Labor economics 7th edition george borjas solutions manual

Labor Economics 7th Edition George Borjas Solutions Manual Visit to download the full and correct content document: https://testbankdeal.com/dow nload/labor-economics-7th-edition-george-borjas-solutions-manual/

CHAPTER 7 7-1. Evaluate the validity of the following claim: The increasing wage gap between highly educated and less educated workers will itself generate shifts in the U.S. labor market over the next decade. As a result of these responses, much of the “excess” gain currently accruing to highly educated workers will soon disappear.

The incentives for young workers to stay in school rose as a result of the increasing wage differential across schooling groups. The widening wage inequality, therefore, would be expected to increase the number of young persons who obtain a college education. This increase in the supply of highly educated workers will eventually narrow the wage gap between the highly educated and the less educated. The extent to which the supply response narrows the “excess gain” depends on two parameters: (1) the elasticity of supply measuring how college enrollments respond to the increasing relative wage of college graduates; and (2) the elasticity of demand measuring the responsiveness of the relative wage of college graduates to an increase in their supply. The greater these elasticities are in the coming years, the greater role the “self-correcting” mechanism will play in reducing wage inequality in the future.

7-2. What effect will each of the following proposed changes have on wage inequality? (a) Indexing the minimum wage to inflation.

Indexing the minimum wage to inflation should reduce wage inequality because the minimum wage helps prop up the wages of less skilled workers. Note that an increase in the minimum wage may have negative employment effects, but the proposed policy is not to increase the minimum wage but rather simply to prevent it from falling in real terms. (b) Increasing the benefit level paid to welfare recipients.

Wage inequality measures the dispersion of wages in the working population. An increase in welfare benefits would likely induce less-skilled workers out of the labor force, and would reduce measured wage inequality by effectively eliminating the bottom of the wage distribution. (c) Increasing wage subsidies paid to firms that hire low-skill workers.

Wage subsidies would increase the demand for less skilled workers, reducing wage inequality.

1 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-3. From 1970 to 2000, the supply of college graduates to the labor market increased dramatically, while the supply of high school (no college) graduates shrunk. At the same time, the average real wage of college graduates stayed relatively stable, while the average real wage of high school graduates fell. How can these wage patterns be explained?

The graphs below show equilibrium movements in the market for high school graduates and in the market for college graduates. The decrease in labor supply among high school graduates and the increase in labor supply among college graduates is taken as given. The analysis, therefore, focuses on labor demand for each type of labor.

Given a lower supply of high school graduates, the only way for their average wage to fall is for labor demand for high school graduates to have decreased (shifted in).

Labor Market for High School Graduates LS2000 LS1970 w1970 w2000 LD1970

LD2000 L2000

L1970

Given a greater supply of college graduates, the only way for their average wage to stay the same is for labor demand for college graduates to have increased (shifted out).

Labor Market for College Graduates

LD1970

LD

LS1970 LS2000

2000

w1970 = w2000

L1970

L2000

2 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-4. (a) Is the presence of an underground economy likely to result in a Gini coefficient that over-states or under-states poverty?

The larger the underground economy, the more the Gini coefficient is likely to over-state poverty as the underground economy tends to employ low-skill, low-income workers. (b) Consider a simple economy where 90 percent of citizens report an annual income of $10,000 while the remaining 10 percent report an annual income of $110,000. What is the Gini coefficient associated with this economy?

As all citizens in each group receive an equal income, the actual Lorenz curve will be a straight line within each group. Let’s suppose there are 1,000 citizens. The 90% of poorest citizens, therefore, receive 0.90 x 1000 x $10,000 = $9 million. The entire economy, though, earns 0.9(10,000)+0.1(110,000) = $20 million. Therefore, the bottom 90% receives 9 ÷ 20 = 45% of total income. The perfect and actual Lorenz curves can now be drawn rather easily.

Share of Income 1.00 Perfect-Equality Lorenz Curve

Actual Lorenz Curve

0.45

0.00 0

0.9 Share of Citizens

1.00

The Gini coefficient is now easily calculated by seeing that the area beneath the actual Lorenz curve is two triangles and one rectangle.

Gini =

(1 / 2) − (1 / 2)(0.9)(0.45) + (0.1)(0.45) + (1 / 2)(0.1)(0.55) = 0.45 .

(1 / 2)

(c) Suppose the poorest 90 percent of citizens actually have an income of $15,000 because each receives $5,000 of unreported income from the underground economy. What is the Gini coefficient now?

The problem is identical to that above, but the income levels change. In this case, per capita GDP is 0.9 x 15,000 + 0.1 x 110,000 = $24,500 so total income of the 1,000 citizens is $24,500,000.

Lastly, the total income share of the poorest 90% of citizens is 900 x 15000 ÷ 24.5 million = 55.1%. (That is, in the graph on the previous page, the income share at 90% of citizens increases from 45% to 55.1%.) The Gini coefficient is not calculated as it was before:

Gini =

(1 / 2) − (1 / 2)(0.9)(0.551) + (0.1)(0.551) + (1 / 2)(0.1)(0.449) = 0.349 (1 / 2) 3

© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-5. Use the two wage ratios for each country in Table 7-4 to calculate each country’s percent increase in the 90-10 wage ratio from 1984 to 1994. Which countries experienced a compression in the wage distribution over this time? Which three countries experienced the greatest percent increase in wage dispersion over this time?

The results are:

Country Germany Canada Norway Japan Finland France Netherlands Australia Sweden United States United Kingdom New Zealand Italy

1984 138.7 301.5 105.4 177.3 150.9 232 150.9 174.6 103.4 266.9 177.3 171.8 129.3

1994 124.8 278.1 97.4 177.3 153.5 242.1 158.6 194.5 120.3 326.3 222.2 215.8 163.8

percent change -10.02% -7.76% -7.59% 0.00% 1.72% 4.35% 5.10% 11.40% 16.34% 22.26% 25.32% 25.61% 26.68%

Thus, Germany, Canada, and Norway (with Japan holding constant) all experienced a compression in the wage distribution over this time. The United Kingdom, New Zealand, and Italy experienced the largest percent increases in wage dispersion.

4 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-6. Recently President Obama has tried to focus public attention on inequality. (a) What is the difference between income inequality and wealth inequality?

Income inequality refers to differences in earned income, sometimes just labor income, sometimes both labor and investment income. Wealth inequality refers to differences in accumulated wealth, which is driven in part by income inequality but also in part by saving and spending behavior. The difference is important, because wealth (accumulated savings) is almost always more unequal than income. (b) Most policies that target inequality either target it at the low end of the income distribution by trying to increase wages of low-income workers, or at the high end of the income distribution by limiting wages of high-income workers. List a few potential policies of each type.

Pell grants and guaranteed student loans are designed to fundamentally lessen inequality by giving children of low-income parents greater access to education. Policies like the minimum wage, the progressive tax system, and the Earned Income Tax Credit are all designed in part to partially offset income inequality by transferring resources from the rich to the poor.

The estate tax is a primary policy aimed at alleviating inequality by targeting the high end as it is supposed to prohibit family dynasties in terms of wealth. (c) In your opinion, should the government focus on the low end or the high end? Why? In many people’s opinion, the government should focus most of its efforts at the low end for a couple of reasons. Most importantly, there are a lot more people at the low end than at the high end, so having affective policies in place (like Pell grants) can give everyone a chance to make decisions to help themselves economically. Also, many proposals to alleviate inequality targeted at the high end would, to some extent, stifle innovation. In simple terms, the question is whether inequality is a problem because Bill Gates created Microsoft or because 20% of minority students drop out of high school and don’t go to college. (d) In order to better understand how sensitive inequality measures are to the choice of measure, provide a graph of an economy with a 90-10 wage gap that is essentially zero but for which the Gini coefficient is close to 1.

Consider an economy where 95% of the economy earns essentially nothing, with 5% of the economic agents earning essentially everything. Such an economy will have a 90-10 wage gap that is essentially zero (as the 90 percentile person earns roughly what the 10 percentile person earns) but also has a Gini coefficient close to 1 as 5% of the agents earn almost all of the income.

Earnings Distribution Share of Income

100%

0% 0% Share of Households 95% 100% 5 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-7. The two points for the international income distributions reported in Table 7-1 can be used to make a rough calculation of the Gini coefficient. Use a spreadsheet to estimate the Gini coefficient for each country. Which three countries have the most equal income distribution? Which three countries have the most unequal income distribution?

If one considers the percent of income received by the poorest and richest 10 percent of households called P and R respectively, the Gini coefficient is [ .5 – (½)(.1)P – .8P – .8(½)(1–R–P) – .1(1–R) – .1(½)R ] / .5.

Conveniently, this equation carefully reduces to Gini = 0.9(R – P). The results are: Country Australia Austria Belgium Canada Chile Dominican Republic France Germany Guatemala Hungary India Israel Italy Mexico Norway Sweden United Kingdom United States

P 0.02 0.03 0.03 0.03 0.02 0.02 0.03 0.03 0.01 0.04 0.04 0.02 0.02 0.01 0.04 0.04 0.02 0.02

R 0.25 0.23 0.28 0.25 0.42 0.38 0.25 0.22 0.43 0.24 0.31 0.29 0.27 0.41 0.23 0.22 0.29 0.30

Gini 0.207 0.180 0.225 0.198 0.360 0.324 0.198 0.171 0.378 0.180 0.243 0.243 0.225 0.360 0.171 0.162 0.243 0.252

Thus, the three countries with the most inequality are Chili (0.360), Mexico (0.360), and Guatemala (0.378). The three countries with the most equality are Sweden (0.162), Germany (0.171), and Norway (0.171). It should be emphasized that these are very crude measures as they rely on only two points in the income distribution.

6 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-8. Consider the following (highly) simplified description of the U.S. wage distribution and income and payroll tax schedule. Suppose 50 percent of households earn $40,000, 30 percent earn $70,000, 15 percent earn $120,000, and 5 percent earn $500,000. Marginal income tax rates are 0 percent up to $30,000, 15 percent on income earned from $30,000 to $60,000, 25 percent on income earned from $60,000 to $150,000, and 35 percent on income earned in excess of $150,000. There is also a 7.5 percent payroll tax on all income up to $80,000. (a) What is the marginal tax rate and average tax rate for each of the four types of households? What is the average household income, payroll, and total tax bill? What percent of the total income tax is paid by each of the four types of households? What percent of the total payroll tax bill is paid by each of the four types of household?

Marginal tax rates: households earning $40,000 is 15 percent + 7.5 percent = 22.5 percent. households earning $70,000 is 25 percent + 7.5 percent = 32.5 percent. households earning $120,000 is 25 percent + 0 percent = 25 percent. households earning $500,000 is 35 percent + 0 percent = 35 percent.

Income tax bill: households earning $40,000 is 15 percent of $10,000 = $1,500. households earning $70,000 is $4,500 + 25 percent of $10,000 = $7,000. households earning $120,000 is $4,500 + 25 percent of $60,000 = $19,500. households earning $500,000 is $27,000 + 35 percent of $350,000 = $149,500.

Payroll tax bill: households earning $40,000 is 7.5 percent of $40,000 = $3,000. households earning $70,000 is 7.5 percent of $70,000 = $5,250. households earning $120,000 is 7.5 percent of $80,000 = $6,000. households earning $500,000 is 7.5 percent of $80,000 = $6,000.

Total tax bill and average tax rates: households earning $40,000 is $4,500 => ATR = 11.25 percent. households earning $70,000 is $12,250 => ATR = 17.5 percent. households earning $120,000 is $25,500 => ATR = 21.25 percent. households earning $500,000 is $155,500 => ATR = 31.10 percent.

Average tax bills over all households are: Income: .5(1,500) + .3(7,000) + .15(19,500) + .05(149,500) = $13,250 Payroll: .5(3,000) + .3(5,250) + .15(6,000) + .05(6,000) = $4,275.

Total: $17,525.

Percent of the total income tax collected by the government that is paid by each household group: $40,000 households pay .5(1,500) / 13,250 = 5.67 percent. $70,000 households pay .3(7,000) / 13,250 = 15.85 percent. $120,000 households pay .15(19,500) / 13,250 = 22.08 percent. $500,000 pay .05(149,500) / 13,250 = 56.42 percent.

7 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Percent of the total payroll tax collected by government that is paid by each household group: $40,000 households pay .5(3,000) / 4,275 = 35.09 percent. $70,000 households pay .3(5,250) / 4,275 = 36.84 percent. $120,000 households pay .15(6,000) / 4,275 = 21.05 percent. $500,000 pay .05(6,000) / 4,275 = 7.02 percent. (b) What is the Gini coefficient for the economy when comparing after-tax incomes across households? (Hint: assume there are 1,000 households in the economy.) What happens to the Gini coefficient if all taxes were replaced by a single 20 percent flat tax on all incomes?

Suppose there were 1,000 households. Total after-tax income is 500($35,500) + 300($57,750) +150($94,500) +50($344,500) = $66,475,000.

The cumulative gross income shares of the four income groups, therefore, are: 500($35,500) / $66.47m = 26.7 percent.

26.7 percent + 300($57,750) / $66.47m = 52.8 percent.

52.8 percent + 150($94,500) / $66.47m = 74.1 percent.

74,1 percent + 50($344,500) / $66.47m = 100.0 percent.

The area under the Lorenz curve, therefore, is (.5) (½)(.267) + (.3)[.267+(½)(.528–.267 )] + (.15)[.528+(½)(.741–.528 )] +(.05)[.741+(½)(1–.741 )] = 0.6675 + 0.11925 + 0.95175 + 0.043525 = 0.3247. The Gini coefficient, therefore, is [ .5 – ..3247 ] / .5 = .3506.

Suppose there was a flat tax of 20 percent. Total after-tax income is 500(.8)($40,000 + 300(.8)($70,000) +150(.8)($120,000) +50(.8)($500,000) = $67,200,000.

The cumulative gross income shares of the four income groups, therefore, are: 500($32,000) / $67.2m = 23.8 percent.

23.8 percent + 300($56,000) / $67.2m = 48.8 percent.

48.8 percent + 150($96,000) / $67.2m = 70.2 percent.

70.2 percent + 50($400,000) / $67.2m = 100.0 percent.

The area under the Lorenz curve, therefore, is (.5) (½)(.238) + (.3)[.238+(½)(.488–.238 )] + (.15)[.488+(½)(.702–.488 )] +(.05)[.702+(½)(1–.702 )] = .0595 + .1089 + .08925 + .04255 = .3002. The Gini coefficient if there was a 20 percent flat tax, therefore, would be [ .5 – ..3002 ] / .5 = .3996. (c) A presidential candidate wants to remove the cap on payroll taxes so that every household would pay payroll taxes on all of its income. To what level could the payroll tax rate be reduced under the proposal while keeping the total amount of payroll tax collected the same?

Suppose there are 1,000 households: 500 pay $3,000, 300 pay $5,250, and 200 pay $6,000. The total payroll tax receipts, therefore, are $4,275,000, while total income is $84 million. Thus, generating $4.275 million of tax on $84 million of income requires a tax rate of 5.089 percent.

8 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-9. Before 1990, the 80-50 and the 50-20 log wage gap was higher for women than for men (see Figure 7-4). What are some possible reasons for this?

This pattern is likely a result of three empirical facts. Before the 1990s (1) women had much lower labor force participation rates than males, (2) women were less likely to be professionals, and (3) women were more likely to work part-time. All of these “facts” are likely to lead to greater wage gaps across the wage distribution. Moreover, all of these patterns have reversed to some degree since 1990. In the 2000’s, for example, more women are in college than men, and in the near future there will be more female doctors and lawyers than male doctors and lawyers. As labor force attachment and professional options have converged for men and women since 1990, Figure 7-4 demonstrates convergence in the gender wage gaps as a result as well.

7-10. Ms. Aura is a psychic. The demand for her services is given by Q = 2,000 – 10P, where Q is the number of one-hour sessions per year and P is the price of each session. Her marginal revenue is MR = 200 – 0.2Q. Ms. Aura’s operation has no fixed costs, but she incurs a cost of $150 per session (going to the client’s house). (a) What is Ms. Aura’s yearly profit?

Find the number of sessions that Ms. Aura will provide by equating the marginal revenue to the marginal cost of a session: setting MR = MC yields 200 – 0.2Q = 150 which solves as Q* = 250.

The price that would generate demand for 250 sessions is $175 as 2,000 – 10(175) = 250. Thus, her annual profit is 175(250) – 150(250) = $6,250 per year. (b) Suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new demand for her services is Q = 2500 – 5P. Her new marginal revenue is MR = 500 – 0.4Q. What is her profit now?

The same kind of calculations as in part (a) but using the new demand curve yields a profit maximizing quantity of 875 sessions at $325 per session and an annual profit of $153,125. (c) Advances in telecommunications and information technology revolutionize the way Ms. Aura does business. She begins to use the Internet to find all relevant information about clients and meets many clients through teleconferencing. The new technology introduces an annual fixed cost of $1,000, but the marginal cost is only $20 per session. What is Ms. Aura’s profit? Assume the demand curve is still given by Q = 2500 – 5P. With the new marginal cost, Ms. Aura will provide 1,200 sessions and charge $260 per session.

Her annual profit will equal $287,000. (d) Summarize the lesson of this problem for the superstar phenomenon.

Superstars command an economic rent because they are, in essence, a monopoly with a favorable demand curve. The greater the demand for the superstar’s product, the higher price the superstar can charge, and the more profit can be earned. Notice also that, going from part (a) to part (b), is the lesson that when demand for your services is high, you provide a lot of service, i.e., an upward sloping labor supply curve.

9 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-11. Suppose two households earn $40,000 and $56,000 respectively. What is the expected percent difference in wages between the children, grandchildren, and great-grandchildren of the two households if the intergenerational correlation of earnings is 0.2, 0.4, or 0.6?

If the intergenerational correlation of earnings is r, the percent difference in earnings of the children is (56,000 – 40,000)r / 40,000 = 0.4r, of grandchildren is .4r2, and of great-grandchildren is .4r3. Therefore, we have that the expected percent difference in earnings is: Correlation 20% 40% 60%

Children 8% 16% 24%

Grandchildren 1.6% 6.4% 14.4%

Great-Grandchildren 0.32% 2.56% 8.64%

7-12. Suppose 50 percent of a population all receive an equal share of p percent of the nation’s income, where 0 ≤ p ≤ 50. (a) For any such p, what is the Gini coefficient for the country?

Calculating the Gini coefficient is most easily done with reference to a graph. Notice, given the set-up of the problem, there are two sections to the graph of the distribution of national income, and both are linear segments.

Share of Income

1

½

p

½

1

Share of Households

So, now the Gini coefficient is the area between the bold line and the dashed bold line divided by two. This is easiest to figure as the area below the bold line (one-half) less the area below the dashed bold line. The area below the dashed bold line equals (0.5)(0.5)p + 0.5p + (0.5)(0.5)(1 – p) = 0.25 + 0.5p. Finally, the Gini coefficient is (0.5 – 0.25 – 0.5p) / 0.5 = 0.5 – p. (b) For any such p, what is the 90 – 10 wage gap?

Each person in the lower half of the distribution receives 0.02pM, where M is national income.

Similarly, each person in the top half of the distribution receives 0.02(1–p)M. As the 10th percentile person is in the lower half and the 90th percentile person is in the upper half, the 90 – 10 wage gap is 0.02(1–p)M / 0.02pM = (1–p)/p.

10 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-13. Consider two developing countries. Country A, though quite poor, uses government resources and international aid to provide public access to quality education. Country B, though also quite poor, is unable to provide quality education for institutional reasons. The distribution of innate ability is identical in the two countries. (a) Which country is likely to have a more positively skewed income distribution? Why? Plot the hypothetical income distributions for both countries on the same graph.

At the outset, there is no reason to think the distribution of income is different between the two countries. However, one could argue that Country A collects more taxes than Country B, and as taxes are likely to fall more heavily on the rich, that the simple act of collecting taxes in Country A will cause it to lessen the skewness in its income distribution relative to Country B. Of course, one could make the alternative argument – that developing countries over-tax their poorest workers more than the rich. The graph below, however, assumes the first case.

Original Wage Distribution

Percent of Workers

Country A: Taxing the Rich Country B: Not Taxing the Rich

Earnings

(b) Which country is more likely to develop faster? Why? Plot the hypothetical income distributions in 20 years for both countries on the same graph.

Country A is likely to develop faster because of its savings and investments into education (human capital).

Wage Distribution after 20 Years

Percent of Workers

Country B Country A

Earnings

11 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

7-14. File sharing software threatens the music industry in part because artists will not be fully compensating for their recording of songs. Suppose that the government decides that file sharing software products are legal anyway. (a) The almost immediate result will be that artists start earning very little money for their recordings but they continue to earn money for live performances. How will income change for the music industry? How does your answer relate to the superstar phenomenon?

Musicians who are also great performers will continue to make new music and will continue to earn a lot of money. Musicians who are good at making new music but not good at giving live performances will see a reduction in their income. For example, rumor has it that Steely Dan and the Steve Miller Band are fairly horrible (or, at least relatively worse than other bands) in concert, although their music is loved by many people. These bands would struggle to earn money under the policy. Other artists that are known to put on great shows (The Rolling Stones) will continue to earn a lot of money. Thus, the public policy doesn’t choose which superstars will continue to do well; it simply redefines what talents are going to be rewarded. (b) Although one would expect lower prices to benefit the music-listening public if the government decides that file sharing software products are legal, in what way(s) could the music-listening public also be hurt from the policy?

The most obvious way such a policy would harm the music-listening public is that fewer people make music as it is less profitable. Thus, the public will have fewer choices of music to listen to.

This is analogous to if the government removed the patent system from new drugs, which would results in fewer new drugs being developed.

7-15. Explain why the intergenerational correlation of earnings would likely be higher or lower than average for the following groups and factors in the United States: (a) Improved educational outcomes for all populations (e.g., minority, low-income, rural) as hoped for by No Child Left Behind.

Improved educational outcomes for all populations should lower the intergenerational correlation of earnings as wealth becomes less of a factor in determining educational outcomes and economic success. (b) The elimination of legacy admits to Colleges and Universities.

The elimination of legacy admits to colleges and universities should lower the intergenerational correlation of earnings as parental education becomes less of a factor in determining educational outcomes and eventually economic success. (c) The implementation of a federal inheritance tax.

The implementation of a federal inheritance tax should lower the intergenerational correlation of earnings as children are less able to benefit from their parent’s wealth.

12 © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.