text:
History of Islamic Civilization/The Formative Period of Islam

History of Islamic Civilization

Abu Bakr
EARLY LIFE

Sayyiduna Abu Bakr real name was Abdullah, and he was given the title of "As Siddique" or"Testifier to the Truth." His father, 'Uthman, was known as Abu Quhafah and his mother, Salma, was known as Ummul Khair. He was two and a half years younger than Sayyiduna Rasulullah. He was the first among the Sahaba to accept Islam.When he told that one to his family his son Sayyiduna Abdur Rahman did not accept him later on. He opposed him and separated away from him but Sayyiduna Abu Bakr did not leave his faith. Sayyiduna Abu Bakr was the first person who used to call people openly toward faith so all the Quraysh people hate them because of that he lost his business and became poor. When Sayyiduna Abu Bakr own clan people hated him and tortured by them he went to Ethiopia. There he meet Ibn al Dhugna by his help he came back to Mecca later on Sayyiduna Rasulullah married Sayyiduna Abu Bakr daughter Aiysha siddiqua. Sayyiduna Abu Bakr accompanied Sayyiduna Rasulullah during the Hijrah to Madinatul Munawwarah. Sayyiduna Abu Bakr was a merchant. He freed many slaves, including Sayyiduna Bilal and Sayyiduna Umayyah bin Qahaf. He participated in all the battles in which Sayyiduna Rasulullah had to fight the Kuffar.

Sayyiduna Abu Bakr loved his faith more than anything else. At the Battle of Badr, his son, Sayyiduna Abdur Rahman, was fighting on the side of the Kuffar. After accepting Islam, Sayyiduna Abdur Rahman said to his father, "O Father, at Badr, you were twice under my sword, but my love for you held my hand back." To this, Sayyiduna Abu Bakr replied, "Son, if I had you only once under my sword, you would have been no more." He was so uncompromising in his faith.

At the time of the Battle of Tabuk, he donated all his wealth to the war effort, and when Sayyiduna Rasulullah asked him, "What have you left for your family,?" he replied, "Allah and His Rasool."

AS A CALIPH

It is very strange that the successors of all the Prophets were selected by almighty Allah but in case of the last Prophet Sayyiduna Rasulullah it was elected by a bunch of aristocrat Arabians[when all the other faithful followers were busy in the tadfeen (burial) of Rasulalla].....during a secret meeting at a thatched hut in Suqaifa.....and subsequently since sayyiduna Abu Bakr,  was the oldest among all others who attended that clandestine meeting,he was elected as the Caliph.

After his election as the Caliph, Sayyiduna Abu Bakr addressed the Muslims with these words: "O People! I have been chosen by you as your leader, although I am no better than any of you. If I do any wrong, set me right. Listen, truth is honesty and untruth is dishonesty. The weak among you are the powerful in my eyes, as long as I do not give them their dues. The powerful among you are weak in my eyes, as long as I do not take away from them what is due to others.

"Listen carefully, if people give up striving for the Cause of Almighty Allah, He will send down disgrace upon them. If people become evil-doers, Almighty Allah will send down calamities upon them.

"Obey me as long as I obey Allah and His Rasul. If I disobey Allah and His Rasul, you are free to disobey me."

Such was the first Caliph of Islam. Indeed, the world would be a better place to live in, if we had leaders like Sayyiduna Abu Bakr.

Sayyiduna Abu Bakr now sent Sayyiduna Usaman on the expedition to Syria to fight the Romans, even though he had to attend to all the internal problems of the Islamic State.

The news that Sayyiduna Rasulullah had passed away, made some new Muslims think that the Islamic State would crumble and they refused to pay the Zakaah. These new Muslims could not yet get used to their faith and its requirements until then. Sayyiduna Abu Bakr declared, "By Allah! Even if a single thread is due from a man, he must give it. If he refuses, I will declare war against him."

RENEGADES AND IMPOSTERS

Some others became imposters and renegades. Tulaiha, Musailimah, Aswad Ansi and a woman named Sajah claimed that they were prophets and caused a great deal of confusion. Sayyiduna Abu Bakr was quick to take action against these imposters. Sayyiduna Khalid bin Walid was sent to deal with Tulaiha who fled to Syria and later became a Muslim. Maalik bin Nuwarah was killed. Sayyiduna Ikramah and Sayyiduna Surahbil were sent to take action against Musailimah, but they were defeated. Sayyiduna Abu Bakr sent Sayyiduna Khalid bin Walid to tackle the notorious Musailamah who married Sajah. In the fight that followed, Sayyiduna Wahshi killed Musailamah. Musailamah and Aswad Ansi also claimed to be prophets while Sayyiduna Rasulullah was alive. Aswad was killed by the Muslims of Yemen.

Sayyiduna Abu Bakr swift and bold steps saved the Islamic State from the serious danger of chaos and confusion. He could now attend to other urgent problems.

ERA OF CONQUESTS

During his Khilaafat, Sayyiduna Abu Bakr had to take action against the Iranian Empire. The Emperor of Iran, Khusrou Parvez, was killed by his son, Shirooya, and the whole empire fell into chaos and disorder. Hurmuz, the Persian governor of Iraq, was very hostile to the Arabs and he was also cruel to the Muslims living in that area. Sayyiduna Abu Bakr sent Sayyiduna Muthamia to take action against the Iranians in Iraq. His forces were not enough and Sayyiduna Khalid bin Walid was then sent with reinforcements. The Muslim army captured vast areas of the Iranian Empire in several battles.

Sayyiduna Abu Bakr then turned his attention to the Romans who were causing trouble in the North-West frontier. Sayyiduna Abu Bakr sent 4 separate armies under Sayyiduna Ubaidah bin Jarrah, Sayyiduna Amr Ibnul As, Sayyiduna Yazid bin Abu Sufyaan and Sayyiduna Surahbil bin Hasnal to deal with the Roman power.

The four armies joined into one unit to face the Romans more effectively. The Romans had amassed 150 000 soldiers, but the total Muslim army was only 24 000. Reinforcements were requested. Sayyiduna Abu Bakr asked Sayyiduna Khalid bin Walid to take charge of the Iraqi front and Sayyiduna Muthanna to rush to the Syrian front to help fight the huge Roman army. The armies met in Yarmuk after Sayyiduna Abu Bakr passed away. In this battle, the Romans were totally defeated.

PASSES AWAY

Sayyiduna Abu Bakr fell ill at this time and passed away on the 21st of Jamadi-ul-Aakhir 13 A.H. (22 August 634). His rule lasted 2 years and 3 months. He was 63 years old. One of the many contributions of Sayyiduna Abu Bakr was the collection and compilation of the Holy Quran.

PERSONAL LIFE

He lived a very simple, pious and upright life. He was a true servant of Almighty Allah and a meticulous follower of Sayyiduna Rasulullah. He wore ordinary clothes and his meals were very simple. He attended to house-hold work and would go out at night and seek the poor and destitute. Humility and modesty were the keynotes of his character. He felt embarrassed when people showered praises on him or showed him immense respect. He often fasted during the day and spent the whole night in Salaah and meditation. He was a great orator and a master of genealogy (one who can trace a person's family line). In personal life, he was a Saint. He used all his powers to promote the interest of Islam and the good of people.

Umar
Hazrat Umar Farooq (Radi Allah Unho)

ELECTION

Before he passed away, Sayyiduna Abu Bakr (radi Allahu anhu) consulted the senior Sahaba and elected Sayyiduna Umar (radi Allahu anhu) as the second Caliph of the Muslims. His election was partially democratic....contrary to the selection process,as it was with the prophets and their successors....the prophets and their successors were selected by almighty Allah but Umar's, Bakr's and uthmam's caliphate were bi-partisan election by a bunch of Arabian aristocrats.

EARLY LIFE

He was the son of Khattab and is famous in Islamic history as "Al Farooq" or "One who Distinguishes between Right and Wrong." His acceptance of Islam is also very famous.

AS A CALIPH

Sayyiduna Umar (radi Allahu anhu) was a very brave and straight-forward person. He was tough and uncompromising in Islamic principles. He was a great and talented ruler. During his Khilaafat, vast areas of the Roman and Persian empires and the whole of Egypt were brought under Islamic rule. He was also a gifted orator. He was very concerned for the welfare of the Muslims. He left a honourable legacy for Muslims after him. The Holy Quran was given to him by Sayyiduna Abu Bakr (radi Allahu anhu) for safe-keeping.

APPOINTS NEW COMMANDER

Sayyiduna Umar (radi Allahu anu) was a strong disciplinarian. He noticed the tremendous popularity of Sayyiduna Khalid bin Walid (radi Allahu anhu). He felt that people will lose trust in Almighty Allah and put all their trust in Sayyiduna Khalid bin Walid (radi Allahu anhu). He feared that the people may think too highly of him, thereby possibly increasing the self-esteem of Sayyiduna Khalid bin Walid (radi Allahu anhu) which would also breed arrogance, so he removed Sayyiduna Khalid (radi Allahu anhu) and appointed Sayyiduna Abu Ubaidah bin Jarrah (radi Allahu anhu) as the Commander in Chief of the Muslim army. Sayyiduna Khalid bin Walid (radi Allahu anhu) happily accepted the orders of Sayyiduna Umar (radi Allahu anhu) and then served as an ordinary soldier. This is an example of the Islamic teachings of obedience to leadership!

DEFEAT OF THE PERSIANS

Sayyiduna Khalid bin Walid (radi Allahu anhu) had left Sayyiduna Muthanna (radi Allahu anhu) in command of the Muslim forces on the Iraqi front when he rushed to Yarmuk. Sayyiduna Muthanna (radi Allahu anhu) was finding it difficult to counter the enemy and went personally to Madinatul Munawwarah to ask Sayyiduna Abu Bakr (radi Allahu anhu) for re-enforcements. Sayyiduna Abu Bakr (radi Allahu anhu) had by that time passed away. Sayyiduna Muthanna (radi Allahu anhu's) absence from the Iraqi front made things worse there. The Iranians regrouped under the command of Rustam and recaptured the lands taken by the Muslims. Rustam sent 2 columns of his army, one to Hirah and the other to Kaskar.

Sayyiduna Umar (radi Allahu anhu) sent Sayyiduna Abu Ubaidah (radi Allahu anhu), as Commander, to deal with the situation. Both the Persian columns were defeated. Rustam sent an even larger army and defeated the Muslims.

Sayyiduna Umar (radi Allahu anhu) raised another army and defeated the Persians. But the Persian court sent yet another larger army, and forced Sayyiduna Muthanna (radi Allahu anhu) to withdraw. The report of the new situation was sent to Sayyiduna Umar (radi Allahu anhu) and reinforcements under the command of Sayyiduna Saad bin Abi Waqqas (radi Allahu anhu) were sent.

The Persian and Muslim army met at Qadisiyah. After a long battle on several fronts, the outnumbered Muslim army defeated the 120 000 Persian soldiers and recaptured Hirah and their areas in the year 14 A.H. (636 C.E).

DEFEAT OF THE ROMANS

Muslims laid siege to Damascus during Sayyiduna Abu Bakr (radi Allahu anhu's) rule as Caliph. It continued, after he passed away, and lasted 70 days during the rule of Sayyiduna Umar (radi Allahu anhu). After the long siege, Sayyiduna Khalid bin Walid (radi Allahu anhu) took the Romans by surprise and entered the city. The Governor surrendered and a peace treaty was signed.

CONQUEST OF JERUSALEM

Meanwhile, Sayyiduna Amr ibn As (radi Allahu anhu) was laying siege to Jerusalem. Sayyiduna Khalid, Sayyiduna Abu Ubaidah and other Sahaba (radi Allahu anhumul ajma'in) also joined him. The Christians had little hope and decided to give in. They also suggested that the keys of Jerusalem be given to Sayyiduna Umar (radi Allahu anhu) himself personally. Sayyiduna Umar (radi Allahu anhu) went to Jerusalem. An agreement was signed that guaranteed the safety of the city and the safety of the Christians.

ASSASSINATION

A Persian non-Muslim, named Firoz and nicknamed "Abu Lulu," complained to Sayyiduna Umar (radi Allahu anhu) about his master, Sayyiduna Mughirah bin Shuba (radi Allahu anhu), who imposed tax on him. Sayyiduna Umar (radi Allahu anhu) told Firoz that the tax was reasonable. This made Firoz angry. The next day, during the Fajr Salaah, he stabbed Sayyiduna Umar (radi Allahu anhu) 6 times in the back, severely wounding the Caliph. Sayyiduna Umar (radi Allahu anhu) passed away 3 days later in 23 A.H. He was 63 years old. He ruled the Islamic State for 10 years, 6 months and 4 days.

REFORMS

In a short space of 10 years, Sayyiduna Umar (radi Allahu anhu) had been well-known for his outstanding achievements and reforms in Islam. Some of these reforms were:- He established the "Baitul Maal" (People's treasury for the state and public). Judicial courts of Justice were set in the country. Judges and Magistrates handled all cases. Establishment of an army headquarters for the defence of the country. Construction of roads and canals. Schools were established. Salaries for Imams, Mu'azzins and Ustaads were organized. Masjids were improved and built in Makkatul Mukarramah and Madinatul Munawwarah. This included facilities for the Haajis. Police Stations and prisons were built. Establishment of the first Islamic Lunar calendar beginning from the Hijrah. Proper weights and measures introduced. Population census established. Built orphanages and welfare homes. Established proper punishment system and banned slavery.

PERSONAL LIFE

Simplicity and devotion were the main characters of Sayyiduna Umar (radi Allahu anhu). He used to wear clothes that had many patches and yet received Governors, convoys and diplomats. He took just enough allowance from the State to have a simple meal and wear simple clothes. At times he was very poor. He used to visit the old people and sick and even do their house work. He used to visit the houses of the soldiers and inquire about their families. He stayed awake at night in Salaah and often kept Fast. He always supported and upheld the cause of Islam, with his wisdom, energy, dynamism, bravery and little wealth.


text: User talk:Uk.woo

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Uk.woo


text:
History of Islam/The Mutazilites-Asharites debate

1. Basic tenets of the Mutazilite teaching and its early endorsement by Abbasid Caliphs

According to the well know sources on Mutazilism, there are five basic doctrines  or principles of Mutazilism. The first is the Divine unity, al-tawhid in Arabic. The second is the Divine justice, al-`adl. The third is the Divine promise and threat, al-wa`d wa-al-wa`id. The fourth is the place between the two places, al-manzilah bayn al-manzilatayn. The fifth is commanding the good and prohibiting the evil, al-amr bi al-ma`ruf wa-al-nahy `an al-munkar.

The first Mutazilite tenet, the Mutaziltes understand that God is One and His oneness makes Him differ from all existent beings created by Him. The Mutazilites deny any similarity between God and His created creatures. Due to their understanding of God's oneness, the Mutazilites interpret metaphorically all the quranic verses indicating any similarity or likeness between God and His creatures such as the Koranic verses stating about God's hands, eyes, sitting on the throne and face. For the Mutazilites, the quranic anthropomorphic verses should be interpreted metaphorically because if those verses of the quran are understood literally, they attribute some similarities between God and His creatures. The literal understanding of the Koranic anthropomorphic verses is very much against the tenet of God's oneness in the eyes of the Mutazilites.

God's transcendentalism is indeed emphasized emphatically by the Mutazilites. They are very strict and serious against the anthropomorphists, the mushabbihah or the mujassimah, among Muslims. Because of their strict adherence to God's transcendentalism, their opponents called them al-mu`atillah (those who denied God's attributes). The Mutazilites replied to their opponents that they themselves do not deny God's attributes but what they indeed deny from God is His attributes are different from His essence. For the Mutazilites, God's essence does not differ from God's attributes. In other words, God's attributes are identical and inseparable from His essence. For this type of understanding regarding the relationship between God's essence and His attributes, the Mutazilites say and uphold that God is powerful by His essence, and in Arabic said, Allah qadir bi-dhatih. Meanwhile, the opponents of the Mutazilites like the Asharites understand and state that God is powerful with His power, Allah qadir bi-qudratih.

In line with their understanding of God's transcendentalism, the Mutazilites deny that God can be seen even by the peoples of Paradise in the hereafter. The Mutazilites argue that if the peoples of Paradise can see God, God must be in any material form since human eyes can only see the material things or forms. Since God is a non-material being, human eyes are impossible to see Him even in the Paradise. The Mutazilites do not differentiate between the natures of human beings in this world and their natures in the hereafter. For the Mutazilites, human eyes in this world are impossible to see God as evident from the Prophet Moses wanted to see God with his own eyes and he could not see God. What is impossible for human eyes to see in this world is also impossible for human eyes to see in the hereafter. For the Mutazilites, human eyes need light, proper distance and location to see the seen object. Since God is unseen being, He cannot be seen by human eyes. It is impossible for human eyes to see God because God is an immaterial being, unseen being.

The Mutazilites deny the Christian concept of Divine trinity. The Trinity in Christianity states the three persons of the Godhead namely the Father, Son, and Holy Spirit. For the Mutazilites, the principle of the Trinity is contrary to God's transcendentalism that stresses nothing similar or identical with God either in His essence or His attributes.

The Mutazilites deny that the Koran is eternal and the speech of God. For them, the Koran was created by God like other created creatures. The Mutazilites deny the uncreatedness of the Koran because for them only God is eternal. Other beings are temporal, transient and finite. God is eternal and infinite. They want to defend the Divine unity when they deny the uncreatedness of the Koran. The Koran is limited and finite because it consists of letters and sentences understood by human minds. The Koran was revealed for human beings. Human beings are limited and finite. Whatever is created by God is limited and finite. Hence the Koran is limited and finite because it was created by God to be the book of guidance to all human beings.

The second tenet of the Mutazililtes is the Divine justice. They understand that God is indeed just and fair to all created creatures. To prove their understanding of God's justice, the Mutazilites advocate the concept or principle of human free will. The concept stresses that man is free to choose and act on what he has chosen. Nothing forces man either to do or not to do if he decides either to do or not to do. Man is free to carry on his intended plan or intention. The Mutazilites totally disagree with the Jabarites who advocate human predestination. The Mutazilite concept of human free will is very identical and similar with the Qadarite concept of human free will. The Qadarites are the opponents of the Jabarites in their understanding of the human power and will and God's power and will. For the Jabarites, man has no will and power to act on his own choice or preference. Man has to rely or depend on God's will and power before he is able to will and act. For the Qadarites, man has his own will and power created by God for himself to will and act or not to will and not to act. Moreover, man is free to will and to act on whatever he wills. If man decides on certain actions, he can act on them. With the power created by God in man's nature, man is capable of willing and acting or doing according to his own wishes. Since man is free from any compulsion, he consequently deserves the rewards or punishments based on his choices and actions. If man does the bad and evil actions, he deserves the punishments from God, and if man does the good and useful actions, he deserves the rewards from God. The Mutazilites deny any injustice attributed to God. God is just and He does not want or He does not will injustice. Injustice takes place because of human beings, not because of God. Indeed, God does not do injustice to any human being.

To defend the Divine justice, the Mutazilites deny the concept or the principle of Divine intercession in the hereafter. For the Mutazilites, the Divine intercession contradicts the Divine justice. The Divine intercession in the hereafter is said to be for the Muslims who committed the grave sins and tney became the grave sinners before they died. For the Mutazilites, God will not intercede or help the grave sinners and God will put them in the Hell because they chose to commit the grave sins prohibited by God. God will not help them. God will judge them according to their own deeds, bad or good deeds. In other words, because of the Divine justice, God will punish the grave sinners in the Hell. The opponents of the Mutazilites like the Asharites uphold the view that God will intercede the grave sinners and take them out from the Hell after they have completed their punishemnts in the Hell.

In line with the Divine justice, God does the better and best things for human beings. For examples, God created human beings in the best form of human bodily structure in comparison with animals. God granted human beings with minds that are not available among animals. God sent His prophets to guide human beings and sent down His books of revelations to human beings from time to time until the last and final revelation revealed to the last and final prophet named Muhammad in the seventh century in Arabia. He was sent by God to all human beings.

The Mutazilite concept of God's doing the better and the best things for human beings is known in Arabic as fi`l al-salah wa-al-aslah lil-nas. God showed human beings the two different ways or broadways namely the good and the evil ways. The good way is leading to the good life in this world and then in the hereafter. Meanwhile, the evil way is leading to the evil and miserable life in this world and then in the hereafter. In other words, God showed and proved to human beings the two opposite ways, God's way and Satan's way. Human beings who follow God's way are going to the Paradise in the hereafter and human beings who follow Satan's way are going to the Hell in the hereafter. Human beings have no any reason or word to blame God for their own bad and miserable fates or destinations in this world and then in the hereafter since God did the better and the best things for human beings. God's just and fair actions are evident and apparent to all human beings.

The third Mutazilite tenet is the Divine promise and threat. This one is very much to complement the second Mutazilite tenet. According to the Mutazilites God promises human beings with the rewards if they obey God's commands and God threats human beings with the punishments if they disobey God's commands. God keeps and fulfills all His promises to all human beings. God also will punish all human beings who have disregarded and disobeyed God's commands. There is no possibility of thinking and assuming that God does not keep His promises. The Mutazilites understand that God makes the promises and He will fulfill them. God makes the threats and He will accomplish His threats. For this third tenet of the Mutazilites, the opponents of the Mutazilites like the Asharites claimed that the Mutazilites have imposed on God the duty or obligation to fulfill His promises and to carry out His threats. The Mutazilites reply to their opponents that God Himself imposes on Himself to keep all His promises and to carry out all His threats. Hence human beings cannot claim that God does not keep His promises. Not keeping the promise is bad among human beings and in God's divine law, and God does not do bad action. Fulfilling the promise is good and commanded by God's divine law and God fulfills His promises because it is a good thing to do. God does not do the bad, evil and ugly things. Human beings do all the bad, evil and ugly things if they choose to disobey God's commands.

The fourth Mutazilite tenet is the place between the two places. It means that the Muslims who have committed the grave sins cannot be placed among the Muslims nor among the disbelievers. The grave sinners have to be placed between the Muslims and the disbelievers. The grave sinners cannot be equated with the disbelievers because they still have faith in their hearts while the disbelievers do not have any faith in their hearts. The grave sinners cannot be equated with the Muslims because they have committed the grave sins prohibited by God. Hence, the Mutaziltes introduce the third place for the Muslims who have committed the grave sins. Their place is between the disbelievers and the Muslims who do not commit the grave sins.

The fifth Mutazilite tenet is commanding the good and prohibiting the evil. This one is for human beings to attain the rewards from God since God promises human beings with the rewards if they do the good actions in this world. Commanding human beings to do the good actions is a good action. Prohibiting human beings from doing the evil actions is a good action. If all Muslims command themselves and others to do the good actions, they are all good Muslims who deserve to attain what God has promised for them. If all Muslims prohibit themselves and others from doing the bad and evil actions, they are all good Muslims who deserve to attain what God has promised for them. The fifth Mutazilite tenet is related to commanding the good and prohibiting the evil among human beings for human peaceful life and prosperity in this world. If all Muslims implement the Mutazilite fifth tenet, there would be no crimes and criminals in all Muslim societies.

The Abbasid caliphs known in Muslim history who have endorsed the five basic tenets of Mutazilism are al-Ma'mun, al-Wathiq and al-Mu`tasim.

'2. Reaction of the scholars and the development and basic tenets of the Asharites' The Mutazilite-Asharite debate took place between the student and teacher of Mutazilism. The teacher was Abu Ali al-Jubbaii who was the leader of the Mutazilite school of Basra. His student was Abu Hasan al-Ashari. Al-Ashari was not convinced by his teacher regarding the Mutazilite concept of free will and the Mutazilite concept of God's doing the better and the best things for human beings.

According to the Mutazilite concept of free will, man is free to decide and strive for his future and final destination. If man does the good deeds in his life and dies, he is surely going to attain the good life in the hereafter i.e. he will be in the Paradise. It is obligatory upon God to reward the good man with the good or better life in the Paradise. If man does the evil deeds in his life and dies, he is surely going to be punished in Hell. It is obligatory upon God to punish the evil man with severe and painful punishment in the Hell. In other words, man is free to choose and act on his choice of good or evil deeds and he will be rewarded or punished accordingly depending on his good or evil choices and deeds. God does not make man a believer or a disbeliever. Man himself decides to be a believer or a disbeliever of God's existence and oneness and then to follow God's commands to do the good deeds and to avoid the evil deeds.

To dispute and refute the two Mutazilite concepts above, al-Ashari posed to his teacher the cases of three brothers whose fates or final destinations were totally different. The first brother lived and died as a believer. The second brother lived and died as a non-believer or an infidel. The third brother died when he was still small or minor.

The first brother was going to the Paradise because he chose to become the faithful or the believer and he did the good deeds. So the case of first brother was in line with the Mutazilite concept of free will and the Mutazilite concept of God's doing the better and the best things for human beings. God surely rewards the believer with the good and better life in the Paradise. In this case, the first brother is in the Paradise because of his good faith and good deeds.

The second brother is going to be in the Hell because he chose to disbelieve and did the evil deeds. He is in Hell because of his choice and free will. He chose and did the evil faith and deeds and the unavoidable consequence of his choice is the Hell in the hereafter. For the second brother, al-Asharite asked his teacher, what was the better or best thing that God did to him? God permitted the second brother to live and die as an infidel and then to be in the Hell. His teacher replied that God punishes the second brother because he chooses the evil faith and deeds in his life in this world. God is just and His justice makes Him punish the wrong doer and reward the good doer.

The third brother is neither in the Paradise nor in the Hell because he did not have enough time to become a believer like his first brother or to become an infidel like his second brother. Again, al-Ashari asked his teacher, what was the better and best thing that God did to the third brother? His teacher replied that God knows the best for him to die when he was still small or a minor because if the third brother were to grow up, he would become an infidel or a non-believer like his second brother. Hence, it is better for the third brother to die when he was still small or a minor.

Al-Ashari said that why did God prolong the life of the second brother even though God knows that he grew up and old and died as an infidel? Being an infidel is not good for the second brother. If the Mutazilite concept of God's doing the better and the best things for human beings was true, as the Mutaziltes claimed, there would be no single infidel living in this world since an infidel is not good to live in this world. In the hereafter, an infidel is going to be in the Hell. God must make all human beings believers because the final rewards for the believers are surely the Paradise in the hereafter, if the Mutazilite concept of God's doing the better and the best things for human beings is an acceptable and reliable concept. In reality, infidels or non-believers are more than believers living in this world. Hence, the Mutazilite concept of God's doing the better and the best things for human beings does not agree with human history in this world.

Although al-Ashari had been the student of al-Jubaii for almost forty years according the very popular story or narrated tradition about their student-teacher relationship, finally al-Ashari debated and disputed the two Mutazilite concepts namely human free will and God's doing the better and the best for human beings. Al-Ashari was doubtful about the two Mutazilte concepts and he soon left his teacher al-Jubaii. Al-Ashari later on known as the founder of the Muslim theological school named Asharism that opposed many Mutazilte concepts and principles of faith or belief.


text:
A-level Economics/OCR

This WikiBook will attempt to create a useful revision resource/textbook for those people undertaking the OCR A-Level Economics qualification.

Modules
Introduction to economics-Whats the problem

Module 2881: The Market System Module 2882: Market Failure & Government Intervention Module 2883: The National And International Economy Module 2884: Economics of Work and Leisure Module 2885: Transport Economics

title: A-level Economics/OCR


text:
A-level Economics/OCR/2885

Measuring Transport Output

 * people/passenger transport - passenger-kilometres (number of passengers \times distance travelled in kilometres)
 * goods/freight transport - tonne-kilometres (weight in tonnes \times distance travelled in kilometres)

Characteristics of Transport

 * Transport is a unique product
 * Demand for transport is largely derived.
 * As a service, it is perishable
 * Transport decisions recognise two key dimensions:
 * distance
 * time
 * Transport generates significant externalities not recognised in the price (Private Costs are not equal to Social Costs) therefore market fails
 * Journeys are indivisible
 * Loading is the % capacity used on a journey
 * Peaking: Demand > Supply, leading to congestion

Transport Infrastructure
Two components:
 * Network
 * Terminals/Nodes

Infrastructure critical to economic success because it affects:
 * transport costs and prices \therefore choice of mode
 * patterns of land use
 * operation of labour markets
 * location of business activity

Can deliver:
 * improved labour mobility\therefore greater efficiency
 * positive externalities through regional development
 * improved competitiveness

In addition:

 * Built up over time through investment:
 * replacement investment (maintenance)
 * net investment (additional capacity)
 * Under-investment since the war leading to relatively poor quality infrastructure
 * Investment:
 * significant lead times (5–30 years)
 * significant amounts of money (billions) from tax, borrowing and private funds
 * long payback (decades)

Transport Modes

 * Methods of moving goods and passengers
 * Often several mode options per situation:
 * Road
 * car, lorry, van, taxi, bus, coach, motorcycle, bicycle, walking
 * Rail
 * Air
 * Sea
 * Pipelines

Key issues in deciding between modes:
 * Relative cost
 * Distance
 * Speed
 * Bulk
 * Urgency (perishable goods)
 * Capacity
 * Convenience
 * Reliability
 * Network extent
 * Risk of delay/accident
 * Pollution
 * Traffic congestion

Demand for transport

 * Derived from economic activity
 * Changes in economic relationships lead to immediate changes in demand for transport
 * In UK, steady rise in demand
 * Increasing domination of road transport

Price and demand for travel

 * Travel can be priced and is demanded like any other product
 * The price of a journey includes the full cost to a passenger, expressed in £ (e.g. car: fuel, delay, risk)
 * Demand expressed through:
 * number of passenger-kilometres
 * number of vehicles
 * Supply is fixed (inflexible service) Although there are more services in peak times of demand.
 * Demand varies hugely (e.g. 8:30am vs 3:00am)
 * Gross under-usage or peaking/congestion
 * Off-peak travel is price elastic
 * Peak travel is price inelastic
 * Low positive cross elasticity of demand

Income and demand

 * Changes in:
 * Rates of economic growth
 * Business cycle
 * lead to large changes in demand for transport

 * Road, rail and air have a high YED and are sustainable
 * Buses have low YEDs, may even be inferior goods

Markets Overview
Emphasis is to:
 * understand theoretical models of markets (at A2 level)
 * explain, analyse and evaluate behaviour in transport industries and markets

In market (capitalist) economies:
 * Entrepreneurs/firms:
 * invest their own capital
 * take risks
 * hire/buy resources/factors of production
 * produce goods and services which they judge the consumers want in order to make at least a normal level of profit
 * always make decisions with competition in mind
 * the nature/extent of competition can be defined in terms of the number and power of firms in a market
 * a core factor which defines the power of firms in a market is barriers to entry/exit
 * where there are low barriers, profits tend to be normal
 * where there are high barriers, profits tend to be supernormal

With new entrants to a market:
 * the supply curve shifts right (an increase)
 * the price decreases
 * the quantity demanded expands
 * the consumer surplus increases
 * the producer surplus decreases

Characteristics

 * Infinite independent firms
 * Homogeneous product, so no advertising
 * Infinite buyers
 * Perfect information
 * No market power, so all firms are price-takers
 * No barriers to entry/exit
 * Perfect resource mobility
 * Firms are all profit-maximisers
 * Normal profits in LR, although losses or supernormal profits are still possible in SR
 * Theoretical model
 * Benchmark to assess all imperfectly competitive markets
 * e.g. window cleaners

Characteristics
Imperfect competition displays at least one of the following to some extent:

 * Finite firms, allowing an individual firm to affect the market
 * Some market power, so all firms are price-makers
 * Differentiated products
 * Barriers to entry
 * Non-price competition
 * Supernormal profits in LR

Characteristics

 * Many firms (all independent)
 * Differentiated product
 * Price-makers to an extent
 * Downward-sloping demand curve
 * Many close substitutes
 * Relatively price elastic
 * No barriers to entry/exit
 * In LR, only normal profits
 * In SR, abnormal profits/losses can occur

Characteristics

 * Few firms
 * Interdependant
 * actions take account of reactions
 * High degree of sales concentration - sales concentrated among a few firms
 * Firms are significant price-makers
 * Differentiated, branded products
 * Non-price competition - advertising/promotion to increase market share
 * Significant barriers to entry/exit
 * Abnormal profits in the LR possible - invested into advertising/R&D
 * economic efficiency is not attainable in the oligopoly

Pricing Characteristics

 * Generally stable prices
 * Loathe to start a price war
 * Uncertain outcomes when changing price:
 * Prices cut:
 * Competitors follow suit
 * Volume gain insignificant (price inelastic)
 * Leads to a loss of revenue
 * Prices raised:
 * Competitors may not follow suit
 * Large decrease in volume (price elastic)
 * Leads to a loss of revenue
 * KinkedDemandCurve.gif

Collusive Oligopoly

 * Firms agree to act together to restrict competition on:
 * price
 * location allocation
 * Price is likely to be higher than the market clearing price meaning output/sales are likely to be lower than they might otherwise be
 * May not maximise profits, in order to create a more secure environment
 * Most efficient firms will be tempted to break ranks by cutting prices, leading to increased market share
 * Inherently unstable
 * Illegal

Monopoly

 * Either a single or dominant (>25\% market share) firm in the market
 * Insurmountable barriers to entry
 * Price-maker - they can set either output or price
 * Abnormal profits in the long run
 * Potential barriers to entry
 * High sunk costs
 * Some legal monopolies (e.g. TOCs)
 * Economies of scale
 * new firms cannot use EoS
 * Predatory pricing
 * Natural monopoly
 * best for consumer if there is a monopoly
 * [[File:SR-Supernormal.gif]]

Comparing perfect competition and monopoly

 * Perfect competition is productively and allocatively efficient
 * Monopolies are not
 * Monopolies are most appropriate where:
 * there is a natural monopoly
 * there are very significant economies of scale
 * abnormal profits are invested in R&D or to reduce costs
 * it would enable a domestic firm to compete internationally

Natural Monopoly
Occurs because:
 * One firm can operate more efficiently that two or more
 * There are high fixed costs \rightarrow significant EoS
 * More likely to be productively efficient
 * Minimum Efficient Scale leading to a high % of market volume/value
 * Cannot be threatened by more efficient new entrants
 * Regulation needed to protect captive consumers (e.g. railways)

Contestable Markets
Recent government intervention:
 * Focus on increasing market competitiveness:
 * More customer-oriented, leading to better products
 * Greater efficiency, leading to lower costs
 * Lower prices
 * Profits

Three policy approaches:
 * Deregulation (e.g. buses, taxis)
 * Privatisation (e.g. rail)
 * Contestability

Barriers to entry

 * Can be technical or economic
 * Determine the degree of competition in a market
 * Lead to LR abnormal profits for monopolists
 * Transport examples:
 * British Rail - pre 1997 (legal monopoly)
 * Laker Skytrain - no-frills airline (predatory pricing)
 * Railways, cross-channel ferries (sunk costs)
 * Economies of scale
 * British Airways (branding)

Theory of contestable markets

 * The threat of entry leads to competitive behaviour:
 * make normal profits
 * productive efficiency
 * allocative efficiency
 * The number of firms is largely irrelevant
 * Contestable markets have:
 * one or few firms
 * minimal barriers to entry
 * minimal sunk costs
 * differentiated product

TOC franchise

 * Lump sum for franchise (contract)
 * Legal right to operate service for a limited period (initially 7 years, now 15 years)
 * Invest own money (which may not be returned upon within the time period)
 * Termination when period ends (loss of sunk costs)

Deregulation
Not appropriate for natural monopolies such as:
 * National Air Traffic Control
 * Network Rail

Bus Deregulation
Up to 1980:
 * Many companies nationalised in 1947
 * Licensing system
 * Local route monopolies
 * Price controls
 * Government subsidies
 * Cross subsidisation

Private hire coaches always privately owned.

1985/1980:
 * Price controls abolished
 * Prices reflected route costs
 * Social, non-profitable routes - out to tender
 * Offered (by local authority) to bid, requiring least subsidy
 * Limited subsidy funds
 * Licensing process abolished
 * Safety regulations remain
 * Any operator free to operate
 * Must notify Traffic Commissioner of closures/alterations of routes

Results:
 * Initial increase in competition
 * More entrants
 * More buses
 * More frequent services
 * Lower fares
 * Buses operated below capacity
 * More congestion and pollution
 * Prompted mergers and acquisitions:
 * Arriva
 * Stagecoach
 * Go-Ahead
 * First Group
 * National Express
 * Nationally, an oligopolistic market
 * Locally a monopolistic market

This leads to:
 * Higher fares
 * Lower levels of service
 * Withdrawal of most marginally commercial routes
 * Some small competitors operate with low margins
 * Large operators cannot entirely neglect the market

Air Transport Deregulation
Air travel has distinctive characteristics:
 * Significant externalities:
 * noise
 * climate change
 * diminished air quality
 * Short-haul particularly polluting
 * To internalise externalities:
 * Short haul: £3
 * Long haul: £20
 * Airports need land leading to urbanisation
 * Airspace and landing slots ('supply') limited
 * Capacity insufficient to accommodate projected demand

Operators:
 * Private (e.g. BA)
 * State-owned (e.g. Iberia)
 * Low-cost (e.g. easyJet)
 * Charter

Market segments:

 * 1st class vs. economy/low-cost
 * Domestic vs. short-haul vs. long-haul
 * Business vs. leisure vs. holiday

Leisure is, for example, a long weekend whereas holiday is, for example, two weeks.

Infrastructure:
 * Airports
 * Air Traffic Control

Core regulation:
 * Flight worthiness
 * Air space security

Deregulation of air services:
 * USA: 1978
 * UK: 1987
 * Europe: 1993

Pre-deregulation:
 * Bilateral agreements between 'flag-carriers'
 * No competitive pressure
 * High fares

Post-deregulation:
 * Replication of US experience
 * Explosion of low-cost operators
 * 'Flag-carriers' under immediate threat
 * EU "Open Skies Policy" under a common regulatory framework
 * 50% new/unused slots allocated to market newcomers

Impact of deregulation:
 * Newcomers had a precarious existence
 * Rising profits for established low-cost operators
 * Premium carriers:
 * Losing passengers
 * Cutting prices
 * Experiencing falls in profit
 * Struggling to differentiate
 * Avoiding competition

Future:
 * Air travel has increased threefold since 1975
 * Freight increased twofold since 1990
 * UK economy depends increasingly on air transport:
 * Consumption
 * Investment
 * Tourism employment
 * Competitiveness
 * Airport demand, on current trends, will double by 2030
 * New capacity being constructed at:
 * Stansted
 * Birmingham
 * Heathrow
 * Edinburgh

Privatisation

 * Applied to buses and trains amongst others (e.g. utilities)
 * Operational decisions based on the needs of shareholders

More recently, two types of quasi-privatisation have been used:

Public Private Partnership

 * Partnership of public sector and private sector
 * Shared funding of a project
 * Shared revenues
 * e.g. London Underground:
 * Track, signals and stations are privately owned (for 30 years)
 * Operations stay in the public sector

Private Finance Initiative

 * Private company finances, builds and operates the infrastructure
 * Government pays fee for its use
 * State ownership in due course
 * Considered suitable for Air Traffic Control

Transport Infrastructure Ownership

 * Roads:
 * Quasi-public good
 * Largely non-rival
 * Partially non-excludable (to an extent)
 * Owned by the state
 * Funded from general taxation
 * Built/maintained by private sector, under tender
 * Rail:
 * Significant change since 1996
 * Network Rail:
 * not-for-profit private company
 * Railtrack plc replaced in 2002
 * Rail regulator (government body)
 * TOCs (private sector)
 * Air:
 * Airports and air service operators in the private sector
 * Air Traffic Control partially privatised (PFI to ensure adequate investment funds)

Rationale for privatisation

 * Profit incentive
 * No operational subsidies (money can be spent elsewhere)
 * Investment in latest technology
 * Introduce a business culture (competitive approach)
 * Operate more efficiently:
 * Lower LRAC
 * Lower prices
 * Be more customer-oriented leading to improved service
 * Significant source of funding, after decades of state neglect
 * More contestable market

Criticisms of privatisation

 * Assumes competitive environment in LR (e.g. buses)
 * Greater neglect of negative externalities
 * Reduced pay/conditions\rightarrow
 * demotivation
 * transfer of welfare to shareholders and consumers
 * Profit maximisation (investors want quick return)
 * Profit vs. performance vs. safety (conflicting stakeholder objectives)
 * Natural monopoly
 * Regulator needed to achieve economic efficiency
 * Private firms ignore equity issues

Price Discrimination
Charging different prices to different customer groups for the same product for reasons unrelated to cost in order to increase profits

Examples:
 * (Off-)Peak Pricing - not price discrimination, the products are different
 * Different Classes - not price discrimination, the products are different
 * Discounts - tend to be price discrimination, as the price is different for the same product

Price discrimination requires:
 * Different price elasticities of demand in each sub-market (e.g. OAP vs. business traveller)
 * No market seepage (i.e. reselling between sub-markets is impossible)
 * Firms are price-makers (i.e. operate in an imperfectly competitive market)

There are three types of price discrimination:

First Degree Price Discrimination

 * Must know how much each customer is willing to pay
 * Not very likely
 * e.g. Allocation of limited seats to the highest bidder first
 * All consumer surplus transferred to the firm:
 * [[File:ConSur.gif]]

Second Degree Price Discrimination

 * Selling off excess capacity at lower prices than previously charged
 * e.g. Airlines after 9/11
 * Used when a firm is:
 * left with huge amounts of capacity
 * desperate to maintain cash flow
 * need to increase occupancy rate
 * A firm sells at a price initially, but clears at the marginal cost of each unit
 * Employed by European low-cost airlines:
 * Attempt to fill all seats
 * Increase price progressively as seats are sold
 * Flight revenue and profits are maximised
 * Strategy explains strong sales growth over recent years

Third Degree Price Discrimination

 * Allows firms to increase revenue and profit by charging different prices for the same product to different market segments
 * e.g. rail travel:
 * For students, the fare is a higher % of income meaning student demand is price elastic
 * For commuters, the fare is a lower % of income meaning commuter demand is more price inelastic
 * For business travellers, the fare is almost irrelevant meaning business traveller demand is extremely price inelastic

Costs

 * Most business decision made in SR
 * Businesses will initially experience "increasing returns"
 * Eventually, "diminishing returns" will be experienced

In SR:
 * Output increases at an increasing rate initially, then at a decreasing rate
 * Fixed costs stay the same
 * Variable costs increase with output
 * Total costs will increase with output
 * MC falls initially
 * [[Image:MC-AC.gif]][[Image:TC-VC-FC.gif]]

In LR:
 * Businesses typically benefit from economies of scale
 * This leads to a lower AC in LR
 * At a certain point, AC plateaus (productive efficiency)
 * Beyond the plateau, a business experiences diseconomies of scale

Economies of scale are important because they motivate businesses to develop. There are two types of economy of scale and two matching types of diseconomies of scale:

Internal Economies of Scale
Those economies of scale accrued within a business (business-specific). For example:
 * Technical: Improved use of technology/machinery
 * Financial: More, cheaper sources of finance available
 * Marketing Budget: need not increase proportionally
 * Purchasing: Bulk-purchase discounts
 * Research & Development: Budget need not increase proportionally
 * Managerial: Cost of management become more dissipated

External Economies of Scale
Those economies of scale that a market can exploit. For example:
 * A readily available skilled workforce
 * Locally accessible specialist suppliers
 * Good transport network

Internal Diseconomies of Scale
These diseconomies of scale may be caused by:
 * Division of labour benefits fully exploited
 * Management out of touch
 * Slower decision-making
 * Poorer communication
 * Worsening labour relationships

External Diseconomies of Scale
These diseconomies of scale may arise when:
 * Resources are scarce
 * There is congestion on the transport network

Revenues
Revenue patterns depend on the type of market. For example:
 * In a perfectly competitive market, MR doesn't change.
 * In an imperfectly competitive market, $$MR=\frac{1}{2}D=\frac{1}{2}AR$$

Profit

 * Profit = TR - TC
 * Reward for risk-taking
 * Cost of entrepreneurship

Two types of profit:
 * Normal: The minimum profit needed to continue trading
 * Abnormal: Anything above normal profit

Economics assumes that firms are profit-maximisers.

Profit-maximising output is where MC = MR

Profit-maximising price is AR above MC = MR

Economics does recognise other objectives:
 * Survival
 * Growth
 * Profit
 * Meeting needs of stakeholders

Definitions

 * Allocative efficiency: the efficiency with which markets are allocating resources. A market will be allocatively efficient if it is producing the right goods for the right people at the right price. Alternatively, you cannot make anyone better off without making someone else worse off.
 * Average revenue (AR): the TR divided by the level of output. It is equivalent to the price because it is the revenue the firm receives for each unit.
 * Barriers to entry/exit: barriers that prevent the entry of new firms into a market. Barriers to entry may be technical barriers, legal barriers, cost (or investment) barriers or barriers that arise from strong branding of the product.
 * Bilateral: affecting or undertaken by two sides equally, binding on both parties.
 * Business cycle: the tendency of economies to move, over time, through periods of boom and slump. In other words, the fluctuations in the rate of economic growth that take place in the economy. (aka trade cycle)
 * Captive consumers: consumers who do not have any choice as to how they access a service/product. Often occurs within a monopoly.
 * Congestion: over-crowding of a particular service/resource.
 * Consumer surplus: when people are able to buy a good for less than they would have been willing to pay. In other words they are receiving an effective benefit from buying the good. The consumer surplus is shown as the area between the equilibrium price and the demand curve.
 * Contestable market: a market in which there is always a threat or possibility of competition. This will still have the effect of making firms in the industry behave as if it is competitive as they will be concerned about the threat of other firms entering the market.
 * Cross elasticity of demand (XED): a measure of the responsiveness of demand for one good to a change in the price of another. $$XED=\frac{\%\Delta P_{A}}{\%\Delta P_{B}}$$. If the value is positive then the goods are substitutes, and if the value is negative then the goods are complements.
 * Cross subsidisation: where one group pays a relatively high price and thus enables another group to pay a relatively low price.
 * Deregulation: the removal of regulation or the removal of controls on a particular market.
 * Derived demand: where the demand for one thing depends on the demand for another. In other words the amount of demand for good A depends in turn on the amount of demand for good B.
 * Diminishing returns: a situation where the addition of a variable factor of production results in a fall in marginal product. The firm may be trying to expand by using more of its variable factors, but finds that the extra output they get each time they add more of the variable factor gradually falls.
 * Diseconomies of scale: a situation where average costs increase as production increases. This is the opposite to economies of scale and often happens where there are communication problems in larger organisations. They are also known as decreasing returns to scale.
 * Economic growth: an increase in a country's total output of goods and services. It is measured by changes in real GDP.
 * Economies of scale: where average cost falls as production increases. They are happening because larger firms are able to lower their unit costs. This may happen for a variety of reasons. A larger firm may be able to buy in bulk, it may be able to organise production more effectively, it may be able to organise cheaper loans and so on. They are also known as returns to scale.
 * Equity: a situation where the distribution of income is considered to be 'fair' or 'just'. An equitable distribution will not be the same as an equal distribution of income.
 * Externalities: spillover effects from production or consumption for which no payment is made. Externalities can be positive or negative.
 * Government intervention: when the government intervenes in a particular market. This may mean the introduction of price controls or it may mean intervention buying and selling in an attempt to stabilise the market.
 * Homogeneous product: all products are perceived to be of the same nature and value by the consumer.
 * Income elasticity of demand (YED) a measure of the responsiveness of demand to a change in income. $$YED=\frac{\%\Delta D}{\%\Delta Y}$$. A positive figure means that the good is a normal good whilst a negative figure means that the good is an inferior good.
 * Increasing returns: a situation where increasing the quantity-variable factor of production causes marginal product to rise.
 * Inferior goods: goods where an increase in income leads to a fall in the quantity consumed. They will have a negative income elasticity of demand.
 * Infrastructure:7 the basic underlying networks necessary to support economic activity. This includes roads, bridges, ports, sewers, hospitals and schools.
 * Interdependence: when the actions of one firm has an effect on its competitors. It is common in oligopolistic market structures where there are only small numbers of firms.
 * Lead time: the time interval between the initiation and the completion of a production process.
 * Legal monopoly: a market in which the government has allowed a particular firm to become a monopolist.
 * Long run (LR): all factors of production are variable.
 * Marginal cost (MC): the cost of producing one extra unit. It is the increase in total cost when one more unit is produced.
 * Marginal revenue (MR): the revenue earned from selling one more unit of a good or service. It is the increase in total revenue that occurs when one more unit is sold.
 * Market clearing price: the price at which equilibrium between supply and demand is reached.
 * Market seepage: no reselling between sub-markets.
 * Minimum Efficient Scale: lowest level of output at which the lowest AC occurs.
 * Modes of transport: methods of moving goods and passengers.
 * Natural monopoly: a situation where a single company tends to become the only supplier of a product or service over time because the nature of that product or service makes a single supplier more efficient than multiple, competing ones.
 * Non-excludability: once the good is provided it is not possible to stop people benefiting from it.
 * Non-rivalry: consumption by one person does not reduce the amount available for another.
 * Normal profit: the level of profit required for a firm to keep the resources they are using in their current use. In other words it is enough profit to keep them in the industry. Anything in excess of normal profits is called abnormal or supernormal profits.
 * Peaking: demand for a good is higher at a particular time.
 * Perishable goods: goods which have a limited life-span from when they are produced.
 * Predatory pricing: where a firm reduces price in the short run to try to force competitors out of the industry.
 * Price elasticity of demand (PED): a measure of the responsiveness of demand to a change in price. $$PED=\frac{\%\Delta D}{\%\Delta P}$$ If a good is elastic (a value for the elasticity of more than one), it is considered to be responsive to changes in price. If inelastic (a value below one) then it is unresponsive.
 * Price makers: firms who are able to influence price as their output represents a significant share of the market. Firms in monopoly and oligopoly will tend to have a high level of price setting power.
 * Price takers: firms whose output does not influence price.
 * Private sector: the part of the economy privately owned and in the control of individuals and companies.
 * Privatisation: the process of moving economic activity from the public sector to the private sector. The most common form of privatisation is the sale of government-owned shares in private sector companies or the sale of whole companies to private investors.
 * Producer surplus: the difference between the minimum price a producer would accept to supply a given quantity of a good and the price actually received. It is the gap between the marginal cost curve (supply curve) and the equilibrium price.
 * Productive efficiency: when a firm produces at the lowest unit cost. This will be at the minimum point of the average cost curve (where MC = AC).
 * Profit maximisers: firms which aim to make the highest level of profit possible (the largest surplus of revenue over cost) as opposed to other objectives.
 * Public goods: goods that would not be provided in a pure free-market system. This is because they display non-rivalry and non-excludability.
 * Public sector: the section of the economy under government control. In the UK it includes the health and education services, the police, fire service and ambulance service.
 * Quasi-privatisation: the use of private sector money within the public sector.
 * Quasi-public good: a near-public good. It has many but not all the characteristics of a public good.
 * Real: excluding the effects of inflation.
 * Resource mobility: the ease with which resources can move between different uses and locations.
 * Revenue: the money received from the sale of output.
 * Short run (SR): at least one factor of production is fixed.
 * Subsidies: payments made to firms or consumers designed to encourage an increase in output. A subsidy will shift the supply curve to the right and therefore lower the equilibrium price in a market.
 * Sunk costs: unrecoverable past expenditure.
 * Supernormal profit: when profit exceeds the amount a firm must receive to carry on production. If supernormal profits persist in an industry this will tend to attract new firms in, supply will increase, prices will fall and normal profits will be restored in the industry.
 * Tender: companies bid for the lowest subsidy they would need to complete the work required.
 * Total revenue (TR): the number of goods sold multiplied by the price charged for each one.
 * Total cost (TC): the total amount spent by a firm on producing a given level of output. It is made up of the fixed costs and the variable costs of production.
 * Transport: the movement of goods and passengers from one place to another.
 * Urbanisation: the social process whereby cities grow and societies become more urban.

title: A-level Economics/OCR/2885


text:
User talk:Odd bloke~enwikibooks

Copyright
Hi, I just wanted to check that OCR_A-Level_Economics/2885 does not violate copyright. Can you put some info on the discussion page to say where that material comes from? Thanks Juliusross 18:15, 27 November 2005 (UTC)

are you here
I read your Economics module, and it looks really good. Needs to be formatted some, but it's a nice list of all the content that needs to be in the book. Are you still around? drop me a line sometime. DettoAltrimenti 16:30, 16 December 2005 (UTC)

How to troll
How do I access How to troll, now it's been deleted? Research purposes only.--80.4.252.114 01:26, 17 January 2006 (UTC). Sorry - I'm User: Shtove on Wikipedia - don't know if it links.

UK Constitution
Have you considered voting for UK Constitution and Government again this month, as it has been renominated. It relly is a very good book.

OCR A-Level Economics
Odd bloke,

I've been cleaning up the Economics Bookshelf, and am unsure about what I should do with the module OCR A-Level Economics. Currently it seems to be in note form, and hasn't had any major changes since November 2005. If you would like to expand it into a wikibook, I'm all for it- I was just curious if you had any plans for the module? Leave me a message on my user talk page. Thanks, DettoAltrimenti 05:38, 26 May 2006 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Odd bloke. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Odd bloke~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

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Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:19, 19 April 2015 (UTC)

title: User talk:Odd bloke~enwikibooks


text:
FHSST Biology/Contents/Index/DCC/Origin of species/Theories/Creationism

Creationism is a belief that all life in its current form was created by a god or gods. For example some creationists claim that the universe and everything in it was created in 6 days, as is written in the Genesis book of the Christian bible. Creationism rejects Darwinian evolution as an explanation for the origin of life. It is considered an irrational belief with no basis in science.


text:
Topology/Quotient Spaces

The quotient topology is not a natural generalization of anything studied in analysis, however it is easy enough to motivate. One motivation comes from geometry. For example, the torus can be constructed by taking a rectangle and pasting the edges together.

Definition: Quotient Map
Let $$ X $$ and $$ Y $$ be topological spaces; let $$ f : X \rightarrow Y $$ be a surjective map. The map  f  is said to be a  quotient map  provided a $$ U \subseteq Y $$ is open in  Y  if and only if $$ f^{-1} (U) $$ is open in  X .

Definition: Quotient Map Alternative
There is another way of describing a quotient map. A subset $$ C\subset X $$ is  saturated  (with respect to the surjective map $$ f : X \rightarrow Y $$) if  C  contains every set $$ f^{-1}(\{y\}) $$ that it intersects. To say that  f  is a quotient map is equivalent to saying that  f  is continuous and  f  maps saturated open sets of  X  to open sets of  Y . Likewise with closed sets.

There are two special types of quotient maps:  open maps  and  closed maps .

A map $$ f : X \rightarrow Y $$ is said to be an  open map  if for each open set $$ U \subseteq X $$, the set $$ f(U) $$ is open in  Y . A map $$ f : X \rightarrow Y $$ is said to be a  closed map  if for each closed $$ A \subseteq X $$, the set $$ f(A) $$ is closed in  Y . It follows from the definition that if $$ f : X \rightarrow Y $$ is a surjective continous map that is either open or closed, then  f  is a quotient map.

Definition: Quotient Topology
If  X  is a topological space and  A  is a set and if $$ f : X \rightarrow A $$ is a surjective map, then there exist exactly one topology $$ \tau $$ on  A  relative to which  f  is a quotient map; it is called the  quotient topology  induced by  f .

Definition: Quotient Space
Let  X  be a topological space and let ,$$ X^{*} $$ be a partition of  X  into disjoint subsets whose union is  X . Let $$ f : X \rightarrow X^{*} $$ be the surjective map that carries each $$ x \in X $$ to the element of $$ X^{*} $$ containing it. In the quotient topology induced by  f  the space $$ X^{*} $$ is called a  quotient space  of  X .

Theorem
Let $$ f : X \rightarrow Y $$ be a quotient map; let  A  be a subspace of  X  that is saturated with respect to  f ; let $$ g : A \rightarrow f(A) $$ be the map obtained by restricting  f , then  g  is a quotient map.

1.) If  A  is either opened or closed in  X .

2.) If  f  is either an open map or closed map.

Proof: We need to show: $$ f^{-1}(V) = g^{-1}(V) $$ when V $$ \subset f(A)$$

and

$$ f(U \cap A) = f(U) \cap f(A) $$ when $$ U \subset X $$.

Since $$ V \subset f(A) $$ and  A  is saturated, $$ f^{-1}(V) \subset A $$. It follows that both $$ f^{-1}(V) $$ and $$ g^{-1}(V) $$ equal all points in  A  that are mapped by  f  into  V . For the second equation, for any two subsets  U  and $$ A \subset X $$

$$ f(U \cap A) \subset f(U) \cap f(A).$$

In the opposite direction, suppose $$ y = f(u) = f(a) $$ when $$ u \in U $$ and $$ a \in A $$. Since  A  is saturated, $$ A \subset f^{-1}(f(a)) $$, so that in particular $$ A \subset u $$. Then $$ y = f(u) $$ where $$ u \in U \cap A $$.

Suppose  A  or  f  is open. Since $$ V \subset f(A) $$, assume $$ g^{-1}(V)$$ is open in $$ A $$ and show  V  is open in $$ f(A) $$.

First, suppose  A  is open. Since $$ g^{-1}(V) $$ is open in  A  and  A  is open in  X , $$ g^{-1}(V) $$ is open in  X . Since $$ f^{-1}(V) = g^{-1}(V) $$, $$ f^{-1}(V)$$ is open in  X .  V  is open in  Y  because  f  is a quotient map.

Now suppose  f  is open. Since $$ g^{-1}(V) = f^{-1}(V) $$ and $$ g^{-1}(V) $$ is open in A, $$ f^{-1}(V) = U \cap A $$ for a set  U  open in  X . Now $$ f(f^{-1}(V)) = V $$ because  f  is surjective; then

$$ V = f(f^{-1}(V)) = f(U \cap A) = f(U) \cap f(A). $$

The set $$ f(U) $$ is open in  Y  because  f  is an open map; hence  V  is open in $$ f(A) $$. The proof for closed  A  or  f  is left to the reader.

title: Topology/Quotient Spaces


text:
Guide to Social Activity

Wikibooks Guide to Social Activity /Authors/

 * 1) /Alcohol/ social drinking
 * 2) /Body Language/
 * 3) /Courtship/ dating
 * 4) /Driving/ cars or other motor vehicles
 * 5) /Observing Sports/ for example, football

title: Guide to Social Activity


text:
Talk:Calculus/Newton's Method

This is my first shot at this section, all feedback, edits, criticisms, and witicisms welcome. -- Etscrivner 8:27, 27 November 2005 (UTC)

Alternate Formula
I removed the following formula for $$x_{x+1}$$:
 * $$x_{n+1}=x_0-\sum_{i=0}^n\frac{f(x_i)}{f^\prime(x_i)}$$

This form still requires a knowledge of all previous $$x_i$$'s, and it requires many more operations than the formula
 * $$x_{n+1}=x_n-\frac{f(x_n)}{f^\prime(x_n)}$$

, so it seems to me to have no usefulness. Please feel free to restore it if you disagree, but I'd be curious to know your reasoning. --Greenbreen (discuss • contribs) 23:37, 15 July 2011 (UTC)

title: Talk:Calculus/Newton's Method


text:
People's Tactics/Command & Officers

People's Tactics has a command, supply and transfer system that is the envy of many commercial games. Without a chain of command, your units will not be able to receive supply, be directed in battle or be reinforced (via transfers). The basic chain of command is that a formation has a tactical HQ, that a tactical HQ has a Strategic HQ and that towns deliver their production and supply to the Strategic HQ.

Strategic Headquarters (SHQ)
The Strategic Headquarters (most frequently refered to as SHQ) is a non-combat unit the highest level of command hierarchy. Supply and production is delivered from towns to SHQs. Regimes need at least one SHQ to do anything and can have up to fifty. SHQs are always land units.

Tactical Headquarters (THQ)
The Tactical Headquarters (most frequently refered to as THQ) is a combat unit in the middle of the hierarchy. THQs receive supply and reinforcements from SHQs, and must be assigned to one in order to function effectively. An SHQ may have assigned to it as many THQs as the player sees fit (there are working/efficiency restrictions, that we will discuss later, but at this moment there is no design limit). THQs are always land units.

Formations
Formations are combat units at the bottom of the hierarchy. Formations receive supply from their THQ, and must have one assigned. Formations receive reinforcements from SHQs, but can only receive reinforcements from the SHQ that their THQ is assigned to. A THQ may have assigned to it as many Formations as the player sees fit (there are working/efficiency restrictions, that we will discuss later, but at this moment there is no design limit). Formations may be land, air or sea units.

Changing command
Change Command Button You can set the chain of command for formations and THQ’s using the change command button. Doing this will use up the rest of the unit’s movement points, also, it will give a readiness penalty and increase the disruption of the unit. When the command of a THQ is changed, all formations assigned to that THQ will receive disruption, but no readiness penalty.

It is vital that you set up a THQ for each formation, a SHQ for each THQ and a SHQ for each town. The counters of formations that have a broken chain of command will turn red to warn the player they are not receiving enough supplies to sustain them.

Officers
The chain of command is not abstract. Officers play an important role in Peoples Tactics and are defined by the following characteristics: Name, Land/Naval/Air combat skill level, Reputation(Fame points), Retreat level and, if applicable, the Disruption level in the Chain of Command (the white numbers that appear over the Officer’s portrait). Of these characteristics, only Reputation and Disruption change during the game.

Officers have skill levels between one and nine in three different theatres of war. As a rule of thumb, a unit with a level nine officer will be one-and-a-half times more effective than a unit with a level 1 officer.

Next to that, fame points also have an effect. 1 fame point is about 20% improvement, 10 fame points about 60% improvement and 25 fame points about 100% improvement. Fame points are earned by destroying enemy units in combat. The higher the officer’s body count, the more skilled and deadly he will become. Reputation increases at the rate of 1 Fame point per each 4.000 points of net losses inflicted in one combat (in the default rules). Once gained, it is never lost and has no maximum limit.

Disruption is caused by replacing an officer, or by defeat in or retreat from combat. Disruption may grow up to 75%, but no further. It will decrease each turn at the following rate:

Int [ DISRUPTION * ( 1 - OFFICERSKILL/20 ) ] - Int [ Sqr ( OFFICERFAME ) ] - 10

In this formula, Int and Sqr are the Integer and Square root funtions, and OFFICERSKILL is the applicable Officer’s skill, i.e. the commanding officer of a Land Unit uses his Land skill value, the commanding officer of a sea formation uses his Sea skill value and the commanding officer of an air formation uses his Air skill value.

During a battle, all the officers in the chain of command are taken into account. The officer of the formation has a 50% influence, the THQ’s officer has an influence of 33%, and the SHQ’s officer has an influence of 16%. For a Formation, the lowest level, the impact of the Chain of Command is given by the formula (1*SHQ+2*THQ+3*UnitCO)/6.

Each officer also has a retreat value. This is expressed as a percentage (i.e. a value between 0 and 100). The lower the value, the less likely the formation is to retreat, the higher the value, the more likely the formation is to retreat. Again, all the officers in the chain of command, not just the one in direct control, influence the unit in combat.

The Officer Pool
Officer Pool Button The Officer Pool enables you to buy new officers (costing Political Points) and swap officers between the pool button and the currently selected unit. It is possible to store officers in the officer pool (for use later), or to dismiss them forever. To change the commanding officer of a unit already on the map:

 * Select the unit whose commanding officer you want to change
 * Click on the “Officer pool” button
 * Select an officer from the pool
 * Click on the “Swap Officer” button

Disruption occurs when you play with the chain of command. So make changes in officers and bosses sparingly otherwise your whole army will become disrupted and fight poorly. Furthermore, due to the Chain of Command, disruption at an higher echelon extends to the units of lower echelons.

In larger scenarios it is an intelligent strategic choice to put your best people as high in the chain of command as possible. 16% bonus (SHQ) over 20 units or 33% bonus (THQ) over 4 units is more than 50% bonus over 1 unit.

title: People's Tactics/Command & Officers


text:
People's Tactics/Supply

Without adequate supply your units cannot recover readiness. Without adequate supply, or with no supply at all, your units will lose readiness, even when doing nothing. It is vital for your military to have and maintain good lines of supply.

Basically, a hex can be supplied in one of three different ways. The first, and easiest to maintain, is through a traceable land route. Secondly, through a traceable land and sea route in which case both a sending port and receiving port are under your control. The third method is through a traceable land and sea route but with only a sending port under your control. This method is known as “amphibious supply” and it carries a 50% penalty due to the difficulty of the medium

The line of supply is traced from a formation to their SHQ. If you have multiple SHQs, there will be multiple lines of supply. A formation uses the SHQ of its THQ for supply.

If there is not enough supply available in the SHQ to supply all its formations it will send partial supply to all.

A SHQ can save up to a certain amount of unspent supply. This can be used in the future or used for air supplying units.

A SHQ has a certain maximum limit to where it can supply formations. Formations further than half this limit away get penalties. If they are out of limit they will get no supply and their counter will turn orange as a warning for the player.

Keep in mind that units that do nothing will use almost no supply, while units that move and battle a lot will use lots more of supply.

Keeping your formations too far away from their respective THQs will result in supply loss.

Use the hex info button in the status report to get detailed info on how a hex is supplied. Especially if you have multiple SHQ this could be interesting and affect your strategy.

title: People's Tactics/Supply


text:
People's Tactics/Production

Without production, no supply will be produced for your units, nor new troops and equipment. Each town automatically produces supply and sends it to its SHQ, as long as there is a land or sea (using 2 harbours) connection.

Next to this, you can set the production of a town, either to Political Points or to a specific unit type. Any units produced in the town will be delivered to your choice of SHQ (see production screen). The selected SHQ must be within a land supply line to the town, however, having a town sending production to an overseas SHQ will not work. The game will show a little red “N” in the bottom of the town hex to warn you if this situation might occur.

If a town has no reachable SHQ set, even using ports, it displays a little red “NP” in the bottom of the hex indicating that it cannot produce anything since it cannot deliver the production anywhere.

Not every people can produce every unit type depending upon the scenario you are playing.

title: People's Tactics/Production


text:
Calculus/Related Rates

Introduction
One useful application of derivatives is as an aid in the calculation of related rates. What is a related rate? In each case in the following examples the related rate we are calculating is a derivative with respect to some value. We compute this derivative from a rate at which some other known quantity is changing. Given the rate at which something is changing, we are asked to find the rate at which a value related to the rate we are given is changing.

How to Solve
These general steps should be taken in order to complete a related rates problem.

 * 1) Write out any relevant formulas and information about the problem.
 * 2) *The problem should have a variable you "control" (i.e. have knowledge of the value and rate of) and a variable that you want to find the related rate.
 * 3) *Usually, related rates problem ask for a rate in respect to time. Do not panic if your equations do not appear to have any relationship to time! This will be handled later.
 * 4) Combine the formulas together so that the variable you want to find the related rate of is on one side of the equation and everything else is on the other side.
 * 5) Differentiate the formula with respect to time. Any other variable not a simple constant (such as $$\pi$$) should be differentiated as well. Be wary! Chain Rule usually should be used.
 * 6) The other variables that you have differentiated should have been given in the question or should be calculated separately. Nevertheless, plug-in known information and simplify.
 * 7) The value you get here is your answer.

The steps to solve a related rates problem is strikingly similar to an optimization problem, except that the main variable to find is not assigned to be 0 (it is supposed to be found) and that the extra variables in the optimization problem algorithm are actual variables in this case and are treated as variables instead of constants when differentiating.

Notation
Newton's dot notation is used to show the derivative of a variable with respect to time. That is, if $$f$$ is a quantity that depends on time, then $$\dot f=\frac{df}{dt}$$, where $$t$$ represents the time. This notation is a useful abbreviation in situations where time derivatives are often used, as is the case with related rates.

Examples
Example 1: A cone with a circular base is being filled with water. Find a formula which will find the rate with which water is pumped—if the rate that water was being filled and the measurements of the cone were known.

 * Write out any relevant formulas or pieces of information.
 * $$V=\frac{1}{3}\pi r^2h$$

 * Take the derivative of the equation above with respect to time. Remember to use the Chain Rule and the Product Rule.
 * $$V=\frac{1}{3}\pi r^2h$$
 * $$\dot V=\frac{\pi}{3}\left(r^2\dot h+2rh\dot r\right)$$

Answer: $$\dot V=\frac{\pi}{3}\left(r^2\dot h+2rh\dot r\right)$$

A spherical hot air balloon is being filled with air. The volume is changing at a rate of 2 cubic feet per minute.
 * Example 2:

How is the radius changing with respect to time when the radius is equal to 2 feet?

 * Write out any relevant formulas and pieces of information.
 * $$V_{sphere}=\frac{4}{3}\pi r^3$$
 * $$\dot V=2$$
 * $$r=2$$

 * Take the derivative of both sides of the volume equation with respect to time.
 * $$V=\frac{4}{3}\pi r^3$$

 * $$\dot V$$
 * $$=\frac{4}{3}3\pi r^2\dot r$$
 * $$=4\pi r^2\dot r$$
 * }
 * $$=4\pi r^2\dot r$$
 * }

 * Solve for $$\dot r$$.
 * $$\dot r=\frac{\dot V}{4\pi r^2}$$

 * Plug-in known information.
 * $$\dot r=\frac{2}{16\pi}$$

Answer: $$\dot r=\frac{1}{8\pi}$$ ft/min.

An airplane is attempting to drop a box onto a house. The house is 300 feet away in horizontal distance and 400 feet in vertical distance. The rate of change of the horizontal distance with respect to time is the same as the rate of change of the vertical distance with respect to time. How is the distance between the box and the house changing with respect to time at the moment? The rate of change in the horizontal direction with respect to time is -50 feet per second. ''Note: Because the vertical distance is downward in nature, the rate of change of y is negative. Similarly, the horizontal distance is decreasing, therefore it is negative (it is getting closer and closer).''
 * Example 3:

The easiest way to describe the horizontal and vertical relationships of the plane's motion is the Pythagorean Theorem.

 * Write out any relevant formulas and pieces of information.
 * $$x^2+y^2=s^2$$ (where s is the distance between the plane and the house)
 * $$x=300$$
 * $$y=400$$
 * $$s=\sqrt{x^2+y^2}=\sqrt{300^2+400^2}=500$$
 * $$\dot x=\dot y=-50$$

 * Take the derivative of both sides of the distance formula with respect to time.
 * $$x^2+y^2=s^2$$
 * $$2x\dot x+2y\dot y=2s\dot s$$

 * Solve for $$\dot s$$.

 * $$\dot s$$
 * $$=\frac{2x\dot x+2y\dot y}{2s}$$
 * $$=\frac{x\dot x+y\dot y}{s}$$
 * }
 * $$=\frac{x\dot x+y\dot y}{s}$$
 * }

 * Plug-in known information

 * $$\dot s$$
 * $$=\frac{(300)(-50)+(400)(-50)}{(500)}$$
 * $$=\frac{-35000}{500}$$
 * $$=-70$$ ft/s
 * }
 * $$=-70$$ ft/s
 * }
 * $$=-70$$ ft/s
 * }

Answer: $$\dot s=-70$$ ft/sec.

Sand falls onto a cone shaped pile at a rate of 10 cubic feet per minute. The radius of the pile's base is always 1/2 of its altitude. When the pile is 5 ft deep, how fast is the altitude of the pile increasing?
 * Example 4:

 * Write down any relevant formulas and information.
 * $$V=\frac{\pi}{3}r^2h$$
 * $$\dot V=10$$
 * $$r=\frac{h}{2}$$
 * $$h=5$$

Substitute $$r=\frac{h}{2}$$ into the volume equation.

 * $$V$$
 * $$=\frac{\pi}{3}r^2h$$
 * $$=\frac{\pi}{3}h\left(\frac{h^2}{4}\right)$$
 * $$=\frac{\pi}{12}h^3$$
 * }
 * $$=\frac{\pi}{12}h^3$$
 * }
 * $$=\frac{\pi}{12}h^3$$
 * }

 * Take the derivative of the volume equation with respect to time.
 * $$V=\frac{\pi}{12}h^3$$
 * $$\dot V=\frac{\pi}{4}h^2\dot h$$

 * Solve for $$\dot h$$.
 * $$\dot h=\frac{4}{\pi h^2}\dot V$$

 * Plug-in known information and simplify.

 * $$\dot h$$
 * $$=\frac{4}{\pi(5)^2}10$$
 * $$=\frac{8}{5\pi}$$ ft/min
 * }
 * $$=\frac{8}{5\pi}$$ ft/min
 * }
 * }
 * }

Answer: $$\dot h=\frac{8}{5\pi}$$ ft/min.

Example 5:

A 10 ft long ladder is leaning against a vertical wall. The foot of the ladder is being pulled away from the wall at a constant rate of 2 ft/sec. When the ladder is exactly 8 ft from the wall, how fast is the top of the ladder sliding down the wall?

 * Write out any relevant formulas and information.

Use the Pythagorean Theorem to describe the motion of the ladder.

 * $$x^2+y^2=l^2$$ (where l is the length of the ladder)
 * $$l=10$$
 * $$\dot x=2$$
 * $$x=8$$
 * $$y=\sqrt{l^2-x^2}=\sqrt{100-64}=\sqrt{36}=6$$

 * Take the derivative of the equation with respect to time.

 * $$2x\dot x+2y\dot y=0$$ ($$l$$ is constant so $$\frac{dl^2}{dt}=0$$ .)

 * Solve for $$\dot y$$.

 * $$2x\dot x+2y\dot y=0$$
 * $$2y\dot y=-2x\dot x$$
 * $$\dot y=-\frac{x}{y}\dot x$$

 * Plug-in known information and simplify.

 * $$\dot y$$
 * $$=\left(-\frac{8}{6}\right)(2)$$
 * $$=-\frac{8}{3}$$ ft/sec
 * }
 * $$=-\frac{8}{3}$$ ft/sec
 * }
 * }
 * }

Answer: $$\dot y=-\frac{8}{3}$$ ft/sec.

title: Calculus/Related Rates


text:
People's Tactics/Units

Formation step-up
You can customize your formations during play and make different kind of formations for different tasks. Each formation can consistent of up to 4 types of unit types.

Due to this system, it is not possible to put light infantry and heavy infantry in the same formation. It is possible to put light infantry, humvees, mortars and light tanks in the same formation. The best mix of unit types will depend on the scenario and your tactics. The reason to mix unit types is so that they can work together. Mainly:

Land Mobile
Mobile and armour types can tow or carry infantry and artillery types. Thus increasing the number of movement points of the formation.

Land Support
Artillery types with range=1 participate in a supporting role in land battles. They add to the firepower of the unit, and can only be destroyed if the unit is forced to retreat. They are overrun on the moment they are left without infantry or armour accompaniment. The same goes for mobile unit types, which are purely supportive in the movement and recon area, but bring no combat value whatsoever.

Armour Cover
Infantry will take cover inside armour during battle if possible. Infantry inside or behind vehicles still participate in combat, but they can only be destroyed after the armour they are covered by is destroyed.

Long Distance Artillery
A land formation which has long distance artillery (distance>1) is considered an artillery formation. Infantry and Armour added to the unit can only be used defensively. All attacks the formation participates in will be through indirect fire.

Escort Role
If air units are interdicting, transferring, airlifting of bombing the fighters in the same formation will always escort the other aircraft (transporter or bomber) and engage enemy intercepting fighters. Only after all escorts are destroyed will the transporters and bombers have to fight with the enemy escorts.

Unit type characteristics
Unit Types are the “building blocks” of People’s Tactics and are defined by the variables discussed below. The Unit Type characteristics may be checked, during a game, in two ways: if present in a unit that is not a SHQ, by clicking on its picture (this also works for the characteristics of other player’s Unit Types); if it is a Unit Type that has been researched (or that was available from the start) but not yet built, the City Production Panel has a button that allows to do so.

Name
Unit type name.

Weight
Air formations and land formations (including THQs) have a maximum weight allowance, which limits the number of items that can be placed in those formations. Sea formations do not have a weight limit, or to be more precise, all the naval Unit Types have a weight of zero.

In the default game infantry types (such as light infantry) weigh 100 units, and the maximum weight allowance is 30000. This means that a unit can have a maximum of 300 infantry. A unit with 300 infantry would be full and have no room for say, a tank.

Carrying capacity
Land Mobile (Trucks and Humvees) and Armour Unit Types have carrying capacity. This is used to transport Infantry and/or Artillery types and, if there is enough carrying capacity, the unit’s movement type is upgraded. The Transporter (Air Unit Type), Cargoship and Light Carrier (Naval Unit Types) also have carrying capacity, but it works in a different way: air formations and sea formations transport land units (only one at a time, and it must have Movement Points available at the time of embarkation). Sea formations may also carry air formations, which will adopt the role of naval aviation if the formation includes at least one Light Carrier (and due to the one unit limit, will preclude the transportation of another unit).

Movement allowance
This is the maximum movement points available to the Unit Type. When there is more than one Unit Type in the same formation, the formation’s movement allowance will usually become the lowest of all present. The exception, as noted before, is for land formations (including THQs) that have enough carrying capacity to upgrade to a higher movement type.

The movement allowance for light infantry in the default game is 3, whilst the movement allowance for trunks is 6. If a formation has enough trucks to carry all the infantry (see carrying capacity), the formation will have 6 movement points per turn.

Soft attack value
This characteristic is used to determine how much damage is done to an enemy formation's infantry when attacking.

Soft defence value
This characteristic is used to determine how much damage is done to an enemy formation's infantry when defending.

Hard attack value
This characteristic is used to determine how much damage is done to an enemy formation's armour when attacking.

Hard defence value
This characteristic is used to determine how much damage is done to an enemy formation's armour when defending.

Artillery attack value
This characteristic is used to determine how much damage is done to an enemy formation when attacking with ranged artillery unit types.

Artillery range
This is the maximum distance at which a Ranged Artillery Unit Type may fire, measured in hexes.

Reconnaissance ability
This characteristic is relevant only when the Fog of War option is enabled. It is dependent on a basic reconnaissance level set in the scenario editor (50 points, in the standard set). The number of reconnaissance points of the Unit Type items in a given formation is tallied, to ascertain the reconnaissance ability of the formation. If more than one formation belonging to the same Regime is in a given hex, those formations abilities are added, to give a total “hex” reconnaissance ability.

In order to see as far as X hexes away (for X greater than one, because it is allways possible to see into hexes adjacent to units or terrain owned by a player), the following (minimum) reconnaissance points must be available: Reconnaissance Basis Points * X * X / 2 (e.g., to see 3 hexes away, with the standard set BRP of 50, you would need 50*3*3/2 or 225 recon points). There is one restriction to this formula: it is not possible to see farther than the highest theoretical movement allowance present at the hex (e.g. an air formation filled to capacity with Recon planes will not see more than 12 hexes away, as 12 is the movement allowance of Recon planes).

Supply need
The maximum ammount of supply that a given Unit Type item will require, once it is assigned to a combat formation (i.e., once it leaves the SHQ).

Engineer skill
The skill required to build fortifications, available only to Infantry Unit Types. The number of engineer skill points of the Unit Type items in a given formation is tallied, to ascertain the engineering capability of that formation. Fortifications may then be built (level 1) or upgraded (levels 2 and 3), if there is enough engineering skill, supply points and movement allowance to do so.

Fortifications represent static defensive works built on the side(s) of an hex, and as such are independent from each other, e.g. there could be a level 1 fortification on the East facing side and a level 3 fortification on the West facing side of an hex.

The successive levels of fortification require 250, 750 and 1,500 engineering skill AND supply points (these are deducted from the SHQ stock), and each must be built in one go (i.e., it is not possible to build, say, 2/3 of level 2 in one turn and finish it in the next turn). The unit building the fortification must also have at least 1 MP left (or 2 MPs for the third level).

Anti-air ability
This characteristic is used to determine how much damage is done to an enemy air formation operating (interdict/strategic bombing/airlift/airdrop) within a certain radius of the formation. The radius is 2 for the default game. Only land and sea formations may have an anti-air ability.

Hit points
The amount of damage a unit type takes before it is destroyed. Along with the soft and hard defence values, this is an important factor in combat resolution.

Frontsize
A brilliant concept (no, this part of the manual was not written by Victor). In real life, men and equipment occupy a given amount of real estate. When two forces engage in combat, not all elements on each side are able to squeeze into a line and have a shot at each other (at least, not anymore). This represents that space limitation. In the standard set, Infantry types take 1 unit of space, Artillery takes 10 units of space, and Armour takes 20 units of space. Mobile types don’t engage in combat and thus have no frontsize. As ships and aircraft don’t fight the same way as land units, they have no frontsize, either.

Strategic bombing
Combat related characteristic, reserved to aircraft, and then only to those of the bomber sub-class. Strategic bombing will come into play when doing a bombing raid on a production site. The strategic bombing statistic determines the amount of damage (in prodcution points) done to a production site.

Dogfighting
Combat related characteristic, reserved to aircraft, and then only to those of the fighter and transporter sub-classes. This is the attack value of an aircraft when engaging another aircraft in air combat.

Naval interdiction
Combat related characteristic, reserved to aircraft. This is the attack value of an aircraft when engaging naval units.

Cost
The amount of production points required to build one item.

Creating a new unit
To create a new unit:

 * Select a hex of territory that you own, by clicking on it
 * Click on the “Create unit” buton
 * A pop-up window appears, with the type of unit available — a sea formation may only be built at a Port, or at sea in the same hex of an existing sea formation belonging to the same player. If there are not enough Political Points to build a given type, that type’s button is greyed out
 * Click on the type wanted;
 * The unit counter appears in the map. If the unit is a SHQ or THQ, a pop-up window will appear asking for the unit’s name, otherwise an automatic name will appear (new units get a sequential number, beginning with 2, followed by “Bataljon” — Dutch for Battalion, the default unit “size”, unless the scenario designer defined a different one)
 * Assign a Chain of Command to the unit, by clicking on the "change command" button, on the upper echelon unit and then on the “Do new THQ/SHQ for [unit_name]” button;
 * Transfer some Unit Type items to the new unit (or it will disappear by next turn).

title: People's Tactics/Units


text:
Talk:A-level Economics/OCR/2885

All of the stuff on this page is from my own personal notes, which is why it isn't particularly proseful (if that's a word). This is from a combination of teacher's classnotes and a couple of textbooks, but none is actually copied verbatim because my teacher breaks people's legs for doing that. :p The structure is taken from the OCR syllabus, although I just used the structure we were asked to make notes under.

If that's a problem, I'll happily rectify this (even if it's just plain removal). Odd bloke 21:07, 27 November 2005 (UTC)

title: Talk:A-level Economics/OCR/2885