Common Grammatical Errors Between You and Me

Common Grammatical Errors Between You and Me Let’s start with a pop quiz: Is there a grammar mistake in the title of my blog? If you answered â€Å"Yes† and believe that â€Å"Between You and I† would be correct, you have a lot of company. However, â€Å"Between You and Me† is actually the correct structure. Why do so many of us say â€Å"Between you and I†? My guess is that at some point, maybe around age 8, you may have said to your mother something like, â€Å"Jimmy and me are going to the store.† She corrected you: â€Å"It’s ‘Jimmy and I’† and something clicked in your head, and you thought that if you’re talking about yourself and another person, you should always say â€Å"I† instead of â€Å"me.† I’m here to set the record straight. There are pronouns that belong as the subject of a sentence. They are: I, you, she, he, we, you, they, it. Then there are pronouns that belong as the object of a sentence. They are: me, you, her, him, us, you, them, it. The first thing you need to know is not to mix these two groups together! â€Å"Him and I† for instance takes one pronoun from the object group and one from the subject group. Mixing and matching is always incorrect no matter where in the sentence the pronouns fall. â€Å"Between you and me† is a little trickier because our language uses â€Å"you† as both subject and object. Which group are we in here? Think about it: Would you say â€Å"Between us† or â€Å"Between we†? Of course you would say Between us. Now you know you’re in the object group which includes both â€Å"us† and (would you believe it?) â€Å"me.† A nice easy way to determine what pronouns to use, when you want to include two subjects or objects, is to try out the sentence with just one of the subjects or objects and see how it sounds. For example: â€Å"I [not me] went to the store.† â€Å"He [not him] went to the store. Therefore, â€Å"He and I went to the store.† Notice â€Å"he† and â€Å"I† are in the group with â€Å"we.† â€Å"We went to the store† is of course also correct. Another example: â€Å"Dave went to the store with him [not he].† â€Å"Dave went to the store with me [not I].† Therefore, â€Å"Dave went to the store with him and me† is correct. I realize for some of you that last sentence might sound completely wrong and ungrammatical. Between you and me, I think it’s time to change that perception. There’s a little quiz you can take at UsingEnglish.com: Quiz: Subject and Object Pronouns.   For more on this topic, see the article The English Personal Pronoun System. 🙂 Log in to Reply

Max Born and the Discovery of the Born Rule

Max Born and the Discovery of the Born Rule Max Born (December 11, 1882–January 5, 1970) was a German physicist who played an important role in the development of quantum mechanics. He is known for the â€Å"Born rule,† which provided a statistical interpretation of quantum mechanics and enabled researchers in the field to predict results with specific probabilities. Born won the 1954 Nobel Prize in Physics for his fundamental contributions to quantum mechanics. Fast Facts: Max Born Occupation: PhysicistKnown For: Discovery of the Born rule, a statistical interpretation of quantum mechanics.Born: December 11, 1882 in Breslau, PolandDied: January 5, 1970 in Gà ¶ttingen, GermanySpouse: Hedwig EhrenbergChildren: Irene, Margarethe, GustavFun Fact: The singer and actress Olivia Newton-John, who starred in the 1978 musical film Grease with John Travolta, is the granddaughter of Max Born. Early Life Max Born was born on December 11, 1882 in Breslau (now Wroclaw) Poland. His parents were Gustav Born, an embryologist at the University of Breslau, and Margarete (Gretchen) Kaufmann, whose family worked in textiles. Born had a younger sister named Kthe. At a young age, Born attended school at the Kà ¶nig Wilhelms Gymnasium in Breslau, studying Latin, Greek, German, history, languages, math, and physics. There, Born may have been inspired by his math teacher, Dr. Maschke, who showed the students how wireless telegraphy worked. Born’s parents died at an early age: his mother when Born was 4, and his father shortly before Born finished school at the Gymnasium. College and Early Career Afterwards, Born took courses on a variety of science, philosophy, logic, and math subjects at Breslau University from 1901–1902, following his father’s advice to not specialize in a subject too soon at college. He also attended the Universities of Heidelberg, Zà ¼rich, and Gà ¶ttingen. Peers at Breslau University had told Born about three mathematics professors at Gà ¶ttingen – Felix Klein, David Hilbert, and Hermann Minkowski. Born went out of favor with Klein due to his irregular attendance at classes, though he subsequently impressed Klein by solving a problem on elastic stability at a seminar without reading the literature. Klein then invited Born to enter a university prize competition with the same problem in mind. Born, however, did not initially take part, offending Klein again. Born changed his mind and later entered, winning the University of Breslau’s Philosophy Faculty Prize for his work on elasticity and obtaining a PhD in mathematics on the subject in 1906 under his doctoral advisor Carl Runge. Born subsequently went to Cambridge University for about six months, attending lectures by J. J. Thomson and Joseph Larmor. He went back to Gà ¶ttingen to collaborate with the mathematician Hermann Minkowski, who died after a few weeks due to an operation for appendicitis. In 1915, Born was offered a professor position at the University of Berlin. However, the opportunity coincided with the beginning of World War I. Born joined the German air force and worked on sound ranging. In 1919, after World War I, Born became a professor at the University of Frankfurt-am-Main. Discoveries in Quantum Mechanics In 1921, Born returned to the University of Gà ¶ttingen as a professor, a post he held for 12 years. At Gà ¶ttingen, Born worked on the thermodynamics of crystals, then became primarily interested in quantum mechanics. He collaborated with Wolfgang Pauli, Werner Heisenberg, and a number of other physicists who would also make groundbreaking advances in quantum mechanics. These contributions would help lay out the foundation of quantum mechanics, particularly its mathematical treatment. Born saw that some of Heisenberg’s calculus was equivalent to matrix algebra, a formalism that is used extensively in quantum mechanics today. Furthermore, Born considered the interpretation of Schrà ¶dinger’s wavefunction, an important equation for quantum mechanics, which had been discovered in 1926. Though Schrà ¶dinger had provided a way to describe how the wavefunction describing a system changed over time, it was unclear exactly what the wavefunction corresponded to. Born concluded that the square of the wavefunction could be interpreted as a probability distribution that would predict the result given by a quantum mechanical system when it was measured. Though Born first applied this discovery, now known as the Born rule, to help explain how waves scattered, it was later applied to many other phenomena. Born was awarded the 1954 Nobel Prize in Physics for his work on quantum mechanics, with particular emphasis on the Born rule. In 1933, Born was forced to emigrate due to the rise of the Nazi party, which caused his professorship to be suspended. He became a lecturer at Cambridge University, where he worked with Infeld on electrodynamics. From 1935–1936, he stayed in Bangalore, India at the Indian Institute of Science and worked with Sir C.V. Raman, a researcher who won the 1930 Nobel Prize in Physics. In 1936, Born became a professor of natural philosophy at the University of Edinburgh, staying there for 17 years until his retirement in 1953. Awards and Honors Born won a number of awards during his lifetime, including: 1939 – Fellowship of the Royal Society1945 – Gunning Victoria Jubilee Prize, from the Royal Society of Edinburgh1948 – Max Planck Medal, from the German Physical Society1950 – Hughes Medal, from the Royal Society of London1954 – Nobel Prize in Physics1959 – Grand Cross of Merit with Star of the Order of Merit, from the German Federal Republic Born was also made an honorary member of several academies, including the Russian, Indian, and Royal Irish academies. After Born’s death, the German Physical Society and the British Institute of Physics created the Max Born Prize, which is awarded annually. Death and Legacy After retiring, Born settled in Bad Pyrmont, a spa resort near Gà ¶ttingen. He died on January 5, 1970 at a hospital in Gà ¶ttingen. He was 87 years old. Born’s statistical interpretation of quantum mechanics was groundbreaking. Thanks to Born’s discovery, researchers can predict the result of a measurement performed on a quantum mechanical system. Today, the Born rule is considered one of the key principles of quantum mechanics. Sources Kemmer, N., and Schlapp, R. â€Å"Max Born, 1882-1970.†Landsman, N.P. â€Å"The Born Rule and Its Interpretation.†O’Connor, J.J., and Robertson, E.F. â€Å"Max Born.†

Examining the Challenges Faced By Teachers in the Inclusion of Pupils Assignment

Examining the Challenges Faced By Teachers in the Inclusion of Pupils with Autistic Spectrum Disorders (ASD) in the Mainstream C - Assignment Example 3 Causes of Autistic Spectrum Disorders ............................................................................ 4 Inclusion Defined †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 5 Characteristics of children with Autistic Spectrum Disorders †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 5 Expectations of teachers †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 7 Challenges Teachers face in the inclusion ASD pupils in mainstream classrooms .......... 7 Way forward to eliminate the challenges teachers face †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦... 12 Conclusion ............................................................. .............................................................. 15 Introduction Behavioural, Emotional and Social Difficulties (BESD) is a term which describes a range of complex and chronic difficulties experienced by many children and young people. Such people demonstrate features of emotional and behavioural difficulties such as being withdrawn or isolated, disruptive and disturbing, hyperactive, failing to make friends and lacking concentration and mature social skills; and presenting challenging behaviours. It may also cover people with anxiety, who self-harm, have school phobia or depression and those whose behaviour or emotional wellbeing are seen to be deteriorating (DFES, 2001). BESD and learning difficulties Children suffering from BESD face many challenges in learning such as struggling to overcome trust issues, hence fail to make relationships with others, ability to cope with school routines and relationships, failure to reason appropriately. As such, their emotional and behavioural difficulties make them fail to fit well in an environment where they can learn like other normal children. Their failure to fit in the learning environment contravenes with the learning theories advanced by different psychologists such as Bandura, Piaget, Pavlov, Thorndike and Skinner. These theories imply that learning can only take place where there is punishment or reward, observation, imitation, social interaction, attachment to others and pre-existing mental cognition (DCSF, 2007, Midgley, 2008, Cooper, 2008 and Bandura, 1999). Causes of BESD There are several causes of BESD, which are from within or outside the child. Inner causes are very much associated with biological traits within an individual child. However, external causes may include single parenthood, poverty, lack of attachment, parental conflicts, erratic discipline and neglect, (Jull, 2008). Autistic Spectrum Disorders (ASD) Defined Autistic Spectrum Disorders (ASD) is a lifelong disability that affect s how a person communicates with, and relates to, other people. It is a form of BESD which also affects how they make sense of the world around them since it affects ability to understand people, interpret events, communicate, and interact with others. This implies that, just like BESD does, ASD also plays a vital role in the learning of individuals. The term ‘Spectrum’ is used, because, autistic children experience a board band of problems which are grouped into having difficulty with social communication, social interaction and social imagination. For example, a child with autistic spectrum disorders is argumentative, disobedient, annoying, blames others for own mistakes, easily annoyed, resentful, vindictive, likes fighting, destructive, truant, a bully, intimidating, tormenting

Day of leisure Essay Example | Topics and Well Written Essays - 1000 words

Day of leisure - Essay Example To begin with, leisure is such a word that cannot be defined by a single statement, as there is so much to it than meets the eye. It is thus agreed that the best way to really cover its meaning is to define it as an activity, as time, and as a state of mind. Leisure as time defines leisure as being free from obligations or duties that may be either paid or unpaid or tasks that are essential for our existence. Leisure time in this case is seen as residual time. While there are those who see all the time that they spend away from work is leisure time, the truth is only a small percentage of this time is essentially spent for leisure. Some of the time spared after work can be used to do other activities that are crucial to our survival, say eating or sleeping. As an activity, leisure does not entail life maintenance tasks such as sleeping or general house cleaning. Leisure in this case means the activities that we engage in for relaxation, growth, meditating, competition, engaging in certain sport activity, painting and so on. These tasks are not done for our existence but for fun. As an activity, leisure is solely dependent on an individual. As a state of mind, it relates to the above definition in that leisure is dependent on an individual’s perception of what they are doing and whether they perceive that to be leisure. Concepts that come into play here include perceived freedom or competence, intrinsic motivation, and the positive effect of the activity. Remember it is the above effect that helps the individual knows whether a certain experience was pleasurable to them. To elaborate a little on the above, we would say that in perceived freedom, the individual is free to choose the activity they want to engage in without any obligation to do so. In intrinsic motivation, the individual is not influenced by any external force to engage in a given activity and that such motivation comes from within. Perceived competence refers to an individual

Music vs. Book Essay Example for Free

Music vs. Book Essay Books and music are not a direct comparison normally but when it comes to youngsters and their lives both have a very strong influence. When we are bored, it is the time we listen to music or read a book. These two are the common things we are doing in our leisure time. People should be influenced by music and book. Music can have both a positive as well as negative impact on an individual’s life. The nature and kind of music defines that what type of message they render on the youngster. While books of any type give you either eye opening or well meaning but misguided information on subjects ranging from the simplest subjects to the more sophisticated. Books can even be used by those who are looking for answers in life. Many people report finding the perfect book to answer the burning questions in their minds. Books are more limited: fiction like novels and short stories and non-fiction like memoir, history, biography, self help, and philosophy. Reading books require a larger share of our time. We cannot also do another thing while reading a book. We cannot read a book while washing clothes. Books are more intellectually stimulating and has bigger journey than music. On the contrary, music doesnt answer questions by itself. Music answers feeling or disturbed emotions looking for an outlet. It exists in an extraordinarily wide array of genres and styles like vocal music (song, choral music, and opera), solo instrumental, chamber, orchestral, band and etc. We will listen to the music we love countless times over the course of our lives. We can multitask while listening to music. We can listen to music while running or washing clothes. Music are more passion and emotional than books. Whether you want to listen to music or read a book, they can both give positive and negative influences, affect all kinds of age groups, and cause different views of the world.

Blessing’ by Imtiaz Darker and Presents From Pakistan by Moniza Alva :: English Literature

Blessing’ by Imtiaz Darker and Presents From Pakistan by Moniza Alva. The two poems are similar because they both give a different view about culture and religion. The two poems are about southwest Asian Comparison – ‘Blessing’ vs. ‘Presents From Pakistan’ I am going to compare 2 poems, which are called ‘Blessing’ by Imtiaz Darker and ‘Presents From Pakistan’ by Moniza Alva. The two poems are similar because they both give a different view about culture and religion. The two poems are about southwest Asian countries. The poets are also linked with the countries. I know this because of their names therefore their parents or relative can be from Pakistan or India. The poet’s show how they feel about other countries and hoe it affects them and their culture. Culture can be made up in different ways. Some religions like Islam on allow Muslims to enter Saudi Arabia. This makes up a religious culture. Some people live by their race or ethnicity like in north Europe many people like to live with people from there and people who are the same colour as them. In some countries some people don’t mind, they just live with a normal life style in their own world. In central Africa the majority of people live with a similar culture but t they are differed because of the languages spoken. I am going to explore the elements of the poems, to see how they go along with cultures and how they give us an insight to other culture. First of all the poem blessing is a poem that shows the feeling of someone seeing some villagers suffer because there is no water for them near by. He describes what it is to be like there and how the people feel. He also shows that the water is very precious to them. He says that a few drops of water are like money that can by a chocolate bar. He also says that it’s a gift from god, he explains why it is so pecous because the women have to walk miles to get to a rive or a well and they also have a big heavy pot on their heads. In addition ‘p.f.pk’ has a similar view but it shows how the narrator feels about herself and how her culture is affecting her lifestyle. She receives some of the finest clothes and jewellery from her relatives in Pakistan The narrator describes the gifts she receives from Pakistan as being very beautiful, but she doesn’t feel comfortable wearing them because she’s too modern and English. In the

Coase(1972) †durable and monopoly[2] Essay

R. H. COASE Universityof ChicagoLaw School that A SSUME a supplier owns the total stock of a completely durable good. At what price will he sell it? To take a concrete example, assume that one person owns all the land in the United States and, to simplify the analysis, that all land is of uniform quality. Assume also that the landowner is not able to work the land himself, that ownership of land yields no utility and that there are no costs involved in disposing of the land. If there were a large number of landownersand the price were competitively determined, the price would be that at which the amount demandedwas equal to the amount of land in the United States. If we imagine this fixed supply of land to be various amounts either greater or smaller, and then discover what the competitively determinedprice would be, we can trace out the demand schedule for American land. Assume that this demand schedule is DD and that from this a marginal revenue schedule, MR, has been derived. Both schedules are shown in Figure I. Let the total amount of land in existence be OQ. Then, if the price were competitively determined,the price would be OB (see Figure I). We now have to determine the price which the monopolistic landowner would charge for a unit of land in the assumed conditions. The diagramwould seem to suggest (and has, I believe, suggested to some) that such a monopolistic landownerwould charge the price OA, would sell the quantity of land OM, thus maximising his receipts, and would hold off the market the quantity of land, MQ. But suppose that he did this. MQ land and money equal to OA X OM would be in the possession of the original landowner while OM land would be owned by others. In these circumstances, why should the original landownercontinue to hold MQ off the market? The original landownercould obviously improve his position by selling more land since he could by this means acquire more money. It is true that this would reduce the value of the land OM owned by those who had previously bought land from him-but the loss would fall on them, not on him. If the same assumption about his behaviour was made as before, he would then sell part of MQ. But this is not the end of the story, since some of MQ would still remain unsold. The process would continue as long as the original landowner retained any land, that is, until OQ had been sold. And if there were no costs of disposing of the land, the whole process would take place in the twinkling of an eye. 143 144 THE JOURNAL OF LAW AND ECONOMICS Figure D I z mj A † _ o Q : D 0 M Q QUANTITY MR It might be objected to this supposedbehaviourunder which land is sold in separate transactions involving blocks of land, probably of diminishing size, that it would be even better if the landowner sold the land by infinitesimal units, thus maximising his total revenue. But this is neither here nor there. Whatever the intermediatesteps are assumed to be, OQ land will be sold. And given that OQ is going to be sold, the value of a unit of land is going to be OB and given this, no buyer of land will pay more than OB for it. Although the demand schedule may be correctly drawn in that, if the quantity of land is OM, the price would be OA, the landownerwould find himself in the position that, if he were charged more than OB, he would sell nothing. The demand schedule facing the original landowner would be infinitely elastic at the competitive price and this even though he was the sole supplier. With complete durability, the price becomes independent of the number of suppliers and is thus always equal to the competitive price. DURABILITYAND MONOPOLY 145 How could the landowner avoid this result? He could do this and obtain the price OA from the sale of OM land by making special contractual arrangements with the purchasersof land by which, as a condition of sale, he agreed to hold unsold in perpetuity the quantity of land MQ. Alternatively, he could agree to buy back any land that was offered to him in the future at a price just under OA, thus making it against his interest to sell more than OM land. Another way in which essentially the same result could be obtained would be for the landowner not to sell the land but to lease it for relatively short periods of time. It would then be comparatively easy for him to assure lessees that no increasein supply will occur during the lease period either by entering into all leases at the same point in time, or by announcing that he would not change the rental price during the lease period or by agreeing to adjust the prices charged to existing lessees if a lower charge is made to others during the lease period. In any case, even if such contractual arrangementscannot be made, lessees have some reason to believe that the landownerwill not, in fact, lease more than OM land by charging lower prices for some of the unutilised land (after having entered into contracts at OA) because it would not be in his self-interest to do so. With this kind of leasing, the total earnings of the landowner depend largely on the rents at which land can be leased in future periods and the yield from these rents will tend to be higher the greater the confidence the lessees have that the amount of land leased during the lease period will not be more than OM. That confidence would obviously be weakened and the rent that could be charged in future reduced, if extra land above OM is leased during the current lease period. It is this which would tend to give lessees confidence that such extra land will not be leased. Of course, the negotiating of such rental contracts for short periods for each piece of land might be extremely costly and indeed might be so costly as to offset the gain in revenue from the limitation in the amount of land utilised. But, if not too costly, leasing would tend to ensure that only OM land was utilised. Another alternative would be for the landowner to give MQ land to someone who is less concernedabout money-makingthan he is. For example, the landowner might donate MQ land to the government to be used â€Å"in the public interest†. Some such contractual or institutional arrangementsas these would enable the landowner to charge the monopoly price. But in the absence of such arrangements,the price charged will be the competitive price. It may be thought that this argument does not apply if the permanently durable good is produced by a monopolist supplier rather than being part of nature. But this is not so. Assume that the demand schedule for this good is DD, representingthe present value of its future services for various quantities of the good. Assume that it is produced by a single firm and that marginal costs are constant. MR representsthe marginal revenue schedule and MC the 146 THE JOURNAL OF LAW AND ECONOMICS marginalcost schedule. All schedulesare shown in Figure II. Cost and demand conditions are assumed to remain the same in the future. In effect, this means that if the competitive output, OQ, is produced originally, nothing will be producedin later periods. A similar argument to that used in the case of the landowner will demonstrate that the price that this producer will charge (assuming outright sale) will not be OA, the apparentmonopolyprice, but will be OB, since the demand for his output of this good is infinitely elastic at this price up to the output OQ. Again, it is possible to introduce conditions into the contract for sale which would avoid this. An agreement not to produce any more of the good afterOM has been produced,an offer to buy back the good at any time in the future at a price just under OB, or the use of leasing rather than outright sale, would all have the effect of making it possible to charge OA (just as similararrangementswould enable the monopolist landowner to achieve the monopoly price). Figure 1T A QB CL MC 0 /l M IA ! Q M-r-rvMR ~U-lM 11 I DURABILITYAND MONOPOLY 147 Some of these arrangementsmay not be legally enforceableand, in any case, are likely to involve additional costs as against those incurredin outright sale. There is, however, an alternative which was not available to the hypothetical landownerand that is to make the good less durable. This may raise the costs of providing the stream of services affordedby the durable good, may result in charges over the future which have a present value greater than OA and a supply of services less than that affordedby OM of the durable good. Profits will also be less than they would be if this firm could sell OM at price OA. But this is not a real alternative in the absence of the various contractual arrangementsmentioned. If the durable good is produced, the output will be OQ at price OB. If a less durable good is produced, a higher price can be charged because consumers do not have to fear an increase in supply if they buy at the monopoly price. The productionof a less durable good as against a more durable good is very similar to a policy of leasing since, by making the good less durable,the producersells the services providedby the good for short periods of time (because the good wears out) whereas in leasing the same result is achieved by selling the services of a given durable good in short period segments. The reason why making a good less durable enables a producer to charge higher prices than he could if the good were extremely durable is that it makes it in his self-interest not to increase supply since, if he did this, it would tend to lead consumers to believe that he might do this again in the future, a belief which would make it impossible for him to charge the monopoly price (as was explained in the case of land for leasing). Another circumstance reinforces the conclusion that making a good less durable will enable the monopolist producer to charge a higher price. What a consumer has to fear is an increasein supply during the period in which he (or someone to whom he transfers the good) is deriving services from the good. The less durable the good, the shorter is this period. But the shorter the period that the supplierhas in which to increase supply, the greater will be the additional costs of increasing supply. Lessened durability reduces the gain from an increase in supply and thus reduces the likelihood that it will occur. The analysis up to this point has proceededon the assumption that marginal costs were constant for the durable good. It needs modification if marginal costs rise with increases in the rate of output. With constant marginal costs, production would take place in the first period and would then cease. With rising marginalcosts, productionwould extend over a period of time, although, since price would fall as the stock of the durable good increased, the rate of production would decrease as time passed. Since sales occur sequentially, in setting the price in later periods, the producer will not take into account the fall in the value of the existing stock (which is, of course, owned by others). To this extent the behaviourof the producerwill inevitably be com- 148 THE JOURNAL OF LAW AND ECONOMICS petitive in character and the stock (and price) will move towards the competitive level. Because of this, consumers will pay less (and the producer’s profits will be less), than they would if, throughan agreementas to the total quantity that could be produced or an agreement on a re-purchaseprice or through the use of leasing, production were limited to the monopoly output. Reducing the durability of the good is an alternative policy which might be more profitable (as was argued in the case of constant marginal costs). There is an additional element introduced by the fact that production will continue over a period of time. The producerwill have to consider the effect his actions have on the expectations of consumersabout his actions in future periods. He can in general be counted upon to refrain from expanding output when any gain that he might make through disappointingconsumers’expectations (if they thought he would restrict production) would be less than the loss he would suffer in future from not fulfilling them. However, there is no reason why conditions should not be such that it would always pay to disappoint consumers’expectations of a restrictionin output (if they held such expectations) and in such circumstances,output in all periods would be such as to make marginalcost equal to price (if some of the arrangementsmentioned earlierwere not used). This result is particularly likely since, in the assumed conditions of rising marginal costs, prices and production will decline over time. Even in conditions in which the producer would not wish to disappoint consumers’expectations of a restrictionin production, it is by no means easy to say how things would work out in practice since neither the producer nor the consumers would necessarily have clear, or the same, ideas about the future. A full analysis of this situation would be very complicated but could not affect the main contention of this note, that with durability some contractualor institutional arrangementof the type mentioned earlier may be a less costly and perhaps the only way of achieving a monopoly price or that reduceddurability may prove to be a better way out of the difficulty. Oneother qualification should be mentioned. The analysis up to this point has assumed that demand and cost conditions remained unchanged, in effect, that the economy was in a stationary state. The present value of any given amountof the durablegood will always take into account future demands,but if demand remains the same, the present value of its future services (for any givenamount of the durablegood) will remain the same as time passes. However,with increasing demands present values will rise and future production will be greater than has been assumed (with constant marginal costs there willbe some future productionas against none). This enhances the importance ofthe considerationsdiscussed in the previous paragraph,since the future loss fromnot restricting output will tend to be greater. Whether the expected increasein demand would be sufficient to lead the producer to restrict output DURABILITYAND MONOPOLY 149 in earlier periods depends on its extent, on the rate of discount, on the nature of the cost schedule, on whether costs are expected to increase in the meantime (and by how much) and on the confidencewith which these views about the future are held. An expected increase in demand may or may not obviate the need for the contractual arrangementsmentioned earlier (or a reduction in durability) if the monopolist producer of a durable good is to secure the monopoly price. The business practices which I have suggested as devices which a monopolist supplier might use to cope with the problem of durability may, of course, be adopted for reasons which have nothing to do with my argument. A land developer, in selling land on which houses are to be built, may agree to hold neighbouringland off the market to improve the amenities; the supplier of a durable good may agree to buy it back at some specified price in the future because consumers are willing to pay for this reduction in risk; leasing is often a less costly way for the consumer to obtain the services of a durable good; a reduction in durability may enable a supplier to provide a given stream of services at lower cost. Even when these practices are adopted to avoid the consequencesof durability on demand, they are not necessarily undesirable-an agreementnot to produce more than a certain quantity may be a necessary condition in the competitive supply of a durable good for which marginalcost is less than average cost. Nevertheless, these business practices, including reduced durability, may be essential elements in securing a monopolistic price. However, these practices have their costs and they may not, in fact, always be feasible. Furthermore,some of the contractual arrangements will not be enforceable over a long period. In such circumstances, the competitive outcome may be achieved even if there is but a single supplier.