37 Top Scholarships for High School Sophomores and Freshmen

37 Top Scholarships for High School Sophomores and Freshmen SAT/ACT Prep Online Guides and Tips It's never too soon to fire setting aside up cash for your advanced degree. Regardless of whether you are just in your first or second year of secondary school, there are a lot of chances to begin getting cash that will pay for your educational cost, books, charges, and everyday costs a few years down the line. You may be shocked to discover that there are actuallyhundreds of grants accessible to underclassmen.If you're simply beginning your chase, utilize this rundown of the 37 best grants for secondary school first year recruits and sophomores to begin. This rundown incorporates an assortment of scholarshipsforfreshmen and sophomores. I've separated them into the accompanying classes: Article Scholarships Exceptional Interest Scholarships Inventive Scholarships Interest and Activity-Based Scholarships Area based Scholarships Simple Scholarships These grants arenot restricted to one school or university,so understudies who win these honors will have the option to utilize them for an assortment of schools. Step by step instructions to Use This List of Scholarships for Sophomores and Freshmen Before we go over the grants you can apply for, how about we rapidly audit the most ideal ways you can utilize this rundown of grants for sophomores and first year recruits. Rule 1: Play to Your Strengths Begin by taking a gander at the various classifications beneath. Is it true that you are inventive? At that point consider applyingto a portion of the grants that require work of art or a film for their applications. In case you're a solid author, then again, consider applying to grants that require articles. Rule 2: Apply to Many Scholarships The magnificence of beginning your grant chase early is that you have a great deal oftime! So use it astutely to apply to however many grants as could reasonably be expected. We prescribe applying to anyplace somewhere in the range of five and 30 scholarships.Most grants on this rundown and past are serious, which means numerous understudies will apply for them. You'll build your odds of winning cash on the off chance that you don't tie up of your assets in one place! Rule 3: Pay Attention to Details Ensure you read all the guidelines cautiously before you apply for a grant, and be sure that your articles and other application materials address what is being inquired. It's an exercise in futility to apply to grants in case you're going to wind up excluded basically on the grounds that you neglected to adhere to the directions. Also, ensure tostay on significant cutoff times. You would prefer not to pass up an extraordinary grant since you inadvertently missed adue date! Rule 4: Do Your Own Research Remember that this rundown is only a beginning stage. There are a lot more grants accessible to more youthful understudies, and there may be some that are progressively fit to your abilities and interests. Try not to be hesitant to dosome Google searches to see whether there are any grants out there that compare to one of your one of a kind characteristics. Keep in mind, the more dark a grant is,the better your opportunity of winning it will be! Article Scholarships To begin, how about we investigate grants that expect understudies to compose and submit articles as a major aspect of their applications. Oklahoma City National Memorial Museum Student Essay Contest The Oklahoma City National Museum has an exposition challenge for understudies in grades 5-12. Points rotate around thoughts identified with the Oklahoma bombings in 1995. Understudies ingrades 9 and 10 can submit 500-word articles. Prizes: first spot: $200 second spot: $150 third spot: $100 Ayn Rand Essay Contest Secondary school first year recruits and sophomores can compose an article on one of a few points identified with the bookAnthem by Ayn Rand. The cutoff time to apply is April 25, 2019. Prizes: first spot: $2,000 (one champ) second spot: $250 (three champs) third spot: $100 (five champs) Finalists: $25 (50 champs) NRA Civil Rights Defense Fund Essay Contest To participate in this challenge, secondary school understudies must compose a 1,000-word paper responding to the inquiry, What does the subsequent revision intended to you? The cutoff time is December 31, 2018. Prizes: first spot: $1,000 second spot: $600 third spot: $200 fourth spot: $100 Armada Reserve Association Essay Contest Understudies in grades 7-12 can participate in this paper challenge by presenting an article of close to 350 words on What Freedom of Speech Means to Me.The cutoff time is December 1, 2018. Prizes: Stupendous national prize: $5,000 1stplace: $2,500 2ndplace: $1,500 3rdplace: $1,000 Unigo $10K Scholarship Understudies 13 or more seasoned can apply for an opportunity to win one thousand prize of $10,000. Your application must incorporate a 250-word reaction to the brief: Envision a verifiable figure is breathed life into back. Who right? What's their preferred versatile app?The cutoff time is December 31, 2018. Gen and Kelly Tanabe Scholarship Secondary school studentscan present a 250-word exposition on a subject of their decision for the opportunity to be gone into an opposition to win a $1,000 prize. There are two challenges for every year. The fall challenge cutoff time is December 31, 2018, and the spring challenge cutoff time is July31, 2019. Youthful Patriots Essay Contest All US secondary school understudies can apply to win. They should present an article of close to 1,500 words on a theme identified with recent developments and additionally open approach. Prizes: 1stplace: $5,000 2ndplace: $2,500 3rdplace: $1,500 Profile in Courage Essay Contest Understudies in grades 9-12 can present a 700-to 1,000-word exposition around a demonstration of political fearlessness by a US chose official who served during or following 1917, the year John F. Kennedy was conceived. Essays must have at any rate five sources.The cutoff time during the current year's challenge is January 18, 2019. Prizes: 1stplace: $10,000 2ndplace: $3,000 Finalists: $1,000 (five champs) Semifinalists: $100 (eight champs) We the Students Essay Contest US understudies selected evaluations 8-12 can apply to this grant to win one of 15awards running from $500 to $5,000.You must finish the online application and present a paper of close to 800 words on the point refered to on the site. The cutoff time is February 14, 2019. Prizes: 1stplace: $5,000 Other participants: $1,250 (six champs) Decent Mention: $500 (eight champs) Positive thinker International Essay Contest US understudies younger than 19 can present an article on the subject When All the World’s Problems are Solved, is Optimism Still Necessary? Club victors advance to the District challenge to vie for a $2,500 grant. The cutoff time for accommodation is February 28, 2019. Visionary Scholarship Program Any right now selected US secondary school understudy can apply to get a prize from $1,000 to $5,000. Candidates must present a finished application, a duplicate of their latest (informal) secondary school transcript, and a 500-word paper on Why College is Important to Me. The cutoff time during the current year's challenge is May 1, 2019. Unique Interest Scholarships These next grants require a unique activity with respect to the candidate, from electing to playing an internet game. Humankind Rising Service Challenge Secondary school understudies who volunteer for a non-benefit that meets Humanity Rising’s measures may apply for this grant by sharing their administration story. You should make a record so as to get to the grant subtleties and apply for the challenge.Awards run from $500 to more than $2,000, and all cutoff times are rolling. HR Block Budget Challenge US understudies in grades 9-12can apply to win one of 10 $20,000 grants. Understudies must play a web based game that recreates grown-up life as far as monetary proficiency. While understudies can't enlist themselves, educators may enlist classes just as individual understudies. Inventive Scholarships Is it true that you are the imaginative kind? This next arrangement of grants for rookies and sophomores is about imaginative capacity and inventiveness. For these challenges, you'll have to present a bit of workmanship, regardless of whether that is a story, painting, video, photo, and so forth. Make Real Impact Contest Any understudy between the ages of 14 and 22 can submit either a bit of composing (100-600 words), a video, a work of art,or a bit of music they've made on the point out of how to address crazy driving. Deciding on passages starts October 2, 2018. Prizes: Fantastic prize: $1,500 (four victors, one for each class) Top Schools prize: $1,000 (three champs) Top Online Vote Getter prize: $500 (four champs, one for every class) Spanish Category Award: $1,500 (one champ) Sports Team Award: $1,500 (one champ) TeenDrive365 Video Challenge All US secondary school understudies in any event 13 years old canenter this challenge by making a one of a kind 30-to 60-second video that features more secure adolescent driving. The video must end withthe TeenDrive365 Video Challenge Call to Action slide, which you can download from the TeenDrive365 site. The accommodation cutoff time is in February 2019. Prizes: 1stplace: $15,000 2ndplace: $10,000 3rdplace: $7,500 Individuals' Choice: $5,000 fourth tenth spot: $2,500 Territorial prizes: $1,000 (four champs) Doodle 4 Google Understudies from kindergarten to 12thgrade can apply for this grant. Candidates must present a Google Doodle identified with the current year's subject. All entries are partitioned and decided by age gathering. The cutoff time is in March 2019. Prizes: National Winner: $30,000 (in addition to a $50,000 innovation grant for the champ's school) National Finalists: $5,000 (four champs, one for every age gathering) Educational Art Writing Award Understudies ingrades 7-12with an unmistakable fascination for composing or workmanship may apply to win a Best-in-Grade Award. Understudies in twelfth grade just can likewise apply to win a Portfolio Award. Cutoff times shift by district. Prizes: Portfolio Awardâ€Gold Medal: $10,000 (16 champs) Portfolio Awardâ€Silver Medal: $1,000 (30 champs) Best-in-Grade Award: $500 (24 champs, four for each evaluation level) AutoPetsâ„ ¢ Out-of-the-Box Thinking Scholarship All current secondary school understudies can ap

Evolution Term Paper Example | Topics and Well Written Essays - 1250 words

Advancement - Term Paper Example In addition, such clarification (Mayr, 2002) of the advancement has underlined essentially the God, principal and last reason for appearances of first life form in this world that is the cell. From this reason, there has been development including a huge number of years that empowered the single cell to advance and change into a warm blooded creature, or all the more explicitly, the people. In such manner, the mystical understanding of development has been a truthful clarification of the human advancement while including the job of extraordinary elements as God that started everything. Then again, there exists the hypothesis of advancement by Darwin (Larson, 2004) that has been the most well known name around there of study, and has been effective in affecting and persuading countless world populaces. Particularly researchers that follow Darwin on account of human development, and concur that all animals in this world have come subsequent to advancing from life forms of one cell, and a huge number of years transformed them into different celled life forms. Another clarification of the human development exists in the story that calls attention to the area of East Africa, a vigorously forested locale that was a home for primate occupants of differing sorts roughly ten million years prior. In any case, following 5,000,000 years, the district started to encounter radical climatic adjustments that modified from wet to progressively dry and infertile conditions, and in this manner, the forested locale changed from wet wilderness to a destroyed land. Such adjustment slanted the primates to change their territory from tree to the land that united the most monstrous powers of pirates on the land zone of the globe. Such stories at that point associate the various assortments of wild creatures found in African timberlands nowadays. Also, such change from tree abiding to ground-occupants gave the chance of people to

International Trade Payment Method with Special Reference Essay Example

Universal Trade Payment Method with Special Reference Essay To prevail in today’s worldwide commercial center and win deals against outside contenders, exporters must offer their clients appealing deals terms upheld by suitable installment techniques. Since getting forked over the required funds and on time is a definitive objective for each fare deal, a fitting installment strategy must be picked cautiously to limit the installment chance while additionally pleasing the necessities of the purchaser. This pattern is owing to the expanded globalization of the world economies and the accessibility of exchange installment and money from the universal financial network. As appeared in figure 1. 1, there are four essential techniques for installment for worldwide exchanges. During or before contract dealings, we ought to consider which technique in the figure is commonly attractive for both me and my client. Figure 1. 1. Installment Risk Diagram Key Points †¢ To prevail in today’s worldwide commercial center and win deals against International exchange presents a range of hazard, which causes vulnerability over the planning of installments between the exporter (dealer) and shipper (remote purchaser). †¢ For exporters, any deal is a blessing until installment is gotten. Along these lines, exporters need to get installment as quickly as time permits, ideally when a request is put or before the merchandise are sent to the shipper. †¢ For merchants, any installment is a gift until the merchandise are gotten. †¢ Therefore, merchants need to get the products as quickly as time permits however to defer installment as far as might be feasible, ideally until after the merchandise are exchanged to create enough pay to pay the exporter. Target of the examination: The goals of the investigation are: 1. Talk about hypothetical parts of universal exchange installment and money. 2. Talk about Bangladesh parts of global exchange installment and account. We will compose a custom article test on International Trade Payment Method with Special Reference explicitly for you for just $16.38 $13.9/page Request now We will compose a custom paper test on International Trade Payment Method with Special Reference explicitly for you FOR ONLY $16.38 $13.9/page Recruit Writer We will compose a custom paper test on International Trade Payment Method with Special Reference explicitly for you FOR ONLY $16.38 $13.9/page Recruit Writer Hypothetical Aspects: There are four norm and regular installment techniques that are being used to make or get installment for global exchange showcase. It fundamentally implies got of installment against fare and making installment against import: 1. Money in Advance. 2. Open Account/Supplier credit. 3. Narrative assortment. 4. Narrative Credit/Letters of Credit L/C. Money in-Advance: From the very title clearly money will be ahead of time. With money ahead of time installment terms, the exporter can maintain a strategic distance from credit chance since installment is gotten before the responsibility for merchandise is moved. Wire moves and charge cards are the most regularly utilized money ahead of time choices accessible to exporters. Be that as it may, requiring installment ahead of time is the least appealing choice for the purchaser, since it makes income issues. Remote purchasers are additionally worried that the merchandise may not be sent if installment is made ahead of time. Consequently, exporters who demand this installment technique as their sole way of working together may lose to contenders who offer increasingly appealing installment terms. There are a few highlights of Cash ahead of time * Interest of exporter is completely secured. Enthusiasm of shipper isn't ensured. * Banks are engaged with the way toward moving installments. * Documents are shipment are straightforwardly handle by the exporters. * It is guided by Purchase and Sale Agreement. * It is one of the least expensive and least well known techniques on the planet. Open Account: An open record exchange is where the merchandise a re transported and conveyed before installment is expected, which is for the most part in 30 to 90 days. Clearly, this alternative is the most beneficial choice to the merchant as far as income and cost, yet it is thus the most elevated hazard choice for an exporter. In view of extreme rivalry in trade markets, outside purchasers frequently press exporters for open record terms since the augmentation of credit by the dealer to the purchaser is increasingly regular abroad. In this way, exporters who are hesitant to broaden credit may lose a deal to their rivals. In any case, the exporter can offer serious open record terms while considerably relieving the danger of non-installment by utilizing of at least one of the proper exchange fund procedures, for example, trade credit protection. There are a few highlights of Open record * Interest of shipper is completely ensured * Interest of exporter isn't secured. Banks are engaged with the way toward moving installments. * Documents are shipment are legitimately handle by the exporters * It is the most famous technique on the planet. Narrative Collections: A narrative assortment (D/C) is an exchange whereby the exporter endows the assortment of an installment to the dispatching bank (is the bank on the counter of which archives are put together by exporter, gather installment from merchant for its benefit), which sends reports to a gathering bank (is the bank that is engaged with the procedure of narrative assortment other than the transmitting bank), alongside directions for installment. Assets are gotten from the merchant and transmitted to the exporter through the banks engaged with the assortment in return for those reports. D/Cs include utilizing a draft that requires the shipper to pay the face sum either at sight (archive against installment) or on a predefined date (report against acknowledgment). The draft gives guidelines that indicate the archives required for the exchange of title to the merchandise. In spite of the fact that banks do go about as facilitators for their customers, D/Cs offer no confirmation procedure and restricted plan of action in case of non-installment. Drafts are commonly more affordable than LCs. There are two techniques for narrative assortment: * Documents against installment * Documents against acceptanc Documents Against Payment (D/P) For this situation records are discharged to the shipper just when the installment has been finished. This is in some cases likewise referredâ as Cash against Documents/Cash on Delivery. In actuality D/P implies payable at sight (on request). The gathering bank hands over The transportation archives including the report of title (bill of filling) just when the merchant has covered the tab. The drawee is generally expected to pay inside 3 working long stretches of introduction. Archives Against Acceptance (D/A) For this situation records are discharged to the merchant just against acknowledgment of a draft. Under Documents Against Acceptance, the Exporter permits credit to Importer, the time of acknowledge is alluded to as Usance, The shipper is required to acknowledge the bill to make a marked guarantee to cover the tab at a set date later on. At the point when he has marked the bill in acknowledgment, he can take the records and clear his products. Figure 1. 2. Procedure of narrative Collection The accompanying rundown of records frequently utilized in global exchange: †¢ Air Waybill Bill of Lading †¢ Certificate of Origin †¢ Combined Transport Document †¢ Draft or Bill of Exchange †¢ Insurance Policy (or Certificate) †¢ Inspection Certificate Air waybill: The Air Waybill (AWB) is the most significant archive given by a bearer either legitimately or through its approved specialist. It is a non-debatable vehicle record. It cov ers transport of load from air terminal to air terminal. Bill of Lading: A bill of replenishing is produced by a shipper, subtleties aâ shipmentâ ofâ merchandise, givesâ titleâ to the products, and requires the bearer to convey the product to the proper party. Testament of Origin: The Certificate of Origin is required by the custom authority of the bringing in nation to force import obligation. It is typically given by the Chamber of Commerce and contains data like seal of the chamber, subtleties of the great to be moved, etc. Consolidated Transport Document: Combined transportâ is a structure ofâ intermodal transport, which is the development of merchandise in very much the same stacking unit or street vehicle, utilizing progressively at least two methods of transport without dealing with the products themselves in evolving modes. Joined vehicle isâ intermodal transport where the significant piece of the excursion is by rail,â inland waterwaysâ orâ sea, and any underlying as well as definite legs completed by street are as short as conceivable Draft or Bill of Exchange: A Bill of Exchange is an extraordinary sort of composed record under which an exporter solicit merchant a specific sum from cash in future and the shipper additionally consents to pay the shipper that measure of cash at the latest the future date. Protection arrangement: Also known as Insurance Policy, it ensures that products shipped have been guaranteed under an open strategy and isn't significant with little insights regarding the hazard secured. Investigation Certificate: Certificate of Inspection is a record arranged on the solicitation of dealer when he needs the transfer to be checked by an outsider at the port of shipment before the products are fixed for conclusive transportation. There are a few highlights of Documentary Collection * Interest of merchant hazard ensured. * Interest of exporter is preferred ensured over open record * It is guided by Purchase Sale Agreement and URC 522 * It could be unsafe for the exporter if reports are not gotten by the merchant * All the banks associated with narrative assortment are the operators of exporter. Narrative Credit or Letters of Credit: Letters of credit (LCs) are one of the most secure instruments accessible to worldwide dealers. A LC is a responsibility by a bank for the purchaser that installment will be made to the exporter, gave that the terms and conditions expressed in the LC have been met, as confirmed through the introduction of all require

The Accomplishments of George Washington - Free Essay Example

George was born on February 22, 1732 in Virginia. Growing up he worked on his fathers farm which taught him responsibility at a young age. He was no good at spelling but he was very good at math. At age 11, his father died a sudden death and George took over his fathers farm. George was a fair, kind, and responsible man. The most important thing he did was fight for the country of America. In 1749, at the age of 17, George became surveyor (a person who investigates or examines something, especially boats of seaworthiness) of Culpepper County, Virginia. He was very good at doing this job. Being good in math helped him succeed doing this type of work. With the money he made George bought land for himself. In 1775, George was made Commander of the Virginia Militia (a volunteer army). Earlier that year George was sent on a dangerous mission which started the French and Indian War. The English Major General Braddock led his army to fight. He was soon killed and left behind some members of his army members. George led Braddocks surviving army members back to their homes. George learned from this that a truly great leader must always learn or die. In January 1776, America got its first flag. It had 13 red and white stripes, which stood for the thirteen colonies. On July 4, 1776 the colonies became a country when the Continental Congress signed the Declaration of Independence. The Declaration stated that America was no longer a group of colonies under English rule, but one nation free to rule itself. On April 6, 1789, George was unanimously elected to be the first president of the United States. Parades, parties, and cheering crowds of people broke out, as he traveled from Mount Vernon to New York.Everyone saluted George as president and celebrated with fireworks and bonfires. In 1792, George again was unanimously elected president. George tried to be a fair president and stated that the president of the United States should only serve the country for two terms (8 years) and someone else should take over. George Washington accomplished so much during the course of his life up until he died on December 14, 1799. George Washington fought for the country of America and the American people. George is also the reason why the country of America has independence.

The American Revolution - 1371 Words

The American Revolution was revolutionary by definition because it was successful in bringing about political, economic, and social reform. The colonies fought to be free of the British monarchy and replace it with self-government and with representatives elected by the citizens to govern to the will of the people. This was a radical change in the political stage where the people were ruled by a distant king that had no interest in the welfare of the colonies beyond its enrichment to the crown. The colonies gained an economic benefit from their detachment from England as well. All of the revenue created by the colonies was now their own. The trade restrictions created by the idea of mercantilism were no longer in place. All of the raw materials and natural resources that the colonies supplied England with such as indigo, cotton, tobacco, and rice were now owned by the colonies solely. The new political structure also brought about major changes to the social norms. People of all classes had a role in their own government. The differences between the social classes became a little less prominent since all had a say in the government. The colonies’ revolt from England politicized women and African Americans and even though the major changes for these classes came later in history it is important to recognize that the Revolution was the beginning of these changes. The new government, through the powerful new constitution, opened the door for individual roles to continueShow MoreRelatedThe American Revolution : The Revolution1367 Words   |  6 PagesThe American Revolution Revolutionizes the World It was the first revolution to majorly succeed and change how people saw their countries, it was the American Revolution. The American Revolution was the first successful revolution against a European empire that provided a model for many other colonial peoples who realized that they too could break away and become self-governing nations (New world Encyclopedia, 1).The American Revolution was vital to history because ideas seen by other countries startedRead MoreThe Revolution Of The American Revolution999 Words   |  4 PagesBetween 1770 and 1776, resistance to imperial change turned into a full-on revolution. The American Revolution, also known as the Revolutionary War, was a time of revolting and political uprising, in which the 13 colonies separated from the British Empire, forming the independent nation known as the United States of America. Though the American Revolution began because the colonies wanted independence from Britain, many important historical events and revolts also lead to the tensions and resistanceRead MoreThe Revolution Of The American Revolution1362 Words   |  6 PagesEvery 4th of July, Americans are told the story of the American Revolution. We remember the oppressed colonists fighting against the tyrannical King George III and the formidable red coats. Patriotic heroes are remembered, evil kings are cursed, and the liberties and freedoms won from the war are celebrated. Though America often likes to look back to the revolution, the question of just how much a revolution was the American Revolution is rarely asked. While the American revolution was not as radicalRead MoreThe Revolution Of The American Revolution863 Words   |  4 PagesThere are many different views on how the American Revolution came to be and how it actually was. One way is that the colonists that had money and were known as the elite were trying to preserve their power from the British and this is what caused the revolutionary war. Then on the other hand bef ore the revolutionary war occurred when the colonists were being over controlled by the British, then in result of the American Revolution the colonists were able to win against the British and become strongerRead MoreThe Revolution Of The American Revolution1582 Words   |  7 Pagesâ€Å"The revolution was effected before the war commenced. The revolution was in the minds and hearts of the people.† - John Adams, 1818 This quote means that the revolution actually took place metaphorically before the actually fighting began. It took place in the emotions and thoughts of the Americans. The Road to Revolution After the Seven Years’ War created a financial problem for Britain The British tried to shoulder some of the financial responsibilities onto the Americas in the form of variousRead MoreThe Revolution Of The American Revolution850 Words   |  4 PagesIn regards to the American Revolution, the point that armed rebellion became inevitable arrived when after nearly five constant years of American colonist protesting. American s had enough and needed to take a stand for the numerous inequalities they were forced to deal with. It was foreseeable that the American Revolution took place due to the unfair taxes that the British were giving Americans. Also, England was not allowing Americans their freedom, along with violence and the political dominanceRead MoreThe American Revolution. The American Revolution Started1581 Words   |  7 PagesThe American Revolution The American Revolution started when King George the 3rd decided to make the American Colonies pay a large amount of money for the debt of the French and Indian War by giving the colonist different types of taxes like the Sugar Act in 1764. The sugar Act of 1764 was a British Law that was passed on April 5, 1764, that collected incomes from the 13 colonies. The act put a huge tax on the sugar and molasses that were imported into the colonies which were a huge impact for theRead MoreThe American Revolution1337 Words   |  6 PagesThe American Revolution was much more than an insurrection against British tariffs and patronage decree. Rather, it was a bureaucratic catastrophe in which colonists from the thirteen American colonies denied the British sovereignty, eradicated the jurisdiction of Great Britain and established the United States of America. The upheaval was a primitive modern revolution in which generality traversed for liberty in the statute of law, constitutional privilege and supremacy. Ensuing years of contentionRead MoreThe American Revolution889 Words   |  4 PagesThe American Revolution was one of the most vital events in American History lasting form 1775 to 1783, it effected the nation socially, economically and politically. The American Revolution brought upon many changes in America, and freedom of the nation. The Revolutionary War was a stepping stone to what we are as a nation today, it created both short and long-term effects on the world. When wanting to blame a certain side, the British politicians or the American agitators, several key points leadRead MoreThe American Revolution993 Words   |  4 PagesThe topic of the American Revolution is a topic that has been discussed on multiple levels and is extremely well-known, especially within the United States. The details are a little on the generic and basic side but it is at least understood on some level. Most people are aware of the American standpoint, the what, why, how, and when , but there is much more depth to what occurred. The war was obviously between the Americas and the Mother country of Britain, but there were more than just those two

Analysis Of The Sermon On The Mount And The Allegory...

Human Knowledge During the first few weeks of class we’ve gone through various texts in order to better our understanding of human knowledge. We have talked about Christianity St. Matthew â€Å"The Sermon on the Mount†, Plato and â€Å"The Allegory of the Cave†, â€Å"The Four Idols† of Sir Francis Bacon, Robert Frost’s â€Å"Mending Wall†, and even Carl Jung and â€Å"The Structure of the Psyche†. All these texts may have been written in different eras and different places, but they have one thing in common, and that is their understandings of human nature and knowledge, and how they demonstrate to us epistemology (how we know) and metaphysics (what human beings know). To begin with, we have Christianity of St. Matthew â€Å"The Sermon on the Mount†. After that, we have Plato and the Allegory of the Cave. In this text Plato distinguishes between people who mistake sensory knowledge for the truth and people who really do see the truth. The story begins in the cave where there are three prisoners, those three prisoners have never seen life outside the cave and have stayed in the cave since their birth day. Outside the cave people carry animals, plants, and etc. The only thing the people inside the cave see are the shadows, not the real object itself. Plato along with the prisoners guess the objects they will see next. Then, one of prisoners escapes from their bindings and leaves the cave. When he is out he is very surprised to what is outside the cave and then realizes that his former view of realityShow MoreRelatedPlato s Allegory Of The Cave And The Gospel Of Matthew s Sermon On The Mount1757 Words   |  8 PagesTwo distinct texts that may seem at odds when superficially compared, hinge on shared foundational values. Course stu dy and personal analysis of Plato’s â€Å"Allegory of the Cave† and the Gospel of Matthew’s Sermon on the Mount indicate both appeal against ignorance and warn against egotistic behavior. Both texts take a tactful and thoughtful examination of man’s inability to comfortably, consistently, and effectively look beyond their individual selves as the key figures in a normalized and standardized

Ethical and Unethical Leadership Plan

Question: Discuss about the Ethical and Unethical Leadership Plan. Answer: Introduction: From my experiences leaders are often inconstant in their communications and in their actions. These inconsistencies are truly noted from the followers thus dampening the morale of followers leading to lower efficacy and effectiveness that often spreads ramped throughout the organizational culture as a whole. Senior leadership often takes a top down approach that oftenmisses the small details that can make a huge difference in the operations of an organization where the tasks are being completed (Pecukonis, 2014). Therefore, it is important that the leaders should have a personal development plan. There are various improvement areas that leaders can focus on. In this personal leadership plan I would focus on value based leadership, teamwork and ethics. A values-based leader uses strong ethics and morals to lead and leading by example in a way that encourages the entire organization to follow suit. Open communication is a key component to making it all work. It would be correct to say that leader sets the tone for his or her organization and isthe one on which the reputation of the organization hinges with both internaland external stakeholders (Talan, 2014). In short, Ithink that values-based leadership starts at the top and that it filters downto middle management and rank-and-file employees. Oftentimes, there is a disconnect between the activities of the leader and the intentions of the leader. Leaders sometimes become overwhelmed with the activities and results to step back and recall why they do what they do. The second important dimension of the leadership model is ethics. Daft, (2015) explains that an organizations board that handles unethical behavior is top executives of the organization that form an ethics committee. This ethics committee has the responsibility to oversee the function of ethics in the organization (Daft, 2015). They provide rulings of wrong behavior and in the event leaders are unethical they determine the disciplinary action that should be given to correct the wrongdoing. Even though the organization is profitable, unethical leaders must still be corrected to preserve the ethics and moral standing of the organization at large (Brown Mitchell, 2010). By doing so, this can ensure that the organization remains profitable and stay out of harms way of negative attention of the public and lawsuits that can occur because of unethical activity within the organization. Brown and Mitchell, (2010) also share that unethical leaders can bring out a dark side of organizations. T his is because unethical leadership can cause organizational behaviors to shift to a negative light. This then changes the emotion, fit, and identification of the organization (Brown Mitchell, 2010). This causes harm to the organization being that what leaders are seen followers will then portray doing. Therefore, the ethics committee must enforce proper ethics in the organization to safeguard the organization. It is often too easy to follow the leader in organizations. DuBois (2012) reminded us that doing the right thing is not easy but there are ways to address unethical leadership and righting the ship. DuBois (2012) pointed out that not getting involved with unethical leaders is the first step to protecting yourself but she suggested that if you are involved because of your position bringing to light is not an option. Forcing strict internal policies is a way to weed out unethical behavior. This model suggests that When leaders become unethical, it is the responsibility of the organizational board and ethical committee, if applicable, to get involved. If the leader is acting in an unethical manner but the company is profitable, there will appear to be an ethical dilemma. On one side, the leader is unethical and has avoided the ethical standards of the organization. However, the company is remaining profitable, despite his or her actions. The organizational board must enforce the ethical standards through disciplinary actions of leaders who are unethical. Pascual-Ezama, et al. (2015) stated that unethical behavior could be influence by peer effect, incentives and supervision. If leaders are unethical, their behaviors can carry on to the followers, which can lead to an unethical organization. The third important dimension of my leadership model is teamwork or support from employees. As Plucknette (2014) discusses, leaders tend to invite discussion and debate. This can be an issue for a leader-focused individual because many managers look down upon these qualities and see opposition as insubordination. Conversely, the attitude of many manager-focused individuals is that what they say is law and the final word. This type of managing can inhibit the growth of trust and respect for the manager by the employee(s) (Plucknette, 2014). Leaders may be better set to organize and lead whereas managers may be better at planning and controlling. It is the leader/manager who can meld the two that will be an effective leader.It is important that the leaders must follow on all the three dimensions of this leadership development model. In addition to the three core values or the core dimension of the leadership development model, the model would also have support or non-core attributes. T he core and the Core Values Support/ Non Core Values Value Based Leadership Communication Ethics Collaboration Teamwork Vision The three dimension of my leadership development model can be depicted as: The application of the above leadership model would enable the organization to develop leaders from managers. A managers primary challenge is to solve problems creatively. Managers will analyze, delegate, organize and control which to some people may seem to be a know it best attitude. Managers are more concerned of end results. Leaders approach situations with the attitude that no one person knows it best so they a leader will do something, fix it, try it, change it and do it all over again and are more concerned with satisfaction whether for employees or customers (Graham, 2014). Leaders see people as critical resources to be developed, and this in turn will help the organization to achieve process innovation. Managers view people as an exploitable resource. I think the challenges are accountability; leaders tend to emphasize on mutual accountability as opposed to managers who emphasize on individual accountability. The greatest challenge, according to Clarke (2013) regarding operationalizing strategy of teamwork is because operationalizing has to connect the strategy and its execution within the company. This step is most important and the art of doing it requires finesse and mixes strategic planning and program management. These skills require a different set of skills and discipline than the planning phase. One must understand the strategy, goals and the initiatives they represent. Next, is to group initiatives into programs that are goal-aligned. Mapping the initiatives in terms of impact on the company is next and who will execute. Individuals need to be accountability, which requires clarity of roles and responsibilities relative to the goals. The executor must have the understanding of the innovation in order to execute the plan along with sufficient incentive. The biggest challenge of teamwork is in multicultural environment. The biggest challenge of working with a cross-functional team is to accommodate everyones perspective. Each person or function has a view of the problem and solutions that is based on their vantage point, concerns, and presuppositions. To meet the overall mission of the organization all of this must be weighed out and the best way forward should become clear (Daft, 2013). The purpose of utilizing a cross functional team is the assumption that a small group can accomplish more than an individual based on skills, accountability and commitment. There are a variety of reasons this type of approach could be utilized; overcoming the limits of a hierarchal struggle, improving the quality of decision making, increasing organizational flexibility, and increasing organizational productivity. The application of this leadership model is beneficial not only my personal development but also for the department or group development and the organizational development. As a conclusion, I would like to say that communication and collaboration is the key to implement this model in organizations. Collaborating in the workplace is essential unless you are a super hero with all knowing powers. Working collaboratively sometimes is smooth from the beginning and sometimes it takes a while for each participant to feel like they have an equal voice in the process. Cross-functional teams have been described as team comprised of employees with similar ranked positions within a company (Daft, 2014). It is important that my leadership development model should be implemented with a long-term vision. This model should be implemented as a top-down approach. The senior leadership should communicate about the benefits of this leadership model to different managers in the organization. I think your idea about having meetings and regular communications with the other managers makes a lot of sense. It seems like such a logical solution for the lack of communication. Sometimes those solutions are the ones that are overlooked in the middle of chaos. The above leadership model would address the issue of communication and ensure that the leaders can follow on the core values. References Bliss, D.L., Pecukonis, E. and Snyder-Vogel, M., 2014. Principled Leadership Development Model for Aspiring Social Work Managers and Administrators: Development and Application.Human Services Organizations Management, Leadership Governance,38(1), pp.5-15. Brown, M. E., Mitchell, M. S. (2010). Ethical and Unethical Leadership: Exploring New Avenues for Future Research.Business Ethics Quarterly,20(4), 583-616. Clarke, N., 2013. Model of complexity leadership development.Human Resource Development International,16(2), pp.135-150. Daft, R. L. (2015).Organization theory and design(12th ed.) Mason, OH: South-Western, Cengage Learning. Gifford, W., Graham, I., Eldh, A.C. and Lefebre, N., 2014. Theoretical foundations of dissemination and implementation leadership: a conceptual model for leadership development. InThe 7th Annual Conference on the Science of Dissemination and Implementation, Bethesda, Maryland, USA, 8-9 Dec, 2014. Lepsinger, R., DeRosa, D. (2015). How to Lead an Effective Virtual Team. Ivey Business Journal, 2-6. Pascual-Ezama, D., Dunfield, D., Gil-Gmez de Lia, B., (2015) Organizations Board. Prince Hall. Plucknette, D. (2014). 4 differences between managers and leaders.Plant Engineering,68(10), 16-18. Talan, T.N., Bloom, P.J. and Kelton, R.E., 2014. Building the Leadership Capacity of Early Childhood Directors: An Evaluation of a Leadership Development Model.Early Childhood Research Practice,16(1), p.n1.

Varian Solution free essay sample

Chapter 1 NAME The Market Introduction. The problems in this chapter examine some variations on the apartment market described in the text. In most of the problems we work with the true demand curve constructed from the reservation prices of the consumers rather than the â€Å"smoothed† demand curve that we used in the text. Remember that the reservation price of a consumer is that price where he is just indi? erent between renting or not renting the apartment. At any price below the reservation price the consumer will demand one apartment, at any price above the reservation price the consumer will demand zero apartments, and exactly at the reservation price the consumer will be indi? erent between having zero or one apartment. You should also observe that when demand curves have the â€Å"staircase† shape used here, there will typically be a range of prices where supply equals demand. Thus we will ask for the the highest and lowest price in the range. We will write a custom essay sample on Varian Solution or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 1. 1 (3) Suppose that we have 8 people who want to rent an apartment. Their reservation prices are given below. To keep the numbers small, think of these numbers as being daily rent payments. ) Person Price = A = 40 B 25 C D 30 35 E 10 F 18 G 15 H 5 (a) Plot the market demand curve in the following graph. (Hint: When the market price is equal to some consumer i’s reservation price, there will be two di? erent quantities of apartments demanded, since consumer i will be indi? erent between having or not having an apartment. ) 2 THE MARKET (Ch. 1) Price 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8 Apartments (b) Suppose the supply of apartments is ? xed at 5 units. In this case there is a whole range of prices that will be equilibrium prices. What is the highest price that would make the demand for apartments equal to 5 units? $18. $15. A, B, C, D. $10 to $15. (c) What is the lowest price that would make the market demand equal to 5 units? (d) With a supply of 4 apartments, which of the people A–H end up getting apartments? (e) What if the supply of apartments increases to 6 units. What is the range of equilibrium prices? 1. 2 (3) Suppose that there are originally 5 units in the market and that 1 of them is turned into a condominium. (a) Suppose that person A decides to buy the condominium. What will be the highest price at which the demand for apartments will equal the supply of apartments? What will be the lowest price? Enter your answers in column A, in the table. Then calculate the equilibrium prices of apartments if B, C, . . . , decide to buy the condominium. NAME 3 Person High price Low price A B C D E F G H 18 15 18 15 18 15 18 15 25 18 25 15 25 18 25 18 (b) Suppose that there were two people at each reservation price and 10 apartments. What is the highest price at which demand equals supply? 18. Suppose that one of the apartments was turned into a condo- minium. Is that price still an equilibrium price? Yes. 1. 3 (2) Suppose now that a monopolist owns all the apartments and that he is trying to determine which price and quantity maximize his revenues. (a) Fill in the box with the maximum price and revenue that the monopolist can make if he rents 1, 2, . . . , 8 apartments. (Assume that he must charge one price for all apartments. ) Number Price Revenue 1 2 3 4 5 6 7 8 40 40 35 70 30 90 25 100 18 90 15 90 10 70 5 40 (b) Which of the people A–F would get apartments? A, B, C, D. $18. (c) If the monopolist were required by law to rent exactly 5 apartments, what price would he charge to maximize his revenue? d) Who would get apartments? A, B, C, D, F. (e) If this landlord could charge each individual a di? erent price, and he knew the reservation prices of all the individuals, what is the maximum revenue he could make if he rented all 5 apartments? $148. (f ) If 5 apartments were rented, which individuals would get the apartments? A, B, C, D, F. 1. 4 (2) Suppose that there are 5 a partments to be rented and that the city rent-control board sets a maximum rent of $9. Further suppose that people A, B, C, D, and E manage to get an apartment, while F, G, and H are frozen out. 4 THE MARKET Ch. 1) (a) If subletting is legal—or, at least, practiced—who will sublet to whom in equilibrium? (Assume that people who sublet can evade the city rentcontrol restrictions. ) E, who is willing to pay only F, $10 for an apartment would sublet to who is willing to pay $18. (b) What will be the maximum amount that can be charged for the sublet payment? $18. A, (c) If you have rent control with unlimited subletting allowed, which of the consumers described above will end up in the 5 apartments? B, C, D, F. (d) How does this compare to the market outcome? It’s the same. 1. (2) In the text we argued that a tax on landlords would not get passed along to the renters. What would happen if instead the tax was imposed on renters? (a) To answer this question, consider the group of people in Problem 1. 1. What is the maximum that they would be willing to pay to the landlord if they each had to pay a $5 tax on apartments to the city? Fill in the box below with these reservation prices. Person Reservation Price A B C D E F G H 35 20 25 30 5 13 10 0 (b) Using this information determine the maximum equilibrium price if there are 5 apartments to be rented. $13. c) Of course, the total price a renter pays consists of his or her rent plus the tax. This amount is $18. (d) How does this compare to what happens if the tax is levied on the landlords? It’s the same. Chapter 2 NAME Budget Constraint Introduction. These workouts are designed to build your skills in describing economic situations with graphs and algebra. Budget sets are a good place to start, because both the algebra and the graphing are very easy. Where there are just two goods, a consumer who consumes x1 units of good 1 and x2 units of good 2 is said to consume the consumption bundle, ( x1 , x2 ). Any onsumption bundle can be represented by a point on a two-dimensional graph with quantities of good 1 on the horizontal axis and quantities of good 2 on the vertical axis. If the prices are p1 for good 1 and p2 for good 2, and if the consumer has income m, then she can a? ord any consumption bundle, (x1 , x2 ), such that p1 x1 +p2 x2 ? m. On a graph, the budget line is just the line segment with equation p1 x1 + p2 x2 = m and with x1 and x2 both nonnegative. The budget line is the boundary of the budget set. All of the points that the consumer can a? ord lie on one side of the line and all of the points that the consumer cannot a? rd lie on the other. If you know prices and income, you can construct a consumer’s budget line by ? nding two commodity bundles that she can â€Å"just a? ord† and drawing the straight line that runs through both points. Example: Myrtle has 50 dollars to spend. She consumes only apples and bananas. Apples cost 2 dollars each and bananas cost 1 dollar each. You are to graph her budget line, where apples are measured on the horizontal axis and bananas on the vertical axis. Notice that if she spends all of her income on apples, she can a? ord 25 apples and no bananas. Therefore her budget line goes through the point (25, 0) on the horizontal axis. If she spends all of her income on bananas, she can a? ord 50 bananas and no apples. Therfore her budget line also passes throught the point (0, 50) on the vertical axis. Mark these two points on your graph. Then draw a straight line between them. This is Myrtle’s budget line. What if you are not told prices or income, but you know two commodity bundles that the consumer can just a? ord? Then, if there are just two commodities, you know that a unique line can be drawn through two points, so you have enough information to draw the budget line. Example: Laurel consumes only ale and bread. If she spends all of her income, she can just a? ord 20 bottles of ale and 5 loaves of bread. Another commodity bundle that she can a? ord if she spends her entire income is 10 bottles of ale and 10 loaves of bread. If the price of ale is 1 dollar per bottle, how much money does she have to spend? You could solve this problem graphically. Measure ale on the horizontal axis and bread on the vertical axis. Plot the two points, (20, 5) and (10, 10), that you know to be on the budget line. Draw the straight line between these points and extend the line to the horizontal axis. This point denotes the amount of 6 BUDGET CONSTRAINT (Ch. 2) ale Laurel can a? ord if she spends all of her money on ale. Since ale costs 1 dollar a bottle, her income in dollars is equal to the largest number of bottles she can a? ord. Alternatively, you can reason as follows. Since the bundles (20, 5) and (10, 10) cost the same, it must be that giving up 10 bottles of ale makes her able to a? ord an extra 5 loaves of bread. So bread costs twice as much as ale. The price of ale is 1 dollar, so the price of bread is 2 dollars. The bundle (20, 5) costs as much as her income. Therefore her income must be 20 ? 1 + 5 ? 2 = 30. When you have completed this workout, we hope that you will be able to do the following: †¢ Write an equation for the budget line and draw the budget set on a graph when you are given prices and income or when you are given two points on the budget line. †¢ Graph the e? ects of changes in prices and income on budget sets. †¢ Understand the concept of numeraire and know what happens to the budget set when income and all prices are multiplied by the same positive amount. †¢ Know what the budget set looks like if one or more of the prices is negative. See that the idea of a â€Å"budget set† can be applied to constrained choices where there are other constraints on what you can have, in addition to a constraint on money expenditure. NAME 7 2. 1 (0) You have an income of $40 to spend on two commodities. Commodity 1 costs $10 per unit, and commodity 2 costs $5 per unit. (a) Write down your budget equation. 101 + 52 = 40. (b) If you spent all your income on commodity 1, how much could you buy? 4. 8. Use blue ink to draw your budget line in the graph (c) If you spent all of your income on commodity 2, how much could you buy? elow. x2 8 6 4 2 ,,,,,, ,,,,,, Line Blue ,,,,,, ,,,,,, ,,,,,, Red Line ,,,,,, ,,,,,, ,,,,,,Black Shading ,,,,,, ,,,,,, ,,,,,, ,,,,,,,,,,,,, ,,,,,, ,,,,,,,,,,,,, Black Line ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, Blue ,,,,,,,,,,,,, ,,,,,,,,,,,,, Shading ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, 2 4 6 8 x1 0 (d) Suppose that the price of commodity 1 falls to $5 while everything else stays the same. Write down your new budget equation. 51 +52 = 40. On the graph above, use red ink to draw your new budget line. e) Suppose that the amount you are allowed to spend falls to $30, while the prices of both commodities remain at $5. Write down your budget equation. line. 51 + 52 = 30. Use black ink to draw this budget (f) On your diagram, u se blue ink to shade in the area representing commodity bundles that you can a? ord with the budget in Part (e) but could not a? ord to buy with the budget in Part (a). Use black ink or pencil to shade in the area representing commodity bundles that you could a? ord with the budget in Part (a) but cannot a? ord with the budget in Part (e). 2. 2 (0) On the graph below, draw a budget line for each case. BUDGET CONSTRAINT (Ch. 2) (a) p1 = 1, p2 = 1, m = 15. (Use blue ink. ) (b) p1 = 1, p2 = 2, m = 20. (Use red ink. ) (c) p1 = 0, p2 = 1, m = 10. (Use black ink. ) (d) p1 = p2 , m = 15p1 . (Use pencil or black ink. Hint: How much of good 1 could you a? ord if you spend your entire budget on good 1? ) x2 20 15 Blue Line Black Line 10 Red Line 5 0 5 10 15 20 x1 2. 3 (0) Your budget is such that if you spend your entire income, you can a? ord either 4 units of good x and 6 units of good y or 12 units of x and 2 units of y. (a) Mark these two consumption bundles and draw the budget line in th e graph below. 16 12 8 4 0 4 8 12 16 x NAME 9 (b) What is the ratio of the price of x to the price of y? 1/2. (c) If you spent all of your income on x, how much x could you buy? 16. (d) If you spent all of your income on y, how much y could you buy? 8. (e) Write a budget equation that gives you this budget line, where the price of x is 1. x + 2y = 16. 3x + 6y = 48. (f ) Write another budget equation that gives you the same budget line, but where the price of x is 3. 2. 4 (1) Murphy was consuming 100 units of X and 50 units of Y . The price of X rose from 2 to 3. The price of Y remained at 4. a) How much would Murphy’s income have to rise so that he can still exactly a? ord 100 units of X and 50 units of Y ? $100. 2. 5 (1) If Amy spent her entire allowance, she could a? ord 8 candy bars and 8 comic books a week. She could also just a? ord 10 candy bars and 4 comic books a week. The price of a candy bar is 50 cents. Draw her budget line in the box below. What is Amy’s we ekly allowance? $6. Comic books 32 24 16 8 0 8 12 16 24 32 Candy bars 10 BUDGET CONSTRAINT (Ch. 2) 2. 6 (0) In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Prices have been remarkably stable for the last 50 years or so. Potatoes cost 2 crowns per sack, meatballs cost 4 crowns per crock, and jam costs 6 crowns per jar. (a) Write down a budget equation for a citizen named Gunnar who has an income of 360 crowns per year. Let P stand for the number of sacks of potatoes, M for the number of crocks of meatballs, and J for the number of jars of jam consumed by Gunnar in a year. 2P + 4M + 6J = 360. (b) The citizens of this country are in general very clever people, but they are not good at multiplying by 2. This made shopping for potatoes excruciatingly di? ult for many citizens. Therefore it was decided to introduce a new unit of currency, such that potatoes would be the numeraire. A sack of potatoes costs one unit of the new currency while the same relative prices apply as in the past. In terms of the new currency, what is the price of meatballs? 2 crowns. 3 (c) In terms of the new currency, what is the price of jam? crowns. (d) What would Gu nnar’s income in the new currency have to be for him to be exactly able to a? ord the same commodity bundles that he could a? ord before the change? 180 crowns. P + 2M + 3J = (e) Write down Gunnar’s new budget equation. 80. No. Is Gunnar’s budget set any di? erent than it was before the change? 2. 7 (0) Edmund Stench consumes two commodities, namely garbage and punk rock video cassettes. He doesn’t actually eat the former but keeps it in his backyard where it is eaten by billy goats and assorted vermin. The reason that he accepts the garbage is that people pay him $2 per sack for taking it. Edmund can accept as much garbage as he wishes at that price. He has no other source of income. Video cassettes cost him $6 each. (a) If Edmund accepts zero sacks of garbage, how many video cassettes can he buy? 0. NAME 11 b) If he accepts 15 sacks of garbage, how many video cassettes can he buy? 5. 6C ? 2G = 0. (c) Write down an equation for his budget line. (d) Draw Edmund’s budget line and shade in his budget set. Garbage 20 15 10 5 ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,,Budget Line ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, Set Budget ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, ,,,,,,,,, 5 10 15 20 Video cassettes 0 2. 8 (0) If you think Edmund is odd, consider his brother Emmett. Emmett consumes speeches by politicians and university administrators. He is paid $1 per hour for listening to politicians and $2 per hour for listening to university administrators. (Emmett is in great demand to help ? ll empty chairs at public lectures because of his distinguished appearance and his ability to refrain from making rude noises. ) Emmett consumes one good for which he must pay. We have agreed not to disclose what that good is, but we can tell you that it costs $15 per unit and we shall call it Good X. In addition to what he is paid for consuming speeches, Emmett receives a pension of $50 per week. Administrator speeches 100 75 50 25 0 25 50 5 100 Politician speeches 12 BUDGET CONSTRAINT (Ch. 2) (a) Write down a budget equation stating those combinations of the three commodities, Good X, hours of speeches by politicians (P ), and hours of speeches by university administrators (A) that Emmett could a? ord to consume per week. 15X ? 1P ? 2A = 50. (b) On the graph above, draw a two-dimensional diagram showing the locus of consumptions of the two kinds of speeches that would be possible for Emmett if he consumed 10 units of Good X per week. 2. 9 (0) Jonathan Livingstone Yuppie is a prosperous lawyer. He has, in his own words, â€Å"outgrown those con? ing two-commodity limits. † Jonathan consumes three goods, unblended Scotch whiskey, designer tennis shoes, and meals in French gourmet restaurants. The price of Jonathan’s brand of whiskey is $20 per bottle, the price of designer tennis shoes is $80 per pair, and the price of gourmet restaurant meals is $50 per meal. After he has paid his taxes and alimony, Jonathan has $400 a week to spend. (a) Write down a budget equation for Jonathan, where W stands for the number of bottles of whiskey, T stands for the number of pairs of tennis shoes, and M for the number of gourmet restaurant meals that he consumes. 0W + 80T + 50M = 400. (b) Draw a three-dimensional diagram to show his budget set. Label the intersections of the budget set with each axis. M 8 5 20 T W (c ) Suppose that he determines that he will buy one pair of designer tennis shoes per week. What equation must be satis? ed by the combinations of restaurant meals and whiskey that he could a? ord? 20W +50M = 320. 2. 10 (0) Martha is preparing for exams in economics and sociology. She has time to read 40 pages of economics and 30 pages of sociology. In the same amount of time she could also read 30 pages of economics and 60 pages of sociology. NAME 13 (a) Assuming that the number of pages per hour that she can read of either subject does not depend on how she allocates her time, how many pages of sociology could she read if she decided to spend all of her time on sociology and none on economics? 150 pages. (Hint: You have two points on her budget line, so you should be able to determine the entire line. ) (b) How many pages of economics could she read if she decided to spend all of her time reading economics? 50 pages. 2. 11 (1) Harry Hype has $5,000 to spend on advertising a new kind of dehydrated sushi. Market research shows that the people most likely to buy this new product are recent recipients of M. B. A. degrees and lawyers who own hot tubs. Harry is considering advertising in two publications, a boring business magazine and a trendy consumer publication for people who wish they lived in California. Fact 1: Ads in the boring business magazine cost $500 each and ads in the consumer magazine cost $250 each. Fact 2: Each ad in the business magazine will be read by 1,000 recent M. B. A. ’s and 300 lawyers with hot tubs. Fact 3: Each ad in the consumer publication will be read by 300 recent M. B. A. ’s and 250 lawyers who own hot tubs. Fact 4: Nobody reads more than one ad, and nobody who reads one magazine reads the other. (a) If Harry spends his entire advertising budget on the business publication, his ad will be read by 10,000 recent M. B. A. ’s and by 3,000 lawyers with hot tubs. (b) If he spends his entire advertising budget on the consumer publication, his ad will be read by lawyers with hot tubs. 6,000 recent M. B. A. ’s and by 5,000 (c) Suppose he spent half of his advertising budget on each publication. His ad would be read by lawyers with hot tubs. 8,000 recent M. B. A. ’s and by 4,000 (d) Draw a â€Å"budget line† showing the combinations of number of readings by recent M. B. A. ’s and by lawyers with hot tubs that he can obtain if he spends his entire advertising budget. Does this line extend all the way to the axes? No. Sketch, shade in, and label the budget set, which includes all the combinations of MBA’s and lawyers he can reach if he spends no more than his budget. 14 BUDGET CONSTRAINT (Ch. 2) (e) Let M stand for the number of instances of an ad being read by an M. B. A. and L stand for the number of instances of an ad being read by a lawyer. This budget line is a line segment that lies on the line with equation M + 2L = 16. With a ? xed advertising budget, how many readings by M. B. A. ’s must he sacri? ce to get an additional reading by a lawyer with a hot tub? MBAs x 1000 16 2. 12 10 8 6 4 a ,,,,,,,, ,,,,,,,, ,,,,,,,, c ,,,,,,,, ,,,,,,,, ,,,,,,,, b ,,,,,,,, ,,,,,,,, Budget ,,,,,,,, ,,,,,,,, Set ,,,,,,,, ,,,,,,,, ,,,,,,,, ,,,,,,,, ,,,,,,,, ,,,,,,,, 3 5 2 4 8 Budget line 0 12 16 Lawyers x 1000 2. 12 (0) On the planet Mungo, they have two kinds of money, blue money and red money. Every commodity has two prices—a red-money price and a blue-money price. Every Mungoan has two incomes—a red income and a blue income. In order to buy an object, a Mungoan has to pay that object’s redmoney price in red money and its blue-money price in blue money. (The shops simply have two cash registers, and you have to pay at both registers to buy an object. ) It is forbidden to trade one kind of money for the other, and this prohibition is strictly enforced by Mungo’s ruthless and e? cient monetary police. †¢ There are just two consumer goods on Mungo, ambrosia and bubble gum. All Mungoans prefer more of each good to less. †¢ The blue prices are 1 bcu (bcu stands for blue currency unit) per unit of ambrosia and 1 bcu per unit of bubble gum. †¢ The red prices are 2 rcus (red currency units) per unit of ambrosia and 6 rcus per unit of bubble gum. (a) On the graph below, draw the red budget (with red ink) and the blue budget (with blue ink) for a Mungoan named Harold whose blue income is 10 and whose red income is 30. Shade in the â€Å"budget set† containing all of the commodity bundles that Harold can a? ord, given NAME 15 its? wo budget constraints. Remember, Harold has to have enough blue money and enough red money to pay both the blue-money cost and the red-money cost of a bundle of goods. Gum 20 15 10 Blue Lines 5 ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, 5 10 Red Line 15 20 Ambrosia 0 (b) Another Mungoan, Gladys, faces the same prices that Harold faces and has the same red income as Harold, but Gladys has a blue income of 20. Explain how it is that Gladys will not spend its entire blue income no matter what its tastes may be. Hint: Draw Gladys’s budget lines. ) The blue budget line lies strictly outside the red budget line, so to satisfy both budgets, one must be strictly inside the red budget line. (c) A group of radical economic reformers on Mungo believe that the currency rules are unfair. â€Å"Why should everyone have to pay two prices for everything? † they ask. They propose the following scheme. Mungo will continue to have two currencies, every good will have a blue price and a red price, and every Mungoan will have a blue income and a red income. But nobody has to pay both prices. Instead, everyone on Mungo must declare itself to be either a Blue-Money Purchaser (a â€Å"Blue†) or a RedMoney Purchaser (a â€Å"Red†) before it buys anything at all. Blues must make all of their purchases in blue money at the blue prices, spending only their blue incomes. Reds must make all of their purchases in red money, spending only their red incomes. Suppose that Harold has the same income after this reform, and that prices do not change. Before declaring which kind of purchaser it will be, We refer to all Mungoans by the gender-neutral pronoun, â€Å"it. Although Mungo has two sexes, neither of them is remotely like either of ours. ? 16 BUDGET CONSTRAINT (Ch. 2) Harold contemplates the set of commodity bundles that it could a? ord by making one declaration or the other. Let us call a commodity bundle â€Å"attainable† if Harold can a? ord it by declaring itself to be a â€Å"Blue† and buying the bundle with blue money or if Harold can a? ord the bundle by declaring itself to be a â€Å"Red† and buying it with red money. On the diagram below, shade in all of the attainable bundles. Gum 20 15 10 5 ,,,,,,,,,,,, Blue Line ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,, Line Red ,,,,,,,,,,,,, ,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,, ,,,,,,,,,,,,, ,,,,,,,,, 5 10 15 20 Ambrosia 0 2. 13 (0) Are Mungoan budgets really so fanciful? Can you think of situations on earth where people must simultaneously satisfy more than one budget constraint? Is money the only scarce resource that people use up when consuming? Consumption of many commodities takes time as well as money. People have to simultaneously satisfy a time budget and a money budget. Other examplespeople may have a calorie budget or a cholesterol budget or an alcohol-intake budget. Chapter 3 NAME Preferences Introduction. In the previous section you learned how to use graphs to show the set of commodity bundles that a consumer can a? ord. In this section, you learn to put information about the consumer’s preferences on the same kind of graph. Most of the problems ask you to draw indi? erence curves. Sometimes we give you a formula for the indi? erence curve. Then all you have to do is graph a known equation. But in some problems, we give you only â€Å"qualitative† information about the consumer’s preferences and ask you to sketch indi? erence curves that are consistent with this information. This requires a little more thought. Don’t be surprised or disappointed if you cannot immediately see the answer when you look at a problem, and don’t expect that you will ? nd the answers hiding somewhere in your textbook. The best way we know to ? nd answers is to â€Å"think and doodle. † Draw some axes on scratch paper and label them, then mark a point on your graph and ask yourself, â€Å"What other points on the graph would the consumer ? d indi? erent to this point? † If possible, draw a curve connecting such points, making sure that the shape of the line you draw re? ects the features required by the problem. This gives you one indi? erence curve. Now pick another point that is preferred to the ? rst one you drew and draw an indi? erence curve throug h it. Example: Jocasta loves to dance and hates housecleaning. She has strictly convex preferences. She prefers dancing to any other activity and never gets tired of dancing, but the more time she spends cleaning house, the less happy she is. Let us try to draw an indi? erence curve that is consistent with her preferences. There is not enough information here to tell us exactly where her indi? erence curves go, but there is enough information to determine some things about their shape. Take a piece of scratch paper and draw a pair of axes. Label the horizontal axis â€Å"Hours per day of housecleaning. † Label the vertical axis â€Å"Hours per day of dancing. † Mark a point a little ways up the vertical axis and write a 4 next to it. At this point, she spends 4 hours a day dancing and no time housecleaning. Other points that would be indi? erent to this point would have to be points where she did more dancing and more housecleaning. The pain of the extra housekeeping should just compensate for the pleasure of the extra dancing. So an indi? erence curve for Jocasta must be upward sloping. Because she loves dancing and hates housecleaning, it must be that she prefers all the points above this indi? erence curve to all of the points on or below it. If Jocasta has strictly convex preferences, then it must be that if you draw a line between any two points on the same indi? rence curve, all the points on the line (except the endpoints) are preferred to the endpoints. For this to be the case, it must be that the indi? erence curve slopes upward ever more steeply as you move to the right along it. You should convince yourself of this by making some drawings on scratch 18 PREFERENCES (Ch. 3) paper. Draw an upward-sloping curve passing through the point (0, 4) and getting steeper as one moves to the right. When you have completed this workout, we hope that you will be able to do the following: †¢ Given the formula for an indi? erence curve, draw this curve, and ? d its slope at any point on the curve. †¢ Determine whether a consumer prefers one bundle to another or is indi? erent between them, given speci? c indi? erence curves. †¢ Draw indi? erence curves for the special cases of perfect substitutes and perfect complements. †¢ Draw indi? erence curves for someone who dislikes one or both commodities. †¢ Draw indi? erence curves for someone who likes goods up to a point but who can get â€Å"too much† of one or more goods. †¢ Identify weakly preferred sets and determine whether these are convex sets and whether preferences are convex. Know what the marginal rate of substitution is and be able to determine whether an indi? erence curve exhibits â€Å"diminishing marginal rate of substitution. † †¢ Determine whether a preferenc e relation or any other relation between pairs of things is transitive, whether it is re? exive, and whether it is complete. 3. 1 (0) Charlie likes both apples and bananas. He consumes nothing else. The consumption bundle where Charlie consumes xA bushels of apples per year and xB bushels of bananas per year is written as (xA , xB ). Last year, Charlie consumed 20 bushels of apples and 5 bushels of bananas. It happens that the set of consumption bundles (xA , xB ) such that Charlie is indi? erent between (xA , xB ) and (20, 5) is the set of all bundles such that xB = 100/xA . The set of bundles (xA , xB ) such that Charlie is just indi? erent between (xA , xB ) and the bundle (10, 15) is the set of bundles such that xB = 150/xA . (a) On the graph below, plot several points that lie on the indi? erence curve that passes through the point (20, 5), and sketch this curve, using blue ink. Do the same, using red ink, for the indi? erence curve passing through the point (10, 15). b) Use pencil to shade in the set of commodity bundles that Charlie weakly prefers to the bundle (10, 15). Use blue ink to shade in the set of commodity bundles such that Charlie weakly prefers (20, 5) to these bundles. NAME 19 Bananas 40 30 20 10 ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,, ,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, Red Curve ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, Pencil Shading ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, Blue Curve ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, Blue Shading ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,,, 10 20 30 40 Apples 0 For each of the following statements about Charlie’s preferences, write â€Å"true† or â€Å"false. † (c) (30, 5) ? (10, 15). (d) (10, 15) (e) (20, 5) (f ) (24, 4) (g) (11, 14) (20, 5). (10, 10). (11, 9. 1). (2, 49). True. True. True. False. True. (h) A set is convex if for any two points in the set, the line segment between them is also in the set. Is the set of bundles that Charlie weakly prefers to (20, 5) a convex set? Yes. (i) Is the set of bundles that Charlie considers inferior to (20, 5) a convex set? No. rate of (j) The slope of Charlie’s indi? erence curve through a point, (xA , xB ), is known as his marginal substitution at that point. 20 PREFERENCES (Ch. 3) (k) Remember that Charlie’s indi? rence curve through the point (10, 10) has the equation xB = 100/xA . Those of you who know calculus will remember that the slope of a curve is just its derivative, which in this case is ? 100/x2 . (If you don’t know calculus, you will have to take our A word for this. ) Find Charlie’s marginal rate of substitution at the point, (10, 10). ?1. ?4. (l) What is his marginal rate of substitution at the point (5, 20)? (m) What is his marginal rate of substitution at the point (20, 5)? (?. 25). (n) Do the indi? erence curves you have drawn for Charlie exhibit diminishing marginal rate of substitution? Yes. 3. 2 (0) Ambrose consumes only nuts and berries. Fortunately, he likes both goods. The consumption bundle where Ambrose consumes x1 units of nuts per week and x2 units of berries per week is written as (x1 , x2 ). The set of consumption bundles (x1 , x2 ) such that Ambrose is indi? erent between (x1 , x2 ) and (1, 16) is the set of bundles such that x1 ? 0, x2 ? 0, v and x2 = 20 ? 4 x1 . The set of bundles (x1 , x2 ) such that (x1 , x2 ) ? v (36, 0) is the set of bundles such that x1 ? 0, x2 ? 0 and x2 = 24 ? 4 x1 . (a) On the graph below, plot several points that lie on the indi? erence curve that passes through the point (1, 16), and sketch this curve, using blue ink. Do the same, using red ink, for the indi? erence curve passing through the point (36, 0). b) Use pencil to shade in the set of commodity bundles that Ambrose weakly prefers to the bundle (1, 16). Use red ink to shade in the set of all commodity bundles (x1 , x2 ) such that Ambrose weakly prefers (36, 0) to these bundles. Is the set of bundles that Ambrose prefers to (1, 16) a convex set? Yes. (c) Wh at is the slope of Ambrose’s indi? erence curve at the point (9, 8)? (Hint: Recall from calculus the way to calculate the slope of a curve. If you don’t know calculus, you will have to draw your diagram carefully and estimate the slope. ) ?2/3. NAME 21 (d) What is the slope of his indi? erence curve at the point (4, 12)? ?1. Berries 40 30 20 10 ,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, Pencil Shading ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, Red Curve ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,, ,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, Red ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, Blue Curve ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, Shading ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,,,,, 10 20 30 40 Nuts , 0 (e) What is the slope of his indi? erence curve at the point (9, 12)? at the point (4, 16)? ?2/3 ?1. (f ) Do the indi? erence curves you have drawn for Ambrose exhibit diminishing marginal rate of substitution? Yes. (g) Does Ambrose have convex preferences? Yes. 3. 3 (0) Shirley Sixpack is in the habit of drinking beer each evening while watching â€Å"The Best of Bowlerama† on TV. She has a strong thumb and a big refrigerator, so she doesn’t care about the size of the cans that beer comes in, she only cares about how much beer she has. (a) On the graph below, draw some of Shirley’s indi? erence curves between 16-ounce cans and 8-ounce cans of beer. Use blue ink to draw these indi? erence curves. 22 PREFERENCES (Ch. 3) 8-ounce 8 6 Blue Lines 4 Red Lines 2 0 2 4 6 8 16-ounce (b) Lorraine Quiche likes to have a beer while she watches â€Å"Masterpiece Theatre. † She only allows herself an 8-ounce glass of beer at any one time. Since her cat doesn’t like beer and she hates stale beer, if there is more than 8 ounces in the can she pours the excess into the sink. (She has no moral scruples about wasting beer. On the graph above, use red ink to draw some of Lorraine’s indi? erence curves. 3. 4 (0) Elmo ? nds himself at a Coke machine on a hot and dusty Sunday. The Coke machine requires exact change—two quarters and a dime. No other combination of coins will make anything come out of the machine. No stores are open; no one is in sight. Elmo is so thirsty that the only thing he cares about is how many soft drinks he will be able to buy with the change in his pocket; the more he can buy, the better. While Elmo searches his pockets, your task is to draw some indi? erence curves that describe Elmo’s preferences about what he ? nds. NAME 23 Dimes 8 6 4 2 ,,,,,,,,,,,, , , ,,,,,,,,,,,, ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , Blue ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, Red , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , shading ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, shading , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, ,,,,,, ,,,,,,,,,,,, , , ,,,, ,,,,,,,,,,,,,, , ,,,,,,,,,,,, , , , ,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,, , , , ,,,,,,,,,,,,,,,,,, Black ,,,,,,,,,,,,,,,,,, ,,,,,,,,,,,, ,,,,,,,,,,,, , , ,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , lines ,,,,,,,,,,,,,,,,,, , , , ,,,,,,,,,,,,,,,,,, , , ,,,,,,,,,,,,,,,,,, , 2 4 6 8 Quarters 0 (a) If Elmo has 2 quarters and a dime in his pockets, he can buy 1 soft drink. How many soft drinks can he buy if he has 4 quarters and 2 dimes? 2. (b) Use red ink to shade in the area on the graph consisting of all combinations of quarters and dimes that Elmo thinks are just indi? rent to having 2 quarters and 1 dime. (Imagine that it is possible for Elmo to have fractions of quarters or of dimes, but, of course, they would be useless in the machine. ) Now use blue ink to shade in the area consisting of all combinations that Elmo thinks are just indi? erent to having 4 quarters and 2 dimes. Notice that Elmo has indi? erence â€Å"bands,† not indi? erence curves. (c) Does Elmo have convex preferences between dimes and quarters? Yes. (d) Does Elmo always prefer more of both kinds of money to less? No. (e) Does Elmo have a bliss point? No. (f ) If Elmo had arrived at the Coke machine on a Saturday, the drugstore across the street would have been open. This drugstore has a soda fountain that will sell you as much Coke as you want at a price of 4 cents an ounce. The salesperson will take any combination of dimes and quarters in payment. Suppose that Elmo plans to spend all of the money in his pocket on Coke at the drugstore on Saturday. On the graph above, use pencil or black ink to draw one or two of Elmo’s indi? erence curves between quarters and dimes in his pocket. (For simplicity, draw your graph 24 PREFERENCES (Ch. 3) as if Elmo’s fractional quarters and fractional dimes are accepted at the corresponding fraction of their value. ) Describe these new indi? erence curves in words. Line segments with slope ? 2. 5. 3. (0) Randy Ratpack hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences. (a) Sketch an indi? erence curve for Randy where the two commodities are hours per week spent studying economics and hours per we ek spent studying history. Will the slope of an indi? erence curve be positive or negative? Negative. Steeper. (b) Do Randy’s indi? erence curves get steeper or ? atter as you move from left to right along one of them? Hours studying history 8 6 Preference direction 4 2 0 2 4 6 8 Hours studying economics 3. 6 (0) Flossy Toothsome likes to spend some time studying and some time dating. In fact her indi? rence curves between hours per week spent studying and hours per week spent dating are concentric circles around her favorite combination, which is 20 hours of studying and 15 hours of dating per week. The closer she is to her favorite combination, the happier she is. NAME 25 (a) Suppose that Flossy is currently studying 25 hours a week and dating 3 hours a week. Would she prefer to be studying 30 hours a week and dating 8 hours a week? Yes. (Hint: Remember the formula for the distance between two points in the plane? ) (b) On the axes below, draw a few of Flossy’s indi? erence curves and use your diagram to illustrate which of the two time allocations discussed above Flossy would prefer. Hours dating 40 30 Preference direction 20 (20,15) 10 (30,8) (25,3) 0 10 20 30 40 Hours studying , 3. 7 (0) Joan likes chocolate cake and ice cream, but after 10 slices of cake, she gets tired of cake, and eating more cake makes her less happy. Joan always prefers more ice cream to less. Joan’s parents require her to eat everything put on her plate. In the axes below, use blue ink to draw a set of indi? erence curves that depict her preferences between plates with di? erent amounts of cake and ice cream. Be sure to label the axes. (a) Suppose that Joan’s preferences are as before, but that her parents allow her to leave anything on her plate that she doesn’t want. On the graph below, use red ink to draw some indi? erence curves depicting her preferences between plates with di? erent amounts of cake and ice cream. Ice cream Blue curves Red curves Preference direction 10 Chocolate cake 26 PREFERENCES (Ch. 3) 3. 8 (0) Professor Goodheart always gives two midterms in his communications class. He only uses the higher of the two scores that a student gets on the midterms when he calculates the course grade. (a) Nancy Lerner wants to maximize her grade in this course. Let x1 be her score on the ? rst midterm and x2 be her score on the second midterm. Which combination of scores would Nancy prefer, x1 = 20 and x2 = 70 or x1 = 60 and x2 = 60? (20,70). b) On the graph below, use red ink to draw an indi? erence curve showing all of the combinations of scores that Nancy likes exactly as much as x1 = 20 and x2 = 70. Also use red ink to draw an indi? erence curve showing the combinations that Nancy likes exactly as much as x1 = 60 and x2 = 60. (c) Does Nanc y have convex preferences over these combinations? No. Grade on second midterm 80 60 Red curves Blue curves 40 , 20 Preference direction 0 20 40 60 80 Grade on first midterm (d) Nancy is also taking a course in economics from Professor Stern. Professor Stern gives two midterms. Instead of discarding the lower grade, Professor Stern discards the higher one. Let x1 be her score on the ? st midterm and x2 be her score on the second midterm. Which combination of scores would Nancy prefer, x1 = 20 and x2 = 70 or x1 = 60 and x2 = 50? (60,50). (e) On the graph above, use blue ink to draw an indi? erence curve showing all of the combinations of scores on her econ exams that Nancy likes exactly as well as x1 = 20 and x2 = 70. Also use blue ink to draw an indi? erence curve showing the combinations that Nancy likes exactly as well as x1 = 60 and x2 = 50. Does Nancy have convex preferences over these combinations? Yes. NAME 27 3. 9 (0) Mary Granola loves to consume two goods, grapefruits and a vocados. (a) On the graph below, the slope of an indi? rence curve through any point where she has more grapefruits than avocados is ? 2. This means that when she has more grapefruits than avocados, she is willing to give up 2 grapefruit(s) to get one avocado. (b) On the same graph, the slope of an indi? erence curve at points where she has fewer grapefruits than avocados is ? 1/2. This means that when she has fewer grapefruits than avocados, she is just willing to give up 1/2 grapefruit(s) to get one avocado. (c) On this graph, draw an indi? erence curve for Mary through bundle (10A, 10G). Draw another indi? erence curve through (20A, 20G). Grapefruits 40 30 Slope -2 20 10 Slope -1/2 45 0 10 20 30 40 Avocados (d) Does Mary have convex preferences? Yes. 3. 0 (2) Ralph Rigid likes to eat lunch at 12 noon. However, he also likes to save money so he can buy other consumption goods by attending the â€Å"early bird specials† and â€Å"late lunchers† promoted by his local d iner. Ralph has 15 dollars a day to spend on lunch and other stu?. Lunch at noon costs $5. If he delays his lunch until t hours after noon, he is able to buy his lunch for a price of $5 ? t. Similarly if he eats his lunch t hours before noon, he can buy it for a price of $5 ? t. (This is true for fractions of hours as well as integer numbers of hours. ) (a) If Ralph eats lunch at noon, how much money does he have per day to spend on other stu $10. 8 PREFERENCES (Ch. 3) (b) How much money per day would he have left for other stu? if he ate at 2 P. M.? $12. (c) On the graph below, use blue ink to draw the broken line that shows combinations of meal time and money for other stu? that Ralph can just a? ord. On this same graph, draw some indi? erence curves that would be consistent with Ralph choosing to eat his lunch at 11 A. M. Money 20 15 10 5 0 10 11 12 1 2 Time 3. 11 (0) Henry Hanover is currently consuming 20 cheeseburgers and 20 Cherry Cokes a week. A typical indi? erence curve fo r Henry is depicted below. Cherry Coke 40 30 20 10 0 10 20 30 40 Cheeseburgers NAME 29 (a) If someone o? red to trade Henry one extra cheeseburger for every Coke he gave up, would Henry want to do this? No. Yes. (b) What if it were the other way around: for every cheeseburger Henry gave up, he would get an extra Coke. Would he accept this o? er? (c) At what rate of exchange would Henry be willing to stay put at his current consumption level? 2 cheeseburgers for 1 Coke. 3. 12 (1) Tommy Twit is happiest when he has 8 cookies and 4 glasses of milk per day. Whenever he has more than his favorite amount of either food, giving him still more makes him worse o?. Whenever he has less than his favorite amount of either food, giving him more makes him better o?. His mother makes him drink 7 glasses of milk and only allows him 2 cookies per day. One day when his mother was gone, Tommy’s sadistic sister made him eat 13 cookies and only gave him 1 glass of milk, despite the fact that Tommy complained bitterly about the last 5 cookies that she made him eat and begged for more milk. Although Tommy complained later to his mother, he had to admit that he liked the diet that his sister forced on him better than what his mother demanded. (a) Use black ink to draw some indi? erence curves for Tommy that are consistent with this story. Milk 12 11 10 9 8 7 6 5 4 3 2 1 (13,1) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (8,4) (2,7) Cookies 30 PREFERENCES (Ch. 3) b) Tommy’s mother believes that the optimal amount for him to consume is 7 glasses of milk and 2 cookies. She measures deviations by absolute values. If Tommy consumes some other bundle, say, (c, m), she measures his departure from the optimal bundle by D = |7 ? m| + |2 ? c|. The larger D is, the worse o? she thinks Tommy is. Use blue ink in the graph above to sketch a few of Mrs. Twit’s indi? erence curves for Tommy’s consumption. (Hint: Before you try to draw Mrs. Twit’s indi? erence curves, we suggest that you take a piece of scrap paper and draw a graph of the locus of points (x1 , x2 ) such that |x1 | + |x2 | = 1. ) 3. 13 (0) Coach Steroid likes his players to be big, fast, and obedient. If player A is better than player B in two of these three characteristics, then Coach Steroid prefers A to B, but if B is better than A in two of these three characteristics, then Steroid prefers B to A. Otherwise, Steroid is indi? erent between them. Wilbur Westinghouse weighs 340 pounds, runs very slowly, and is fairly obedient. Harold Hotpoint weighs 240 pounds, runs very fast, and is very disobedient. Jerry Jacuzzi weighs 150 pounds, runs at average speed, and is extremely obedient. (a) Does Steroid prefer Westinghouse to Hotpoint or vice versa? He prefers Westinghouse to Hotpoint. (b) Does Steroid prefer Hotpoint to Jacuzzi or vice versa? He prefers Hotpoint to Jacuzzi. (c) Does Steroid prefer Westinghouse to Jacuzzi or vice versa? He prefers Jacuzzi to Westinghouse. (d) Does Coach Steroid have transitive preferences? No. e) After several losing seasons, Coach Steroid decides to change his way of judging players. According to his new preferences, Steroid prefers player A to play er B if player A is better in all three of the characteristics that Steroid values, and he prefers B to A if player B is better at all three things. He is indi? erent between A and B if they weigh the same, are equally fast, and are equally obedient. In all other cases, Coach Steroid simply says â€Å"A and B are not comparable. † (f ) Are Coach Steroid’s new preferences complete? (g) Are Coach Steroid’s new preferences transitive? No. Yes. NAME 31 (h) Are Coach Steroid’s new preferences re? exive? Yes. 3. 14 (0) The Bear family is trying to decide what to have for dinner. Baby Bear says that his ranking of the possibilities is (honey, grubs, Goldilocks). Mama Bear ranks the choices (grubs, Goldilocks, honey), while Papa Bear’s ranking is (Goldilocks, honey, grubs). They decide to take each pair of alternatives and let a majority vote determine the family rankings. (a) Papa suggests that they ? rst consider honey vs. grubs, and then the winner of that contest vs. Goldilocks. Which alternative will be chosen? Goldilocks. (b) Mama suggests instead that they consider honey vs. Goldilocks and then the winner vs. grubs. Which gets chosen? Grubs. (c) What order should Baby Bear suggest if he wants to get his favorite food for dinner? Grubs versus Goldilocks, then Honey versus the winner. d) Are the Bear family’s â€Å"collective preferences,† as determined by voting, transitive? No. 3. 15 (0) Olson likes strong co? ee, the stronger the better. But he can’t distinguish small di? erences. Over the years, Mrs. Olson has discovered th at if she changes the amount of co? ee by more than one teaspoon in her six-cup pot, Olson can tell that she did it. But he cannot distinguish di? erences smaller than one teaspoon per pot. Where A and B are two di? erent cups of co? ee, let us write A B if Olson prefers cup A to cup B. Let us write A B if Olson either prefers A to B, or can’t tell the di? erence between them. Let us write A ? B if Olson can’t tell the di? erence between cups A and B. Suppose that Olson is o? red cups A, B, and C all brewed in the Olsons’ six-cup pot. Cup A was brewed using 14 teaspoons of co? ee in the pot. Cup B was brewed using 14. 75 teaspoons of co? ee in the pot and cup C was brewed using 15. 5 teaspoons of co? ee in the pot. For each of the following expressions determine whether it is true of false. (a) A ? B. (b) B ? A. True. True. 32 PREFERENCES (Ch. 3) (c) B ? C. (d) A ? C. (e) C ? A. (f ) A B. True. False. False. True. True. True. False. True. False. False. False. Fa lse. True. , transitive? (g) B A. (h) B C. (i) A C. (j) C A. (k) A B. (l) B A. (m) B C. (n) A C. (o) C A. (p) Is Olson’s â€Å"at-least-as-good-as† relation, No. No. (q) Is Olson’s â€Å"can’t-tell-the-di? rence† relation, ? , transitive? (r) is Olson’s â€Å"better-than† relation, , transitive. Yes. Chapter 4 NAME Utility Introduction. In the previous chapter, you learned about preferences and indi? erence curves. Here we study another way of describing preferences, the utility function. A utility function that represents a person’s preferences is a function that assigns a utility number to each commodity bundle. The numbers are assigned in such a way that commodity bundle (x, y) gets a higher utility number than bundle (x , y ) if and only if the consumer prefers (x, y) to (x , y ). If a consumer has the utility function U (x1 , x2 ), then she will be indi? rent between two bundles if they are assigned the same utility. If yo u know a consumer’s utility function, then you can ?nd the indi? erence curve passing through any commodity bundle. Recall from the previous chapter that when good 1 is graphed on the horizontal axis and good 2 on the vertical axis, the slope of the indi? erence curve passing through a point (x1 , x2 ) is known as the marginal rate of substitution. An important and convenient fact is that the slope of an indi? erence curve is minus the ratio of the marginal utility of good 1 to the marginal utility of good 2. For those of you who know even a tiny bit of calculus, calculating marginal utilities is easy. To ? d the marginal utility of either good, you just take the derivative of utility with respect to the amount of that good, treating the amount of the other good as a constant. (If you don’t know any calculus at all, you can calculate an approximation to marginal utility by the method described in your textbook. Also, at the beginning of this section of the workbook, we list the marginal utility functions for commonly encountered utility functions. Even if you can’t compute these yourself, you can refer to this list when later problems require you to use marginal utilities. ) Example: Arthur’s utility function is U (x1 , x2 ) = x1 x2 . Let us ? nd the indi? rence curve for Arthur that passes through the point (3, 4). First, calculate U (3, 4) = 3 ? 4 = 12. The indi? erence curve through this point consists of all (x1 , x2 ) such that x1 x2 = 12. This last equation is equivalent to x2 = 12/x1 . Therefore to draw Arthur’s indi? erence curve through (3, 4), just draw the curve with equation x2 = 12/x1 . At the point (x1 , x2 ), the marginal utility of good 1 is x2 and the marginal utility of good 2 is x1 . Therefore Arthur’s marginal rate of substitution at the point (3, 4) is ? x2 /x1 = ? 4/3. Example: Arthur’s uncle, Basil, has the utility function U ? (x1 , x2 ) = 31 x2 ? 10. Notice that U ? (x1 , x2 ) = 3U (x1 , x2 ) ? 0, where U (x1 , x2 ) is Arthur’s utility function. Since U ? is a positive multiple of U minus a constant, it must be that any change in consumption that increases U will also increase U ? (and vice versa). Therefore we say that Basil’s utility function is a monotonic increasing transformation of Arthur’s utility function. Let 34 UTILITY (Ch. 4) us ? nd Basil’s indi? erence curve through the point (3, 4). First we ? nd that U ? (3, 4) = 3? 3? 4? 10 = 26. The indi? erence curve passing through this point consists of all (x1 , x2 ) such that 31 x2 ? 10 = 26. Simplify this last expression by adding 10 to both sides of the equation and dividing both sides by 3. You ? d x1 x2 = 12, or equivalently, x2 = 12/x1 . This is exactly the same curve as Arthur’s indi? erence curve through (3, 4). We could have known in advance that this would happen, because if two consumers’ utility functions are monotonic increasing transformations of each othe r, then these consumers must have the same preference relation between any pair of commodity bundles. When you have ? nished this workout, we hope that you will be able to do the following: †¢ Draw an indi? erence curve through a speci? ed commodity bundle when you know the utility function. †¢ Calculate marginal utilities and marginal rates of substitution when you know the utility function. Determine whether one utility function is just a â€Å"monotonic transformation† of another and know what that implies about preferences. †¢ Find utility functions that represent preferences when goods are perfect substitutes and when goods are perfect complements. †¢ Recognize utility functions for commonly studied preferences such as perfect substitutes, perfect complements, and other kinked indi? erence curves, quasilinear utility, and Cobb-Douglas utility. 4. 0 Warm Up Exercise. This is the ? rst of several â€Å"warm up exercises† that you will ? nd in Wor kouts. These are here to help you see how to do calculations that are needed in later problems. The answers to all warm up exercises are in your answer pages. If you ? d the warm up exercises easy and boring, go ahead—skip them and get on to the main problems. You can come back and look at them if you get stuck later. This exercise asks you to calculate marginal utilities and marginal rates of substitution for some common utility functions. These utility functions will reappear in several chapters, so it is a good idea to get to know them now. If you know calculus, you will ? nd this to be a breeze. Even if your calculus is shaky or nonexistent, you can handle the ? rst three utility functions just by using the de? nitions in the textbook. These three are easy because the utility functions are linear. If you do not know any calculus, ? l in the rest of the answers from the back of the workbook and keep a copy of this exercise for reference when you encounter these utility fun ctions in later problems. NAME 35 u(x1 , x2 ) 21 + 32 41 + 62 ax1 + bx2 v 2 x1 + x 2 ln x1 + x2 v(x1 ) + x2 x1 x2 xa xb 1 2 (x1 + 2)(x2 + 1) (x1 + a)(x2 + b) xa + x a 1 2 M U1 (x1 , x2 ) M U2 (x1 , x2 ) M RS(x1 , x2 ) 2 4 a v1 x1 3 6 b 1 1 1 x1 bxaxb? 1 1 2 x1 + 2 x1 + a axa? 1 2 ? ? ? ?2/3 ? 2/3 ? a/b ? v1 1 x ? 1/x1 ? v (x1 ) ? x2 /x1 2 ? ax1 bx 1/x1 v (x1 ) x2 axa? 1 xb 2 1 x2 + 1 x2 + b axa? 1 1 x2 +1 x1 +2 x2 +b x1 +a a? 1 x1 x2 36 UTILITY (Ch. 4) 4. 1 (0) Remember Charlie from Chapter 3? Charlie consumes apples and bananas. We had a look at two of his indi? erence curves. In this problem we give you enough information so you can ? nd all of Charlie’s indi? erence curves. We do this by telling you that Charlie’s utility function happens to be U (xA , xB ) = xA xB . (a) Charlie has 40 apples and 5 bananas. Charlie’s utility for the bundle (40, 5) is U (40, 5) = 200. The indi? erence curve through (40, 5) includes all commodity bundles (xA , xB ) such that xA xB = 200. So 200 the indi? erence curve through (40, 5) has the equation xB = . On xA the graph below, draw the indi? erence curve showing all of the bundles that Charlie likes exactly as well as the bundle (40, 5). Bananas 40 30 20 10 10 20 30 40 Apples (b) Donna o? ers to give Charlie 15 bananas if he will give her 25 apples. Would Charlie have a bundle that he likes better than (40, 5) if he makes this trade? Yes. What is the largest number of apples that Donna could demand from Charlie in return for 15 bananas if she expects h im to be willing to trade or at least indi? erent about trading? 30. (Hint: If Donna gives Charlie 15 bananas, he will have a total of 20 bananas. If he has 20 bananas, how many apples does he need in order to be as well-o? as he would be without trade? ) 4. 2 (0) Ambrose, whom you met in the last chapter, continues to thrive on nuts and berries. You saw two of his indi? erence curves. One indifv ference curve had the equation x2 = 20 ? 4 x1 , and another indi? erence v curve had the equation x2 = 24 ? 4 x1 , where x1 is his consumption of NAME 37 nuts and x2 is his consumption of berries. Now it can be told that Ambrose has quasilinear utility. In fact, his preferences can be represented v by the utility function U (x1 , x2 ) = 4 x1 + x2 . (a) Ambrose originally consumed 9 units of nuts and 10 units of berries. His consumption of nuts is reduced to 4 units, but he is given enough berries so that he is just as well-o? as he was before. After the change, how many units of berries does Ambrose consume? 14.