Using Calculus to Calculate Price Elasticity of Supply

In introductory economics courses, students are taught that elasticities are calculated as ratios of percent changes. Â  Specifically, they are told that price elasticity of supply is equal to the percent change in quantity supposed divided by the percent change in price. While this is a helpful measure, it is an approximation to some degree, and it calculates what can (roughly) be thought of as an average elasticity over a range of prices and quantities. To calculate a more exact measure of elasticity at a particular point on a supply or demand curve, we need to think about infinitesimally small changes in price and, as a result, incorporate mathematical derivatives into our elasticity formulas. Â  to see how this is done, lets take a look at an example. An Example Suppose youre given the following question: Demand is Q 100 - 3C - 4C2, where Q is the amount of the good supplied, and C is the production cost of the good. What is the price elasticity of supply when our per unit cost is $2? We saw that we can calculate any elasticity by the formula: Elasticity of Z with respect to Y (dZ / dY)*(Y/Z) In the case of price elasticity of supply, we are interested in the elasticity of quantity supplied with respect to our unit cost C. Thus we can use the following equation: Price elasticity of supply (dQ / dC)*(C/Q) In order to use this equation, we must have quantity alone on the left-hand side, and the right-hand side be some function of cost. That is the case in our demand equation of Q 400 - 3C - 2C2. Thus we differentiate with respect to C and get: dQ/dC -3-4C So we substitute dQ/dC -3-4C and Q 400 - 3C - 2C2 into our price elasticity of supply equation: Price elasticity of supply (dQ / dC)*(C/Q)Price elasticity of supply (-3-4C)*(C/(400 - 3C - 2C2)) Were interested in finding what the price elasticity of supply is at C 2, so we substitute these into our price elasticity of supply equation: Price elasticity of supply (-3-4C)*(C/(100 - 3C - 2C2))Price elasticity of supply (-3-8)*(2/(100 - 6 - 8))Price elasticity of supply (-11)*(2/(100 - 6 - 8))Price elasticity of supply (-11)*(2/86)Price elasticity of supply -0.256 Thus our price elasticity of supply is -0.256. Since it is less than 1 in absolute terms, we say that goods are substitutes. Other Price Elasticity Equations Using Calculus To Calculate Price Elasticity of DemandUsing Calculus To Calculate Income Elasticity of DemandUsing Calculus To Calculate Cross-Price Elasticity of Demand

Understanding How Hitler Became the Man He was Essay examples

What comes to mind when people hear the name Adolf Hitler? For some may not have heard of him but others have heard much about him depicting on the fact that someone could have learned about him in a class or even on their own. Most would think about the dictator of Germany who killed millions of people as the image of his notorious mustache pops into ones head. But what if some were to know that he wasn’t always the man everyone saw in 1933. Adolf Hitler may have been the most charismatic and decisive leader Germany has ever seen but also one of the most vile. How did he come to be this way? He surely wasn’t born like that was he? To understand how Hitler became the man he was, one has to start from the beginning and even before he†¦show more content†¦He then decided to leave his mother to study in Vienna. Then in 1908 he applied for the Vienna Academy of Fine Arts but was rejected . While there his mother was home suffering from breast cancer and died a few months later. There is Vienna he became roommates with his friend from Linz, August Kubizek. Kubizek described Hitler by having an unstable personality and a temper. Hitler was prone to sudden bursts of inspiration but never finished anything he started. In Vienna he suffered bouts of depression and sometimes experienced extreme highs. Soon at age 21 Hitler began to become interested in politics which would help play out his soon to be career (Hitler, Adolf). In May 1913, Hiter moved to Munich Germany which he became an advocate for the upcoming war. Hitler wasn’t worried about making a living in Munich because of his faith in the war arising, but Hitler was right. On August 1, 1914 a huge crowd including Hitler gathered in a big public plaza in Munich to celebrate the german proclamation for war. Hearing the news Hitler thanked heaven for him to be alive for the Great War. Two days later, Hitler volunteered for the German Army. Hitler found the trenches of the battlefield to be his new home. 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TO ENSURE YOU MEET THE ASSESSMENT CRITERIA, YOU WILL NEED TO: KNOWLEDGE AND UNDERSTANDING In a brief introduction, explain how German society throughout 1920-1945 was shaped byRead MoreHitler s First World War I Essay1211 Words   |  5 Pages Hitler got his first feel for war in World War 1. He was a runner during the war and was wounded during it. During 1919, there was a meeting for the German Workers’ Party (DAP) in Munich that Hitler went to observe. Hitler had many ties with the Thule Society, which was organized around racial philosophy and a belief in military action. The Thule Society were also strong supporters of Hitler’s idea of a national socialist movement. 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Juvenile Offenders Essay Example For Students

Juvenile Offenders Essay Juvinile Should Juveniles be waived to adult court Philosophy 14 Nov 98 Should juveniles be waived to adult court. There has been tension between teens (pre-teens) and adults for thousands of years, and the question how to deal with the youth of a culture, in a punishment sense, has been with us for just as long. Socrates, for example, stated that children show little respect for there elders. Since Socrates time largely due to the spread of guns and drugs, younger and younger children are committing violent crimes. Children that have special needs or have committed a criminal act have been subject to state protection since, 1838. The first juvenile court was established in Chicago in 1890. The assumption, that was made at that time, was that the criminal justice system should work to help youngsters, not to humiliate or punish them. Along with the creation of the juvenile justice system went the creation of status offenses, these are offenses that if committed by an adult, would not be considered an offense. In the 1950s and 60s many laws were passed to protect the rights of children, in a court of law. The major decisions of this time were: Kent v. United States, In re Gault, and In re Winship. Since the time that these laws were enacted, the number of juveniles committing violent offenses has risen dramatically. There are two distinct schools of thought in this argument: side A believes that a persons age should not prevent that person from feeling the full effect of the adult court system, while side B feels that you simply cannot apply the same rules to juvenile offenders that you do to adults. I will first present side As case then Bs and finally end with my own opinion. Many states have begun enacting new laws about the transfer of juveniles, that are more harsh on juveniles. Minnesota, for example, has a new law that states a 16 or 17 year old person that has been charged with a violent offense has to prove to court why they should be tried in the juven ile system. In cases where the offender is younger than 16 the prosecutor must show why the juvenile should be waived. One of main issues of side A, is that if the offender is too old the sentence would not be severe enough for the crime that had been committed. Another issue is the overcrowding of the juvenile justice system. Many of the offenders in the juvenile system, if a few years older, would have already been sentenced to life sentences in an adult court. Side A does not believe that a persons age should be the lone determining factor for non-waiver. While side A does believe that there are a great many negative influences on todays youth, they believe that these circumstances do not dismiss that crimes that have been committed. The core belief that most of the side A advocates share is, the belief that the small percentage of the juveniles that are committing the serious crimes are past the point where a juvenile court could be of any help. Side A truly feels that by allowi ng serious juvenile offenders to be waived to adult court, thus receiving a stiffer sentence, the community, as a hole, will be much better served. Side B believes, essentially, that no child (juvenile) should be waived. Side B sees several key factors for the rise in juvenile crime. These reasons are ones that are out of the control of the juvenile. The key factors are: (a) Unemployment among teens was 19 percent in 1993, up from 15.3 percent five years earlier, and for black youths the unemployment rates were twice that. (b) Since 1970, Aid to families with dependent children benefits have declined an average of 45 percent in inflation-adjusted dollars, according to the Childrens Defense Fund. (c) In 1992, there were 14.6 million children living below the poverty line, the Childrens Defense Fund says, about 5 million more than in 1973. (d) In 1993, there were 3 million victims of child abuse, according to the National Committee for the Prevention of Child Abuse- a rate 50 percent higher than in 1985. Studies also indicate that the majority of prison inmates were abused as children. (e) Teen suicide rates increased nearly 20 percent during the 1980s. Side B also reminds us that the percentage of kids arrested has remained fairly constant during the past 10 to 15 years. The charges that juveniles that are sent to adult facilities (even if protected from the population) are harassed and even raped at an alarming rate. There is also evidence that when a juvenile is waived, there is very little effort put forth to try and rehabilitate the offender. With my major being Criminal Justice Administration, I have done more than a little research on this subject. I feel that it is very important, to the society, to feel that the juveniles are being punished for their crimes, however, I believe that their rehabilitation is even more important. I believe that, up until the age of 18, every effort should be made to try an steer the juvenile in the right direction. If all t hat we do, as a society, is continue to punish the juveniles, and do nothing to address the root causes of the behavior then we will never see an improvement in the statistics. I feel that we need to realize that we should not throw a child away because a mistake in judgment, made as a child. We should never forget that however we choose to treat our nations children, we are shaping, in them, the future of our country. 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The Sixties Essays - Counterculture Of The 1960s, Hippie

The Sixties The Sixties split the skies. Only Civil and two world wars so neatly divided our history into a Before and After. And the Sixties were more divisive than World War II, which drew more people for the war effort. The Sixties drove people apart ? husbands from wives, children from parents, students from teachers, citizens from their government. Authority was strengthened by World War II. It was challenged by the sixties. Relatively few Americans in 1960 would have predicted that the decade ahead was to be among the most turbulent of the century. Despite the growing restiveness of the nation's African American population, and despite undercurrents of protest and discontent from many other groups, most Americans faced the future with optimism. The civil rights movement spawned social activism. Among the many effects of the civil rights movement as it gained momentum in the early 1960s was its impact on Greensboro sit-ins in 1960, accelerating with the 1961 Freedom Rides, and with the Mississippi Summer project. These movements opened up some eyes to Americans so they could see what was going on in the country at this time. Most of the things that went on in the sixties dealt with the War. The Cold war in which included the Korean War, but mostly dealt with our little rivalry the Soviet Union. There was a lot of division between people because of the War. Many people couldn't handle the thought of War. They were just scared that they had to be in a country that was involve in the War. Others thought that it was the perfect time to start their own groups. Some were Ethnic groups in which gained more power. Though much of American history, most of the nation's dominant institutions had been controlled by middle-class, Protest ant, white males. Nonetheless, throughout those same years, American society was extraordinarily diverse. It included may groups whose political economic, and social outlook was very different from those of the controlling white male population. African American, Native Americans, Hispanic Americans, and members of other ethnic groups were largely excluded from the mainstream of American life. Women lived within sharply defined boundaries. People in the South and the West had different interests from those in the Northeast. The Existence of racial, ethnic, and religious diversity had been the source of many conflicts and adjustments for more than three centuries. In the 1960's, perhaps more than at any other moment in American history, that diversity erupted and helped redefine the nation's life. African Americans, students and women all raised challenges to traditional practices and institutions. So did other groups who felt excluded from the centers of American life. The Counterculture rejected traditional standards and styles. The rise of political radicalism on college campuses occurred alongside an even larger change in the character of American youth: the emergence of what became known as the counterculture. Among the conspicuous features of this was a general contempt among young people for traditional standards. Youths displayed that contempt by wearing long hair, shabby or outrageous clothing, using unconventional speech, and acting in conventional standards of behavior. They also were attracted to drugs, particularly to weed(marijuana) and hallucinogens. In addition, they adopted a new and more permissive view of sexual behavior. Rock music was an increasingly important part of the counterculture. Lying behind these open challenges to traditional lifestyles were the outlines of a philosophy. Like members of the student left (with which it in many ways over lapped, the counterculture challenged the nature of modern American society for its hollowness and artificiality. It called for a more ?natural? world in which men and women would live in closer harmony nature and would have greater freedom to vent their instincts and emotions. This was, in the end, a search for personal fulfillment. Popular phrases of the 1960's expressed something of it s character. ?Do your own thing? or ?if it feels good, do it.? So did the communities created by the so-called hippies. Adherents of the counterculture who attempted to withdraw from the conventional world and the live among people who shared their beliefs. Such communities emerged in the Haight-Ashbury neighborhood of San Francisco and then spread to other large cities. The