage equation yields 7.2 = 3 + 0.5(3) + 0.6(6) = 8.1 = = 0.89 8.1 This approach yields a slightly smaller discriminatory wage gap (11%) than in 23c.
328 Ehrenberg/Smith odern Labor Economics: Theory and Public Policy, Tenth Edition 23h. Half of the women would earn 7.2, while half would earn 8.2, for an average wage of 7.7. Similarly, half of the men would earn 12, while half would earn 11, for an average wage of 11.5. This change in the occupational distribution increases the relative wage of women from 0.6 to 0.67 (7.7/11.5). 24a. See Table 12-3. The number in each occupation can be found by multiplying the percentage male or female (expressed as a fraction) by the total employment. Table 12-3 Occupation #ale #emale Total A 10 40 50 B 20 30 50 C 40 10 50 D 30 20 50 100 100 200 24b. The percentage of the total male or female workers in each occupation can be found by dividing the number of males or females in each occupation by the total male or female population. In this example, the total population is 100 for each sex. The results are presented in Table 12-4. The last column computes the absolute value of the difference between the total male and female percentages in each occupation. Table 12-4 Occupation % ale % emale % -% A 10% 40% 30 B 20% 20% 10 C 40% 10% 30 D 30% 20% 10 80 24c. The index of dissimilarity is 40. S = ½ (30 + 10 + 30 + 10) = 40. This indicates that 40% of the women (or men) would have to change occupation in order to make the occupational distribution of women the same as men. or example, 30% of the women would have to move from A to C, and 10% of the women would have to move from B to D. The main point of this exercise was to show that the index of dissimilarity is computed using the percentage of the total male and female population in each occupation, not the percentage of each occupation that is male and female. 25. Substituting ER = 0.608 and LPR = 0.776 into the employment rate expression yields 0.614 = 0.776(1 UR) UR = 0.209 or 20.9%.
Answers To Chapter 12 329 26a. Profit maximization occurs at that level of employment where the marginal product of labor equals the real wage = P l 15 = 25 0.5L L * = 20 for each group. This equilibrium is shown as point c in igure 12-4. igure 12-4 Ignoring the cost of capital, profit is represented by the area under the marginal product curve and above the wage line. Thus the employment of 20 blacks results in a profit (π) denoted by the area of triangle acg. This area has a value of π = ½ (20)(10) = 100. *26b. A prejudiced employer acts as if the marginal product of blacks is 5 units less than whites at any given employment level. = P l 15 = 25 0.5L 5 L * = 10 for blacks. The new employment of blacks is represented by point e. hite employment remains at 20. Profit from black employment is now given by the area of trapezoid abeg, which has an area of π = ½ (10)(5) = (10)(5) = 75. *26c. To keep black employment at 20 requires that the wage fall to * = P l = 25 0.5(20) 5 = 10 for blacks. This equilibrium is denoted by point f. Profit from black employment is now given by the area of the trapezoid acf h which has an area of π = ½ (20)(10) + (20)(5) = 200.
330 Ehrenberg/Smith odern Labor Economics: Theory and Public Policy, Tenth Edition *26d. At = 10, an unprejudiced employer would hire blacks up to the point where = P l 10 = 25 0.5L L * = 30 for blacks. This equilibrium is represented by point d. Profit from back employment is now given by the area of the triangle adh which has an area of π = ½ (30)(15) = 225. Therefore, whether the prejudiced employer adjusts wages or employment, the prejudiced employer can always earn a higher profit. 27a. The market-clearing relative wage will be 0.5 and 10,000 women will be employed. This equilibrium is represented by point d in igure 12-5. igure 12-5 27b. The increase in the number of non-discriminating employers together with the worsening of discriminatory preferences creates the new market demand curve shown as line aec in igure 12-5. This new demand curve leads to an increase in the relative wage and an increase in employment. The new equilibrium is point f. 28a. A job score of 600 would lead to $50,000 in earnings from a man. Therefore, the women s salary reflects a $10,000 comparable worth earnings gap. 28b. A salary of $40,000 represents only 80% of what a man earns. Therefore, the woman s salary represents a 20% comparable worth earnings gap. Applications 29. Demographic groups that earn more than the U.S. average may still experience discrimination. Recall that wages can be thought of as a function of an individual s personal productive characteristics and the payoff that each characteristic brings in the labor market. Even though the payoffs may be reduced because of the group an individual belongs to, if the person has highly productive characteristics, the wage that is actually received may still be well above average. To measure the discrimination, one could estimate what Russians would earn if they had the same productive characteristics as native-born white Americans. If the estimate reveals Russians would earn less, this would be evidence supporting the hypothesis of discrimination.
Answers To Chapter 12 331 30a. Substituting the appropriate values into the wage formulas yields = 8 = 0.75(12) + 2(1) = 20, = 8 + 0.5(8) = 12 = 12 20 = 0.6 14% earnings gap. 30b. Substituting EXP = 12, OC = 1, and Z = 1 into the women s wage equation yields = 8 + 0.5(12) + 2(1) = 17 = 17 20 = 0.85 30c. After controlling for all premarket characteristics, women earn 15% less than men. 30d. After Substituting EXP = 12, and OC = 1 into the women s wage equation yields = 8 + 0.5(12) + 2(1) = 16 = 16 20 = 0.8. 30e. After controlling for all pre-market characteristics except attitude, women appearing to be experiencing a 20% discriminatory earnings gap. 31a. Profit maximization requires that firms pay a real wage equal to the marginal product of labor in each sector 31b. Total output = 390 + 240 + 240 = 870. 31c. The real wage would equal 60 in each sector. a = 40, b = 70 = c. 31d. Total output = 3(300) = 900. the new distribution of labor is optimal since the marginal product of labor is equal across the sectors. This means that there is no way to reallocate labor and get a higher output. 32a. A 20% turnover rate in a firm with 1,000 employees means that the firm must replace 200 workers annually. If 20% of the new hires are black, the firm will be hiring 40 blacks annually. Provided the turnover rate applies equally across all demographic groups in the firm, 20% of the 100 black workers will leave the firm for a total loss of 20 black workers. 32b. If 20 blacks leave the firm during the first year and 40 are hired, there will be a net gain of 20. Therefore, at the end of year 1, there will be 120 black workers. This represents 12% of total employment, up from 10% at the start of the year.
332 Ehrenberg/Smith odern Labor Economics: Theory and Public Policy, Tenth Edition 32c. The computations in Table 12-5 show that 16.7% of total employment will be black after 5 years of affirmative action. Table 12-5 Year 1 2 3 4 5 # Loss 20 24 27 30 40 New Hires 40 40 40 40 40 Net Gain 20 16 13 10 8 Total 120 136 149 159 167 Percent Black 12 13.6 14.9 15.9 16.7 32d. An increase in turnover would reduce the number of years needed to achieve the goal. or example, if the turnover rate increased from 20% to 30%, 300 new workers would be hired in year 1, 60 of whom would be black. At the same time, 30 blacks would leave the firm in year 1, for a net gain of 30. hen the turnover was 20%, the net gain in year 1 was only 20 black workers.