Local and global maxima and minima for cos(3πx)/x, 0.1≤x≤1.1

In mathematics, the maximum and minimum (plural: maxima and minima) of a function, known collectively as extrema (singular: extremum), are the largest and smallest value that the function takes at a point either within a given neighborhood (local or relative extremum) or on the function domain in its entirety (global or absolute extremum).^[1][2][3]

More generally, the maximum and minimum of a set (as defined in set theory) are the greatest and least element in the set. Unbounded infinite sets such as the set of real numbers have no minimum and maximum.

To locate extreme values is the basic objective of optimization.

Analytical definition[link]

A real-valued function f defined on a real line is said to have a local (or relative) maximum point at the point x^∗, if there exists some ε > 0 such that f(x^∗) ≥ f(x) when |x − x^∗| < ε. The value of the function at this point is called maximum of the function. Similarly, a function has a local minimum point at x^∗, if f(x^∗) ≤ f(x) when |x − x^∗| < ε. The value of the function at this point is called minimum of the function.

A function has a global (or absolute) maximum point at x^∗ if f(x^∗) ≥ f(x) for all x. Similarly, a function has a global (or absolute) minimum point at x^∗ if f(x^∗) ≤ f(x) for all x. The global maximum and global minimum points are also known as the arg max and arg min: the argument (input) at which the maximum (respectively, minimum) occurs.

Restricted domains: There may be maxima and minima for a function whose domain does not include all real numbers. A real-valued function, whose domain is any set, can have a global maximum and minimum. There may also be local maxima and local minima points, but only at points of the domain set where the concept of neighborhood is defined. A neighborhood plays the role of the set of x such that |x − x^∗| < ε.

A continuous (real-valued) function on a compact set always takes maximum and minimum values on that set. An important example is a function whose domain is a closed (and bounded) interval of real numbers (see the graph above). The neighborhood requirement precludes a local maximum or minimum at an endpoint of an interval. However, an endpoint may still be a global maximum or minimum. Thus it is not always true, for finite domains, that a global maximum (minimum) must also be a local maximum (minimum).

Finding functional maxima and minima[link]

Finding global maxima and minima is the goal of mathematical optimization. If a function is continuous on a closed interval, then by the extreme value theorem global maxima and minima exist. Furthermore, a global maximum (or minimum) either must be a local maximum (or minimum) in the interior of the domain, or must lie on the boundary of the domain. So a method of finding a global maximum (or minimum) is to look at all the local maxima (or minima) in the interior, and also look at the maxima (or minima) of the points on the boundary; and take the biggest (or smallest) one.

Local extrema can be found by Fermat's theorem, which states that they must occur at critical points. One can distinguish whether a critical point is a local maximum or local minimum by using the first derivative test or second derivative test.

For any function that is defined piecewise, one finds a maxima (or minima) by finding the maximum (or minimum) of each piece separately; and then seeing which one is biggest (or smallest).

Examples[link]

The global maximum of Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[x]{x} occurs at x = e.

• The function x² has a unique global minimum at x = 0.
• The function x³ has no global minima or maxima. Although the first derivative (3x²) is 0 at x = 0, this is an inflection point.
• The function Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt[x]{x}

has a unique global maximum at x = e. (See figure at right)

• The function x^-x has a unique global maximum over the positive real numbers at x = 1/e.
• The function x³/3 − x has first derivative x² − 1 and second derivative 2x. Setting the first derivative to 0 and solving for x gives stationary points at −1 and +1. From the sign of the second derivative we can see that −1 is a local maximum and +1 is a local minimum. Note that this function has no global maximum or minimum.
• The function |x| has a global minimum at x = 0 that cannot be found by taking derivatives, because the derivative does not exist at x = 0.
• The function cos(x) has infinitely many global maxima at 0, ±2π, ±4π, …, and infinitely many global minima at ±π, ±3π, ….
• The function 2 cos(x) − x has infinitely many local maxima and minima, but no global maximum or minimum.
• The function cos(3πx)/x with 0.1 ≤ x ≤ 1.1 has a global maximum at x = 0.1 (a boundary), a global minimum near x = 0.3, a local maximum near x = 0.6, and a local minimum near x = 1.0. (See figure at top of page.)
• The function x³ + 3x² − 2x + 1 defined over the closed interval (segment) [−4,2] has two extrema: one local maximum at x = −1−^√15⁄₃, one local minimum at x = −1+^√15⁄₃, a global maximum at x = 2 and a global minimum at x = −4.

Functions of more than one variable[link]

For functions of more than one variable, similar conditions apply. For example, in the (enlargeable) figure at the right, the necessary conditions for a local maximum are similar to those of a function with only one variable. The first partial derivatives as to z (the variable to be maximized) are zero at the maximum (the glowing dot on top in the figure). The second partial derivatives are negative. These are only necessary, not sufficient, conditions for a local maximum because of the possibility of a saddle point. For use of these conditions to solve for a maximum, the function z must also be differentiable throughout. The second partial derivative test can help classify the point as a relative maximum or relative minimum.

In contrast, there are substantial differences between functions of one variable and functions of more than one variable in the identification of global extrema. For example, if a bounded differentiable function f defined on a closed interval in the real line has a single critical point, which is a local minimum, then it is also a global minimum (use the intermediate value theorem and Rolle's theorem to prove this by reductio ad absurdum). In two and more dimensions, this argument fails, as the function

Failed to parse (Missing texvc executable; please see math/README to configure.): f(x,y)= x^2+y^2(1-x)^3,\qquad x,y\in\mathbb{R},

shows. Its only critical point is at (0,0), which is a local minimum with ƒ(0,0) = 0. However, it cannot be a global one, because ƒ(4,1) = −11.

The global maximum is the point at the top

File:MaximumCounterexample.png Counterexample

In relation to sets[link]

Maxima and minima are more generally defined for sets. In general, if an ordered set S has a greatest element m, m is a maximal element. Furthermore, if S is a subset of an ordered set T and m is the greatest element of S with respect to order induced by T, m is a least upper bound of S in T. The similar result holds for least element, minimal element and greatest lower bound.

In the case of a general partial order, the least element (smaller than all other) should not be confused with a minimal element (nothing is smaller). Likewise, a greatest element of a partially ordered set (poset) is an upper bound of the set which is contained within the set, whereas a maximal element m of a poset A is an element of A such that if m ≤ b (for any b in A) then m = b. Any least element or greatest element of a poset is unique, but a poset can have several minimal or maximal elements. If a poset has more than one maximal element, then these elements will not be mutually comparable.

In a totally ordered set, or chain, all elements are mutually comparable, so such a set can have at most one minimal element and at most one maximal element. Then, due to mutual comparability, the minimal element will also be the least element and the maximal element will also be the greatest element. Thus in a totally ordered set we can simply use the terms minimum and maximum. If a chain is finite then it will always have a maximum and a minimum. If a chain is infinite then it need not have a maximum or a minimum. For example, the set of natural numbers has no maximum, though it has a minimum. If an infinite chain S is bounded, then the closure Cl(S) of the set occasionally has a minimum and a maximum, in such case they are called the greatest lower bound and the least upper bound of the set S, respectively..

See also[link]

Look up maxima, minima, or extremum in Wiktionary, the free dictionary.

• First derivative test
• Second derivative test
• Higher-order derivative test
• Limit superior and limit inferior
• Mechanical equilibrium
• Sample maximum and minimum
• Saddle point

References[link]

External links[link]

• Maxima and Minima From MathWorld--A Wolfram Web Resource.
• Thomas Simpson's work on Maxima and Minima at Convergence
• Application of Maxima and Minima with sub pages of solved problems

Elizabeth Warren (born June 22, 1949) is an American bankruptcy law expert, policy advocate, Harvard Law School professor, and Democratic Party candidate in the 2012 United States Senate election in Massachusetts. She has written several academic and popular books concerning the American economy and personal finance. She contributed to the oversight of the 2008 U.S. bailout program, and also led the conception and establishment of the Consumer Financial Protection Bureau.

Born in Oklahoma City, Oklahoma, Warren attended The George Washington University and the University of Houston. She received a J.D. from Rutgers School of Law–Newark in 1976. Warren taught law at several universities and was listed by the Association of American Law Schools as a minority law professor throughout the 1980s and 1990s. In the wake of the U.S. financial crisis, Warren served as chair of the Congressional Oversight Panel created to oversee the Troubled Assets Relief Program in 2008. She later served as Assistant to the President and Special Advisor to the Secretary of the Treasury for the Consumer Financial Protection Bureau under U.S. President Barack Obama.

Early life and education[link]

Elizabeth Herring^[1] was born June 22, 1949,^[2] in Oklahoma City, Oklahoma, to working class parents Pauline (née Reed) and Donald Jones Herring.^[3][4][5] She was the Herrings' fourth child, with three older brothers.^[6] When Warren was twelve, her father, a janitor, had a heart attack, which led to a pay cut, medical bills, and eventually the loss of their car. Her mother answered phones at Sears and Warren worked as a waitress.^[6][7]

At Northwest Classen High School she was named "Oklahoma's top high-school debater". She received a debate-team scholarship to George Washington University at the age of 16. Initially aspiring to be a teacher, she left GWU after two years to marry her high-school boyfriend Jim Warren.^[6][8] She moved to Houston to be with her husband, who was a NASA engineer. There she enrolled in the University of Houston where she graduated in 1970 with a degree in speech pathology and audiology.^[9] She taught children with disabilities for a year in a public school. However, she had not taken the required education courses to get a teaching certificate (she previously taught under an "emergency certificate"). After taking several graduate education courses, she decided she no longer wanted to pursue education as a career. She and her husband moved to New Jersey and since she was pregnant with their first child, she decided to stay at home for a few years.^[10][11][12]

After making a decision to study law, Warren enrolled at the Rutgers School of Law–Newark,^[10] where she served as an editor of the Rutgers Law Review, and was a summer associate at Cadwalader, Wickersham & Taft's.^[13] Shortly before her graduation in 1976, she became pregnant with her second child and she worked from home, writing wills and doing real estate closings.^[8][10]

She and Jim had two children before divorcing in 1978: Amelia Warren Tyagi, with whom Elizabeth would later coauthor two books and several articles, and a son, Alexander Warren. Today they have three grandchildren.^[14] In 1980, Warren married Bruce Mann, also a Harvard law professor. She cites Methodist founder John Wesley as an inspiration.^[15]

Academic career[link]

Throughout the 1980s and 1990s she taught law at several universities throughout the country, while researching bankruptcy and middle-class personal finance.^[10] In 1978 Congress had passed a law that made it easier for companies and individuals to declare bankruptcy and Warren decided "to set out to prove they were all a bunch of cheaters... I was going to expose these people who were taking advantage of the rest of us". However, she instead found that the vast majority of those in bankruptcy courts were from hardworking middle-class families: people who had lost their jobs or had family breakups or illnesses that had wiped out their savings. "It changed my vision," she said.^[6]

According to her CV, she taught at the Rutgers School of Law–Newark (1977–78), the University of Houston Law Center (1978–83), the University of Michigan (visiting, 1985), and the University of Texas School of Law (1981–87). She also worked as a research associate at the University of Texas at Austin (1983–87). She joined the University of Pennsylvania Law School in 1987, where she became the William A Schnader Professor of Commercial Law in 1990. She joined Harvard Law School in 1992 as the Robert Braucher Visiting Professor of Commercial Law, and began a permanent position as the Leo Gottlieb Professor of Law in 1995.^[16]

In 1995 Warren was asked to advise the National Bankruptcy Review Commission. She helped to draft the commission's report and then spent several years opposing legislation meant to severely restrict the right of consumers to file for bankruptcy. Warren and others opposing the legislation were not successful and in 2005 the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005 was passed by Congress.^[17]

Warren appeared in the documentary film Maxed Out in 2006, has appeared several times on Dr. Phil to talk about money and families, has been a guest on The Daily Show,^[18] is interviewed frequently on cable news networks,^[19] appears in Michael Moore's Capitalism: A Love Story, has appeared on the Charlie Rose talk show,^[20] and has appeared on the Real Time With Bill Maher talk show.^[21] She has also appeared on the PBS show NOW.^[22]

Warren in 2010 at a Women in Finance symposium held at the U.S. Treasury.

From November 2006 to November 2010, Warren was a member of the FDIC Advisory Committee on Economic Inclusion, which advises the FDIC "on important initiatives focused on expanding access to banking services by underserved populations".^[23] She is a member of the National Bankruptcy Conference, an independent organization which advises the U.S. Congress on bankruptcy law.^[24] She is a former Vice-President of the American Law Institute and a member of the American Academy of Arts and Sciences. From 2005 to 2008, Warren and her law students wrote a blog called Warren Reports, part of Josh Marshall's TPMCafe.

Popular works[link]

In addition to writing more than 100 scholarly articles and six academic books, Warren has written several best-selling books, including All Your Worth: The Ultimate Lifetime Money Plan, coauthored with her daughter, Amelia Tyagi.

Warren and Tyagi also wrote The Two-Income Trap: Why Middle-Class Mothers and Fathers Are Going Broke. Warren and Tyagi point out that a fully employed worker today earns less inflation-adjusted income than a fully employed worker did 30 years ago. To increase their income, families have sent a second parent into the workforce. Although families spend less today on clothing, appliances, and other consumption, the costs of core expenses such as mortgages, health care, transportation, and child care have increased dramatically. The result is that even with two-income earners, families are no longer able to save and have incurred greater and greater debt.

In an article in The New York Times, Jeff Madrick said of Warren's book:

The upshot is that two-income families often have even less income left over today than did an equivalent single-income family 30 years ago, even when they make almost twice as much. And they go deeper in debt. The authors find that it is not the free-spending young or the incapacitated elderly who are declaring bankruptcy so much as families with children... their main thesis is undeniable. Typical families often cannot afford the high-quality education, health care and neighborhoods required to be middle class today. More clearly than anyone else, I think, Ms. Warren and Ms. Tyagi have shown how little attention the nation and our government have paid to the way Americans really live.^[25]

In an article in Time magazine by Maryanna Murray Buechner, "Parent Trap" (subtitled "Want to go bust? Have a kid. Educate same. Why the middle class never had it so bad"), Buechner said of Warren's book:

For families looking for ways to cope, Warren and Tyagi mainly offer palliatives: Buy a cheaper house. Squirrel away a six-month cash cushion. Yeah, right. But they also know that there are no easy solutions. Readers who are already committed to a house and parenthood will find little to mitigate the deflating sense that they have nowhere to go but down.^[26]

In 2005, David Himmelstein and Warren published a study on bankruptcy and medical bills,^[27] which said that half of all families filing for bankruptcy did so in the aftermath of a serious medical problem. The finding was particularly noteworthy because 75 percent of families who fit that description had medical insurance.^[28] This study was widely cited in academic studies and policy debates, though some have challenged the study's methods and offered alternative interpretations of the data.^[29]

TARP oversight[link]

On November 14, 2008, Warren was appointed by United States Senate Majority Leader Harry Reid to chair the five-member Congressional Oversight Panel created to oversee the implementation of the Emergency Economic Stabilization Act.^[30] The Panel releases monthly oversight reports that evaluate the government bailout and related programs.^[15] The Panel's monthly reports under Warren's leadership covered foreclosure mitigation, consumer and small business lending, commercial real estate, AIG, bank stress tests, the impact of the Troubled Asset Relief Program (TARP) on the financial markets, government guarantees, the automotive industry, and many other topics. The Panel has also released special reports on financial regulatory reform and farm loans. For each report, Warren released a video on the Congressional Oversight Panel's website explaining key findings.^[a]

In an interview at Newsweek, Warren commented, "To restore some basic sanity to the financial system, we need two central changes: fix broken consumer-credit markets and end guarantees for the big players that threaten our entire economic system."^[31]

On July 29, 2011, she left her role with the agency to return to academic life at Harvard Law School. Her departing address indicated how she first became involved:

Four years ago, I submitted an article to Democracy Journal that argued for a new government agency called the Financial Product Safety Commission. I threw myself into that piece because I felt strongly that a new consumer agency would make the credit markets work better for American families and strengthen the economic security of the middle class... I leave this agency, but not this fight... the issues we deal with – a middle class that has been squeezed and business models built on tricks and traps – are deeply personal to me, and they always will be.^[32]

Consumer Financial Protection Bureau[link]

Warren has long advocated for the creation of a new Consumer Financial Protection Bureau, a watchdog agency designed to "make basic financial practices such as taking out a mortgage or loan more clear and transparent while ferreting out unfair lending practices," according to CNN. In an interview with the Huffington Post, Warren said "My first choice is a strong consumer agency. My second choice is no agency at all and plenty of blood and teeth left on the floor".^[33] Through Warren's efforts, the bureau was established by the Dodd–Frank Wall Street Reform and Consumer Protection Act signed into law by Obama in July 2010. For the first year after the bill's signing, Warren worked on implementation of the bureau as a Special Assistant to the President in anticipation of the agency's formal opening. While liberal groups and consumer advocacy groups pushed for Obama to nominate Warren as the agency's permanent director, Warren was strongly opposed by financial institutions which had criticized Warren as overly aggressive in pursuing regulations, and by the Republican members of Congress. Furthermore, she did not have the strong support of the Obama administration, particularly Treasury Secretary Tim Geithner. In July 2011, Obama instead announced the nomination of former Ohio Attorney General Richard Cordray as the bureau's director, subject to Congressional approval.^[34] However, in December his nomination was blocked by a Republican-led filibuster in the Senate. Until a director is confirmed, the agency will not gain the full measure of its powers. It can supervise the compliance of banks with existing laws, but the Dodd-Frank financial legislation dictates that it cannot supervise other financial companies or write new rules. On 4 January 2012, President Obama named Ohio Attorney General Richard Cordray the Bureau's Director in a recess appointment.^[35]

2012 US Senate run[link]

The neutrality of this section is disputed. Please see the discussion on the talk page. Please do not remove this message until the dispute is resolved. (May 2012)

On September 14, 2011, Warren declared that she intended to run for the Democratic nomination for the 2012 election in Massachusetts for the United States Senate seat currently held by incumbent Scott Brown.^[36][37] On September 21, a video of Warren explaining the rationale of her economic policy received attention on the Internet.^[38]

Cherokee self-identification controversy[link]

An editor has expressed a concern that this section lends undue weight to certain ideas relative to the article as a whole. Please help to discuss and resolve the dispute before removing this message. (June 2012)

Warren listed herself as a minority in the Association of American Law Schools directory of law professors, from 1986 to 1995.^[39] The Brown campaign, the Native American Rights Fund, and a group of more than 150 Cherokees organized by Cherokee genealogist and activist David Cornsilk^[40][41] have questioned her motives for the claim and its propriety.^{[42][43][44][45][46]} The group, “Cherokees Demand Truth from Elizabeth Warren”, plans a protest at the Massachusetts Democratic Convention on June 2, 2012.^[47]

Genealogist Chris Child at the New England Historic Genealogical Society researched Warren's claimed native ancestry but found nothing conclusive. According to Child, “Once you go back further than 150 years the records are more complicated to go through,” and it may take weeks to months to make a determination.^[48][49][50] Warren said that she had heard family stories about her Cherokee ancestors her entire life ^[51] and had hoped it would create opportunities to meet people like her (even though the directory does not specify which minority professors belong to).^[39] But according to Warren, such opportunities never materialized and she eventually "stopped checking it off".^[52]

A month after the controversy began the Boston Globe discovered documents indicating that the Harvard University Law School had reported employing a Native American professor to the U.S. government in the years immediately before and after Warren left Harvard for a stint at the University of Pennsylvania.^[53] The most recent diversity census, for 2011, still shows one Native American professor. The census says that “Race/Ethnicity designations are from self-report data”.^[39] Warren, who does not meet the federal diversity definition of "Native American," admitted providing the information that she was a Native American to University of Pennsylvania and Harvard faculty in conversations after she was hired but denied that "there was [any] reporting for this".^[53] The Washington Post observed that she had "turned what could have been a small problem into a major story" by the way she had handled the issue.^[54]

According to a Suffolk University/7NEWS (WHDH-Boston) poll of 600 likely voters on May 20-22, 2012 there was 72 percent awareness of the controversy. 69 percent said Warren’s Native American heritage listing was not a significant story and 27 percent said it was.^[55][56]

Recognition[link]

Warren at the 2009 100 Most Influential People in the World reception.

Since about 2009, Warren has been recognized by several institutions as a major political figure. In 2009, the Boston Globe named her the Bostonian of the Year,^[9] and the Women's Bar Association of Massachusetts honored her with the Lelia J. Robinson Award.^[57] She was named one of Time Magazine's 100 Most Influential People in the World in 2009 and 2010.^[58] The National Law Journal has repeatedly named Warren as one of the Fifty Most Influential Women Attorneys in America,^[59] and in 2010 they honored her as one of the 40 most influential attorneys of the decade.^[60]

Warren has been recognized for her dynamic teaching style. In 2009, Warren became the first professor in Harvard's history to win the law school's teaching award twice. The Sacks-Freund Teaching Award was voted on by the graduating class in honor of "her teaching ability, openness to student concerns, and contributions to student life at Harvard."^[61] Warren also has won awards from her students at the University of Pennsylvania, the University of Michigan, and the University of Houston Law Center. She delivered the commencement address at the Rutgers School of Law–Newark in May 2011, where she was awarded an Honorary Doctor of Laws degree and was conferred membership into the Order of the Coif.^[62]

Publications[link]

Selected articles

• Warren, E. (1987). "Bankruptcy Policy". The University of Chicago Law Review 54 (3): 775–814. JSTOR 1599826. 
• Warren, E. (1992). "The Untenable Case for Repeal of Chapter 11". The Yale Law Journal 102 (2): 437–479. JSTOR 796843. 
• Warren, E. (1993). "Bankruptcy Policymaking in an Imperfect World". Michigan Law Review 92 (2): 336–387. JSTOR 1289668. 
• "Principled Approach to Consumer Bankruptcy". American Bankruptcy Law Journal 71: 483. 1997. http://heinonline.org/HOL/LandingPage?collection=journals&handle=hein.journals/ambank71&div=25&id=&page=. 
• "The Bankruptcy Crisis". Indiana Law Journal 73 (4): 1079. Fall 1998. http://www.law.indiana.edu/ilj/volumes/v73/no4/index.shtml. 
• Warren, Elizabeth; Westbrook, Jay Lawrence (January 2000). "Financial Characteristics of Businesses in Bankruptcy". SSRN Electronic Journal 73: 499. DOI:10.2139/ssrn.194750. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=194750. 
• Himmelstein, DU; Warren, E; Thorne, D; Woolhandler, S (2005). "Illness and injury as contributors to bankruptcy". Health affairs (Project Hope) Suppl Web Exclusives: W5–63–W5–73. DOI:10.1377/hlthaff.w5.63. PMID 15689369. 
• "The Vanishing Middle Class". In Edwards, John, ed. (2007). Ending Poverty in America: How to Restore the American Dream. The New Press. ISBN 978-1-59558-176-1. 
• Himmelstein, David U.; Warren, Elizabeth; Thorne, Deborah; Woolhandler, Steffie J. (2005). "Illness and Injury as Contributors to Bankruptcy". SSRN Electronic Journal. DOI:10.2139/ssrn.664565. 
• Himmelstein, DU; Thorne, D; Warren, E; Woolhandler, S (2009). "Medical bankruptcy in the United States, 2007: Results of a national study". The American Journal of Medicine 122 (8): 741–6. DOI:10.1016/j.amjmed.2009.04.012. PMID 19501347. 

Books

• As We Forgive Our Debtors: Bankruptcy and Consumer Credit in America. Oxford University Press. 1989. ISBN 978-0-19-505578-8.  (with Teresa A. Sullivan and Jay Westbrook)
• The Fragile Middle Class: Americans in Debt. Yale University Press. 2001. ISBN 978-0-300-09171-7.  (with Teresa A. Sullivan and Jay Westbrook)
• The Two-Income Trap: Why Middle-Class Parents are Going Broke. Basic Books. 2004. ISBN 978-0-465-09090-7.  (with Amelia Warren Tyagi)
• All Your Worth: The Ultimate Lifetime Money Plan. Simon and Schuster. 2006. ISBN 978-0-7432-6988-9.  (with Amelia Warren Tyagi)
• Casenote Legal Briefs: Commercial Law. Aspen Publishers. 2006. ISBN 978-0-7355-5827-4.  (with Lynn M. LoPucki, Daniel Keating, Ronald Mann, and Normal Goldenberg)
• The Law of Debtors and Creditors: Text, Cases, and Problems (6th ed.). Aspen Publishers. 2008. ISBN 978-0-7355-7626-1.  (with Jay Westbrook)
• Chapter 11: Reorganizing American Businesses (Essentials). Aspen Publishers. 2008. ISBN 978-0-7355-7654-4. 
• Secured Credit: A Systems Approach. Wolters Kluwer. 2008. ISBN 978-0-7355-7649-0.  (with Lynn M. LoPucki)

See also[link]

Biography portal

• Social class in the United States

Notes[link]

References[link]

External links[link]

• Elizabeth Warren U.S. Senate campaign website
• Elizabeth Warren at Harvard Law School
  • Bibliography
• Biography at WhoRunsGov.com at The Washington Post
• Biography, voting record, and interest group ratings at Project Vote Smart
• Issue positions and quotes at On the Issues
• Campaign finance reports and data at the Federal Election Commission
• Appearances on C-SPAN programs
• Appearances on Charlie Rose
• Appearances at the Internet Movie Database
• Collected news and commentary at The New York Times
• Works by or about Elizabeth Warren in libraries (WorldCat catalog)
• Elizabeth Warren collected news and commentary at Salon.com
• Financial information at OpenSecrets.org

Interviews and articles

• Generation, Gap, and interview with Elizabeth Warrn in Guernica Magazine
• Elizabeth Warren: a tough sheriff in finance's Wild West, The Daily Telegraph
• Warren Winning Means You Won't Sell It If You Can't Explain It, Bloomberg
• In fight over credit rules, she wields a plan, Boston Globe
• "The TARP Queen: Why we should all bow before Elizabeth Warren (even if you've never heard of her)". Slate. Archived from the original on April 27, 2009. http://web.archive.org/web/20090427081845/http://www.thebigmoney.com/articles/judgments/2009/04/23/elizabeth-warren-my-hero. 
• Bank Buster, Mother Jones
• The Debt Crusader: Inspired by Dr. Phil, Harvard's Elizabeth Warren has gone to D.C. to change the way America borrows, Newsweek
• Elizabeth Warren on the Economy, NOW on PBS
• Video: Elizabeth Warren, New Yorker, Nov. 16, 2009
• Interview with Yahoo! Finance, Oct. 16, 2009
• Voices of Power Video: Elizabeth Warren, Washington Post, Oct. 8, 2009
• Interview with Elizabeth Warren from Frontline
• Elizabeth Warren on NPR link to full interview for show of May 8, 2009
• UCTV programs with Elizabeth Warren
  • The Coming Collapse of the Middle Class: Higher Risks, Lower Rewards, and a Shrinking Safety Net
  • Conversations with History: Law, Politics, and the Coming Collapse of the Middle Class with Elizabeth Warren
• Warren says Consumer Financial Protection Bureau is Obama's "Strongest Financial Reform" – video report by Democracy Now!

John Stossel
John Stossel outside Fox Studios after a taping of Stossel, June 9, 2010.
Born	John F. Stossel (1947-03-06) March 6, 1947 (age 65) Chicago Heights, Illinois, U.S.
Education	B.A. in Psychology, Princeton University (1969)
Occupation	Journalist, author, columnist, reporter, TV presenter
Years active	1969–present[1]
Notable credit(s)	20/20 Stossel
Spouse	Ellen Abrams
Website
http://www.johnstossel.com/

John F. Stossel (born March 6, 1947) is an American consumer reporter, investigative journalist, author and libertarian columnist. In October 2009 Stossel left his long time home on ABC News to join the Fox Business Channel and Fox News Channel, both owned and operated by News Corp. He hosts a weekly news show on Fox Business, Stossel, which debuted on December 10, 2009. The show airs in prime time every Thursday, repeating on both Saturdays and Sundays. Stossel also regularly provides signature analysis, appearing on various Fox News shows, including weekly appearances on The O'Reilly Factor, in addition to writing the Fox News Blog, "John Stossel's Take".^[2]

Stossel practices advocacy journalism, often challenging conventional wisdom.^[3] His reporting style, which is a blend of commentary and reporting, reflects a libertarian political philosophy and his views on economics are largely supportive of the free market.^[4]

In his decades as a reporter, Stossel has received numerous honors and awards, including nineteen Emmy awards and has been honored five times for excellence in consumer reporting by the National Press Club.^[5] John Stossel is doctor honoris causa from Universidad Francisco Marroquín.^[6] Stossel has written two books recounting how his experiences in journalism shaped his socioeconomic views, Give Me a Break in 2004 and Myths, Lies, and Downright Stupidity in 2007.

Stossel began his journalism career as a researcher for KGW-TV and later became a consumer reporter at WCBS-TV in New York City, before joining ABC News as a consumer editor and reporter on Good Morning America. Stossel went on to be an ABC News correspondent, joining the weekly news magazine program 20/20, going on to become co-anchor.^[7]

ABC is reported to believe "his reporting goes against the grain of the established media and offers the network something fresh and different...[but] makes him a target of the groups he offends."^[8]

Early life[link]

John Stossel was born in Chicago Heights, Illinois, the younger of two sons,^[9] to a prominent Jewish family, and graduated from New Trier High School in Winnetka. He overcame a stuttering problem so he could become a reporter, and is now a supporter and advocate for the Stuttering Foundation of America. Stossel graduated from Princeton University with a BA in Psychology in 1969 and was a member of Princeton Tower Club while there. He began his journalism career as a researcher for KGW-TV in Portland, Oregon. Stossel later became a consumer reporter at WCBS-TV in New York City before joining ABC News in 1981 as consumer editor and reporter on Good Morning America.

Career[link]

[edit] 20/20

Stossel was named co-anchor of ABC News' 20/20 in May 2003. He joined the weekly news magazine program in 1981, initially as a correspondent. His "Give Me a Break" segments featured a skeptical look at subjects from government regulations and pop culture to censorship and unfounded fear. The series was spun off into a series of one-hour specials (which, Stossel stated in an interview with ReasonTV^[10] cost ABC half a million dollars per special), beginning in 1994, with titles including:

• "Give Me a Break" – regular segment
• You Can't Even Talk About It – 2009^[11]
• Bailouts and Bull (in association with ReasonTV) – 2009
• Age of Consent – 2009
• John Stossel's Politically Incorrect Guide to Politics – 2008
• Sex in America – 2008
• Sick in America, Whose Body Is It Anyway? – 2007
• Cheap In America – 2007
• Myths, Lies and Downright Stupidity – 2007
• Cheap in America – 2006
• Stupid in America: How We Cheat Our Kids – 2006^[12]
• Privilege in America: Who's Shutting You Out? – 2006
• War on Drugs: A War on Ourselves – 2002
• Freeloaders – 2001
• John Stossel Goes to Washington – Spring 2001
• Is America #1? – 1999
• Greed – 1999
• Common Sense – 1995
• Are We Scaring Ourselves to Death?
• Junk Science: What You Know That May Not Be So
• Boys and Girls Are Different
• You Can't Say That!
• The Power of Belief

Fox News Channel and Fox Business Network[link]

In September 2009, it was announced that Stossel was leaving ABC News and joining Fox News Channel and Fox Business Network. In addition to appearing on The O'Reilly Factor every Tuesday night, he now hosts a one-hour weekly program for Fox Business Network and a series of one-hour specials for Fox News Channel, as well as making regular guest appearances on Fox News programs.

The program, entitled Stossel, debuted December 10, 2009, on Fox Business Network. The program looks at consumer-focused topics, such as civil liberties, the business of health care, and free trade. His blog, "Stossel’s Take", is published on both FoxBusiness.com and FoxNews.com.^[13][14][15]

Publications[link]

Stossel has written three books. Give Me a Break: How I Exposed Hucksters, Cheats, and Scam Artists and Became the Scourge of the Liberal Media is a 2005 autobiography from Harper Perennial documenting his career and philosophical transition from liberalism to libertarianism. It describes his opposition to government regulation, his belief in free market and private enterprise, support for tort reform, and advocacy for shifting social services from the government to private charities. It was a New York Times bestseller for 11 weeks.^[3] Myths, Lies, and Downright Stupidity: Get Out the Shovel – Why Everything You Know Is Wrong, which was published in 2007 by Hyperion, questions the validity of various conventional wisdoms, and argues that the belief he is conservative is untrue. On April 10, 2012, Threshold Editions, an imprint of Simon & Schuster, published Stossel's third book No, They Can't: Why Government Fails-But Individuals Succeed. It argues that government policies meant to solve problems instead produce new ones, and that free individuals and the private sector perform tasks more efficiently than the government does.^[16]

With financial support from the libertarian Palmer R. Chitester Fund, Stossel and ABC News launched a series of educational materials for public schools in 1999 entitled "Stossel in the Classroom".^[17][18] It was taken over in 2006 by the Center for Independent Thought and releases a new DVD of teaching materials annually. In 2006, Stossel and ABC released Teaching Tools for Economics, a video series based on the National Council of Economics Education standards.^[19]

Charity and other work[link]

Stossel often makes public appearances and speeches, advocating his brand of libertarian thought.^[20] Stossel explained at the end of the December 30, 2010 episode of Stossel that he gives away his earnings from these engagements to charity; they contribute 25% of his income. The three main groups he supports with his donations are the The Doe Fund, the Central Park Conservancy (on whose board he sits), and Student Sponsor Partners (SSP), which partners low-income high school students with donors who mentor the students and pay tuition for the students to attend private school (usually Catholic schools), which Stossel says have higher graduation rates than public schools.^[21]

Stossel and his former ABC News colleague Chris Cuomo are silent investors in Columbus Tavern, a restaurant on Columbus Avenue at 72nd Street on Manhattan's Upper West Side.^[22][23][24]

Political and personal beliefs[link]

Contrarianism[link]

Stossel's news reports and writings attempt to debunk popular beliefs. His Myths and Lies series of 20/20 specials challenges a range of widely held beliefs. He also hosted The Power of Belief (October 6, 1998), an ABC News Special that focused on assertions of the paranormal and people's desire to believe. Another report outlined the belief that opposition to DDT is misplaced and that the ban on DDT has resulted in the deaths of millions of children,^[25] mostly in poor nations.^[26]

Libertarianism[link]

Stossel speaking at the Free State Project's New Hampshire Liberty Forum.

As a libertarian, Stossel says that he believes in both personal freedom^[27] and the free market. He frequently uses television airtime to advance these views and challenge viewers' distrust of free market capitalism and economic competition. He received an Honoris Causa Doctorate from Francisco Marroquin University, a libertarian university in Guatemala, in 2008. He told The Oregonian, on October 26, 1994:

I started out by viewing the marketplace as a cruel place, where you need intervention by government and lawyers to protect people. But after watching the regulators work, I have come to believe that markets are magical and the best protectors of the consumer. It is my job to explain the beauties of the free market.^[28]

I'm a little embarrassed about how long it took me to see the folly of most government intervention. It was probably 15 years before I really woke up to the fact that almost everything government attempts to do, it makes worse.^[29]

Stossel argues that personal greed creates an incentive to work and to innovate.^[30] He has promoted school choice as a way to improve American schools, because he believes that when people are given a choice, they will choose the better schools for their children.^[31] Referring to educational tests that rank American students lower than others he says:

The people who run the international tests told us, "the biggest predictor of student success is choice." Nations that "attach the money to the kids" and thereby allow parents to choose between different public and private schools have higher test scores. This should be no surprise; competition makes us better.^[32]

Stossel has criticized government programs as inefficient, wasteful, and harmful.^[33] He has also criticized the American legal system, opining that it provides lawyers and vexatious litigators the incentive to file frivolous lawsuits indiscriminately, which Stossel contends often generate more wealth for lawyers than deserving clients, stifle innovation and personal freedoms, and cause harm to private citizens, taxpayers, consumers and businesses.^[34] Although Stossel concedes that some lawsuits are necessary in order to provide justice to people genuinely injured by others with greater economic power,^[35] he advocates the adoption in the U.S. of the English rule as one method to reduce the more abusive or frivolous lawsuits.^[36]

Stossel opposes corporate welfare, bailouts^[37] and the war in Iraq.^[5] He also opposes legal prohibitions against pornography, marijuana, gambling, ticket scalping, prostitution, homosexual activity, and assisted suicide,^[38] and believes most abortions should be legal.^[39] He favors replacing the income tax with the FairTax.^[40]

When President Barack Obama altered federal guidelines in April 2010 governing the employment of unpaid interns under the Fair Labor Standards Act,^[41] Stossel criticized the guidelines, appearing in a police uniform during an appearance on the Fox News program America Live, commenting, "I’ve built my career on unpaid interns, and the interns told me it was great – I learned more from you than I did in college." Asked why he did not pay them if they were so valuable, he said he could not afford to.^[42]

Regarding religion, Stossel identified himself as an agnostic in the December 16, 2010 episode of Stossel, explaining that he had no belief in God, but was open to the possibility.^[43]

Praise and criticism[link]

Awards[link]

Stossel has won 19 Emmy Awards. He was honored five times for excellence in consumer reporting by the National Press Club, and has received the George Polk Award for Outstanding Local Reporting and the Peabody Award. In one year, according to Stossel in his book Give Me A Break, "I got so many Emmys, another winner thanked me in his acceptance speech 'for not having an entry in this category'".^[44] According to Stossel, when he was in favor of government intervention and skeptical of business he was deluged with awards, but in 2006 he stated, "They like me less... Once I started applying the same skepticism to government, I stopped winning awards."^[29] On April 23, 2012, Stossel was awarded the Chapman University Presidential Medal, by the current president, James Doti, and chancellor, Danielle Struppa. The award has only been presented to a handful of people over the past 150 years. ^[45]

Praise[link]

The Nobel Prize–winning Chicago School monetarist economist Milton Friedman lauded Stossel, stating: "Stossel is that rare creature, a TV commentator who understands economics, in all its subtlety."^[46] Steve Forbes, the editor of Forbes Magazine, described Stossel as riveting and "one of America’s ablest and most courageous journalists."^[46] P. J. O'Rourke, best-selling author of Eat the Rich and Parliament of Whores praised Stossel, stating:

... about John Stossel's fact-finding. He seeks the truths that destroy truisms, wields reason against all that's unreasonable, and ... puncture(s) sanctimonious idealism.... He makes the maddening mad. And Stossel’s tales of the outrageous are outrageously amusing.^[46]

An article published by the libertarian group Advocates for Self Government notes praise for Stossel.^[47] Independent Institute Research Analyst Anthony Gregory, writing on the libertarian blog, LewRockwell.com, described Stossel as a "heroic rogue... a media maverick and proponent of freedom in an otherwise statist, conformist mass media."^[48] Libertarian investment analyst Mark Skousen said Stossel is "a true libertarian hero".^[49]

Criticism and controversy[link]

Watchdog groups[link]

Liberal media organizations such as Fairness and Accuracy In Reporting (FAIR) and Media Matters for America (MMfA), have criticized Stossel's work,^[50][51] for what was perceived by those groups as a lack of balance of coverage and distortion of facts. For example, Stossel was criticized for a segment on his October 11, 1999, show during which he argued that AIDS research has received too much funding, "25 times more than on Parkinson's, which kills more people." FAIR responded that, "In fact, AIDS killed more than 16,000 people in the United States in 1999," whereas Parkinson's averaged "a death toll in the United States of less than 4,000 per year."^[52]

However, the Centers for Disease Control National Vital Statistics Reports do not support FAIR's claim. The CDC reported that HIV/AIDS killed 14,802 Americans in 1999, compared to 14,593 who succumbed to Parkinson's.^[53] The following year the order was reversed, with 14,478 dying from HIV/AIDS, and 15,682 from Parkinson's.^[54]

Accusation of conflict of interest[link]

In a February 2000 Salon.com feature on Stossel entitled "Prime-time propagandist", David Mastio wrote that Stossel has a conflict of interest in donating profits from his public speaking engagements to, among others, a non-profit called "Stossel in the Classroom" which includes material for use in schools, some of which uses material made by Stossel.^[55][56]

Galbraith and Stossel[link]

University of Texas economist James K. Galbraith has alleged that Stossel in his September 1999 special, Is America #1?, used an out of context clip of Galbraith to convey the notion that Galbraith advocated the adoption by Europe of the free market economics practiced by the United States, when in fact, Galbraith actually advocated that Europe adopt some of the United States' social benefit transfer mechanisms such as Social Security, which is the economically opposite view. Stossel denied any misrepresentation of Galbraith's views, and stated that it was not his intention to convey that Galbraith agreed with all of the special's ideas, but re-edited that portion of the program for its September 2000 repeat, in which Stossel paraphrased, "Even economists who like Europe's policies, like James Galbraith, now acknowledge America's success."^[57][58][59]

Organic vegetables[link]

A February 2000 story about organic vegetables on 20/20 included statements by Stossel that tests had shown that neither organic nor conventional produce samples contained any pesticide residue, and that organic food was more likely to be contaminated by E. coli bacteria. The Environmental Working Group objected to his report, mainly questioning his statements about bacteria, but also managed to determine that the produce had never been tested for pesticides. They communicated this to Stossel, but after the story's producer backed Stossel's recollection that the test results had been as described, the story was rebroadcast months later, uncorrected, and with a postscript in which Stossel reiterated his claim. Later, after a report in The New York Times confirmed the Environmental Working Group's claims, ABC News suspended the producer of the segment for a month and reprimanded Stossel. Stossel apologized, saying that he had thought the tests had been conducted as reported. However, he asserted that the gist of his report had been accurate.^{[60][61][62][63][64]}

Frederick K. Price[link]

In a March 2007 segment about finances and lifestyles of televangelists, 20/20 aired a clip of Rev. Frederick K. Price, a TV minister, that was originally broadcast by the Lifetime Network in 1997. Price alleged that the clip portrayed him describing his wealth in extravagant terms, when he was actually telling a parable about a rich man. ABC News twice aired a retraction and apologized for the error.^[65][66] In August 2010, a lower court's dismissal of the minister's defamation suit against ABC, Price v. Stossel, was overturned by the U.S. 9th Circuit Court of Appeals.^[67]

"Sick Sob Stories"[link]

In an opinion piece published in The Wall Street Journal in September 2007 called "Sick Sob Stories", Stossel described the case of Tracy and Julie Pierce that was explored in Michael Moore's film, Sicko.^[68] Julie Pierce criticized Stossel, saying her husband would have been saved by the Canadian health care system, and she thought Stossel should have interviewed her and her doctor before writing about them.^[69] Stossel expressed sympathy, but said she had been misled to believe the treatment was routinely available in Canada. He said that the treatment is also considered "experimental" in Canada, and is provided there even more rarely than in the U.S.^[70]

Global warming[link]

He challenges the notion that man-made global warming would have net negative consequences, pointing to assertedly warmer periods in human history.^[71] Central to his argument is the idea that groups and individuals get much more public attention, donations, and government funding when they proclaim "this will be terrible" than groups that say "this is nothing to worry about." He points to groups like the World Wildlife Fund, Greenpeace, the Environmental Defense Fund, the Natural Resources Defense Council, and to activists such as Rachel Carson and former U.S. Vice President Al Gore as examples of environmental scaremongers.^[72]

In 2001, the media watchdog organization Fairness and Accuracy in Reporting criticized Stossel's reportage of global warming in his documentary, Tampering with Nature, for using "highly selective...information" that gave "center stage to three dissenters from among the 2,000 members of the UN's Intergovernmental Panel on Climate Change, which recently released a report stating that global temperatures are rising almost twice as fast as previously thought."^[73]

In a 2006 discussion hosted by the Fraser Institute, Stossel stated that he accepts that global warming has occurred in the past century, that it has been about one degree Celsius, and that man-made emissions "may be part of the cause." Nevertheless he groups environmental groups with astrologers and psychics in his second book, Myths, Lies and Downright Stupidity. He stated that the "myths" come in with the debate about proposed solutions to reduce global warming, which he argues will not solve the problem at all and will restrict people's freedom.^[5]

David Schultz incident[link]

On December 28, 1984, during an interview for 20/20 on professional wrestling, wrestler David Schultz struck Stossel after Stossel stated that he thought professional wrestling was "fake". Stossel stated that he suffered from pain and buzzing in his ears eight weeks after the assault.^[74] Stossel sued and obtained a settlement of $425,000 from the World Wrestling Federation (WWF). In his book, Myths, Lies, and Downright Stupidity, he writes that he has come to regret doing so, having adopted the belief that lawsuits harm hundreds of innocent people.^[75][76] Schultz maintains that he attacked Stossel on orders from Vince McMahon, the head of the then-WWF.^[77]

Personal life[link]

Stossel lives in New York City with his wife, Ellen Abrams. They have two grown children.^[78]

Stossel's older brother, Thomas P. Stossel,^[9] is a hematologist at Brigham and Women's Hospital,^[79] and a professor at Harvard Medical School. He has served on the advisory boards of Merck, Biogen Idec and Dyax,^[80] as a senior fellow at the free-market Manhattan Institute,^[81] and as a trustee of the American Council on Science and Health.^[82]

Stossel's nephew is the journalist and magazine editor Scott Stossel.^[83]

See also[link]

• List of newspaper columnists

References[link]