An Introduction to Game Theory: Week 2

A famous game is found in the example of Prisoners Dilemma. In this game two people have committed a crime, have been captured and are now being interrogated by the police. The two players can choose one of two strategies. Either, they can cooperate (stay silent) or they can defect and tell the police that on top of the burglary, they had been planning on arson. The pay-off is – (time spent in prison), as they are trying to limit the extent of their incarceration. If both cooperate, they both get one year in prison. If both defect, they both get 10 years on prison, for burglary and attempted arson. However, if one defects and one cooperates, the person who defects gets to walk away free, for honesty, and the player who cooperates gets a longer prison sentence of 15 years, for withholding information. Here, the Nash Equilibrium is Defect, Defect as neither can improve their situation by cooperating individually, in this situation. So, the best strategy, regardless of the other player’s strategy, is to defect. However, the collective best strategy would be to both cooperate, as the collated prison sentence is shortest. So, prisoner’s dilemma proves individual rationality and group rationality are not necessarily equal.

Coordination games are another form of game, in which there are multiple pure strategy Nash Equilibria. Take the example of 2 friends, collaborating on buying PC’s. When they come to buying keyboards, they face a choice. They can buy a QWERTY keyboard, or a keyboard laid out in a fashion that makes it more efficient to type (call it Optimal keyboard). If the two buy different keyboards, they have a low pay-off, because it is inconvenient to buy different keyboards. If they both buy QWERTY keyboards, they have a higher pay-off, and if they both buy Optimal keyboard’s they have the highest pay-off, as the Optimal keyboard is the most efficient. So, here there are two Nash Equilibria, when they either both buy the QWERTY, or the Optimal keyboard. In these situations, neither can improve their pay-off by individually changing the keyboard they buy. So, you have two Nash Equilibria, one with a higher pay-off then the other. So this illustrates society can be trapped in a ‘bad’ equilibrium, of which it is difficult to escape because everyone needs to simultaneously be committed to shifting strategy to reach the ‘better’ equilibrium.

The presence of multiple Nash equilibria can lead to self-fulfilling prophecies. Take the advent of HD and Blu-ray DVD’s, which are incompatible with DVD players designed for the other DVD design. There are two Nash Equilibria, one where everyone uses HD, and one where everyone uses Blu-ray. The two compete for a larger market share. As more people switch to one form of DVD (say Blu-ray), others believe the ‘end is nigh’ for HD DVD’s, and they also switch to Blu-ray. This causes Blu-ray to become the dominant DVD, and a Nash Equilibrium is reached, based on people’s expectations- a self-fulfilling prophecy. Predicting which Nash Equilibria will prevail is difficult, as it depends on people’s expectations of what others are doing. In this case, people choose their strategy, to switch to Blu-ray, based on a belief others are doing likewise.

So, why and how do people come to play Nash equilibrium? Well, there are three main reasons. One is simply due to rational reasoning. Take the Prisoners Dilemma, for example. Via rational reasoning alone, a player can come to the conclusion that the best strategy is to defect. If both are rational, and come to the same conclusion that the best strategy, regardless of what the other prisoner does, is to defect, an equilibrium is reached. However, usually rationality is not, alone, sufficient to reach Nash Equilibrium. Correct beliefs of others behaviour is also vital. That the combination of rationality and correct beliefs of others behaviour is needed to reach Nash Equilibrium is a central concept.

To form these correct beliefs, a second way people come to play Nash Equilibrium is through pre-play communication. Players communicate beforehand and reach an agreement on how to behave. Because of the nature of Nash Equilibrium, this is a self-enforcing agreement. Neither has an incentive to individually deviate from the agreement, so the behaviour agreed on is guaranteed, and the Nash equilibrium (probably one of many possible depending on the individual situation) is reached. Take the example of battle of the sexes, another famous example. A man and woman plan to meet up, with a choice of two locations, a shopping mall and a football stadium. The pay-off for each situation is shown in the pay-off table of figure 1.

man	woman
		Football	Shopping
	Football	3,2	0,0
	Shopping	0,0	2,3

Figure 1 – pay-off table in ‘Battle of the sexes’ example

 

As you can see, if they go to different locations, they both have a pay-off of 0, as they don’t meet. If they both go to the football, both are happy. The man is the happiest, as they are at his venue of choice. The opposite is true if both go to the Shopping Mall. Here, rational thinking is not sufficient to determine the best strategy, as there are multiple Nash Equilibria. So, they may arrange to meet, say in the Shopping Mall, the day before. This agreement, as the table shows, is self-enforcing. If either deviates from the agreement unilaterally, they don’t meet and they therefore gain a lower pay-off-they have no incentive to deviate.

The third way people come to play Nash Equilibrium is via trial and error adjustment. By accumulating experience, they gain knowledge of which strategies are good, or bad, allowing them to reach Nash Equilibrium.

Dynamic adjustment (another name for trial-and error adjustment) is the most common way in which Nash Equilibrium is reached. However, there is no guarantee the adjustment process always converges to reach a Nash Equilibrium. So, is it useful? Well, yes. This is because of the existence of Stylized facts, a stable mode of behaviour that is repeatedly observed. An example of a stylized fact is convention on escalators. If you are standing, you keep to the left. If you are in a hurry, you therefore have space to walk or run up the right side of the escalator. This forms a sort of Nash Equilibrium. If you defy the convention and stand on the right, your pay-off drops, as you are harassed by people who are looking to hurry past. Thus, the existence of stylized facts that act as a Nash Equilibrium illustrates why Nash Equilibrium is useful, in social sciences for example. Furthermore, it is useful to analyse behaviour in market competition.

All that has been mentioned before now involves pure strategy Nash Equilibria. However, there are also ‘mixed strategy’ equilibria. Take rock-paper-scissors. No matter what strategy you use, you have a 1/3 chance of winning. You have an equal average pay-off, no matter what your strategy. So, in this situation, the best strategy is to adopt a random strategy, and to be unpredictable. Thus, you reach the ‘mixed strategy’ equilibrium.

Fixed point theorem is another game theory concept relating to mixed strategy. Take the game of matching pennies. Players 1 and 2 simultaneously show 1 side of the coin. If both show the same side, player 1 wins. If they show different sides, player 2 wins. Thus you get a cycle that converges towards a fixed point, in terms of the probability of choosing heads. If Player 2 has a high probability of choosing heads, player 1 raises his probability of choosing head, so as to maximise the probability he wins. But if this occurs, player 2 will lower his probability of choosing heads, to maximise his chances of winning. Thus, slowly, the graph depicting of the probability of player 1 choosing heads, against the probability of player 2 dong likewise, converges to a fixed point, a Nash equilibrium where neither can improve their average pay-off by changing their probability of choosing a head individually.

Finally, Nash Equilibrium (possibly in mixed strategies) exists in all games, as long as two criteria are fulfilled; there are finitely many players and finitely many strategies. Of course, there are practically always going to be finite players. However, there may not always be finitely many strategies. Take the location game, where the vendor has infinitely different locations to set up shop. However, by dividing the street into finite slots, you can bypass this issue, approximating the equilibrium by a model of finite strategies. As such, almost all games fulfil the two criteria.

An Introduction to Game Theory: Week 1

First of 4 parts. Based on ‘Welcome to Game Theory’ course by Tokyo University on the Coursera website.

So, what is Game Theory? To answer this, first understand that all competition between individuals (say Republicans vs. Democrats, Google vs. Yahoo, animals fighting for survival with other species) can be formed as ‘games’ in which individuals try do to their best against others. Thus, there is a social dilemma. Because these individuals interact with others, what is best for the individual depends on what others do. This is a strategic position. Game Theory constructs mathematical models to examine how people behave in certain strategic situations. In other words, it allows you to find solutions to any social dilemmas in which individuals are placed in strategic positions.

While you can solve certain social problems using an intuitative ad-hoc approach, all social dilemmas can be analysed by formulating them as a mathematical model-a ‘game’- because all social problems (bar the odd exception) have two things in common. Individuals are trying to do their best against others, and under a certain set of rules. To formulate a ‘game,’ you must specify three items. The ‘players,’ the strategies (the possible moves a player can make) in a strategy set, and the pay-off. Take the example of drivers driving from city x to y, trying to reduce their travel time. The drivers are the players. The possible routes are the strategies. As the drivers are trying to minimise their travel time, the pay-off is – (travel time). Thus, a social problem has been modelled as a game.

Game Theory relies on an assumption of rationality. Individuals try to do their best against others. This is not perfectly accurate (perhaps you may make the wrong choice), but it does capture an important driving force of human behaviour. This assumption means you can assign pay-offs, larger for better alternatives and smaller for worse alternatives. As a result, rational choice can be defined as maximising pay-off, the theory of maximisation. However, this is not enough to determine the best strategy. In a strategic position, the opponent’s behaviour is often not given. Thus, to maximise your pay-off, you must form a belief of your opponent’s behaviour, as in a strategic position, what’s best for you depends on what others do. This is called ‘strategic thinking.’ However, your opponent will also be trying to predict your behaviour. This spiral can continue. Double bluff, triple bluff etc. This is known as the problem of infinite regress. Rationality alone fails to pin down individual behaviour. As such the simple model of maximisation is not enough-a new theory is needed, a ‘governing principle.’

The man who discovered this governing principle was John Nash, the subject of the widely acclaimed film ‘the Beautiful Mind.’ (the film is not a hugely accurate representation of his life, however, by Nash’s own admission!) He discovered the principle while stirring a cup of coffee. The vortex this creates, he reasoned, is similar to human behaviour. Suppose the surface of the coffee represents the set of possible human behaviour. The centre of the vortex is a stable point. Similarly, players in a game all gravitate towards a best strategy. When all players are doing their best against others, a stable position is reached. This is known as Nash Equilibrium. All social problems have this stable point. So, to define Nash Equilibrium. It is the combination of strategies in which no single player can obtain a higher pay-off by changing their strategy unilaterally. It is the point of ‘mutual best reply.’ To take an example, let’s use the traffic game I touched on the second paragraph. Let’s say 150 drivers a commuting from city x to city y. There are 3 routes, one that takes 350 (insert unit distance), one that takes 250, and one that takes 200. So, we have the players and the strategies. To simplify things, let’s say travelling time is equal to the distance of the route plus the number of cars on the route. As the drivers are trying to minimise travelling time, the pay-off is – (travelling time). What would the Nash Equilibrium be? The answer is that it would involve no drivers on the longest route, 50 on the medium sized route, and 100 on the shortest route. Here, no driver can reduce their travelling time if only they change routes. Thus, it is the Nash Equilibrium.

Hotellings location game provides a useful law. On a street, there are two vendors, selling a product of equal price and quality. On the street consumers are linearly spread across the street. They choose the vendor that is closest to them. The question is, how can vendors maximise the number of customers they receive, in a way that whatever their rival does, they will be no worse off. The answer is, for both vendors, to set up shop exactly half way along the street. This is a Nash Equilibrium. If either moves individually, they will receive less customers. So, it shows it is best in certain situations to be as similar to your rival as possible. In fact, the concepts from it can even be used to find out what determines the policies of the democrats and republicans. In this example, instead of a street, in which each location on it represents a strategy (of where to set up shop so as to maximise the number of customers they receive) the line representing the set of possible strategies is a linear line, with very liberal policies on one end, and very conservative policies at the other end. Furthermore, the pay-off for the two parties is not customers, but the votes they receive. Of course, the voter’s views are not linearly spread across this liberal-to-conservative line, so the Nash Equilibrium is not exactly half way through this line. Instead, the median voter’s view, when voters are ordered liberal to conservative, is equal to the Nash Equilibrium, for both parties. The mutual best reply for both parties is to adopt policies suiting the median voter’s views. Thus the Nash Equilibrium predicts that both parties will adopt identical policies. Obviously, this is not true, so Nash Equilibrium is not completely accurate, say as Newton’s law would be. However, it captures an important driving force of player’s behaviour, in this case that political parties are inclined to move closer to another parties policies in order to steel votes.

So, to conclude, any social problem can be solved roughly by forming it as a game, and then applying the Nash equilibrium solution concept. Though not completely accurate, it provides a useful benchmark of analysis.

Why are monopolies seen as market failure?

A pure monopoly is a market where there is only one supplier of the product. The firm with the monopoly has the power to change market prices by shifting supply. Pure monopolies are rare. Monopolistic competition is more common. For example, Microsoft in computer operating systems, who have a market share of over 80%. As opposed to competitive free markets which are said to be productively and allocatively efficient, monopolies can result in inefficiencies, and abuses which lead to decreases in economic welfare for consumers. This means monopolies are often labelled as a market failure, where there is inefficient allocation of resources in the free market. Monopolies can lead to lack of choice for consumers, less dynamic efficiency, lower motivation and therefore productivity and the exploitation of consumers, in some cases via cartels. However, it can also be argued that monopolies can actually increase choice and dynamic efficiency, as well as improving productive efficiency and the ability to compete in foreign firms.

Of course, in a monopolistic market, one firm controls most of the supply of the product and the consumer has less choice of firms in which to buy the product. This gives the supplier power to rise prices without fear of a decrease in marginal revenue as demand, due to a lack of substitutes for consumers, is inelastic.

This is a form of market failure, as allocative efficiency, which is where available economic resources are used to produce the combination of goods and services that best matches people’s preferences, drops as supply is reduced by firms below the market equilibrium so as to raise market prices. This means that output is lower, and prices are higher than in a perfectly competitive market. So, too little of a good is consumed at too high a price, resulting in a fall in economic welfare. This can also happen when a group of companies collaborate, in a cartel, to manipulate prices. OPEC, for example, a cartel containing oil producing countries such as Saudi Arabia, lowered supply by 7% in 2009 to maintain oil prices following the financial crash of 2008. It can be argued, however, that monopolies can actually lead to more choice, as larger firms can afford to stock a larger range of products. As an example, Tesco can stock a far larger range of products than an independent corner shop. However, even though monopolies can result in more choice for consumers, they certainly do allow the monopolies holder to exploit consumers to increase profit margin, thus creating a market failure.

Monopolies can also result in a different kind of market failure arising, due to dynamic inefficiencies. A situation where it is impossible to make one generation better off without making another generation worse off is dynamically efficient. However, lack of competition means there is little incentive to invent and innovate, damaging dynamic efficiency. However, again, it can be argued monopolies actually improve dynamic efficiency. Supernormal profits act as an incentive for research and development (R&D) to invent and innovate, as gains won’t be competed away. Furthermore, the possibility for technological progress is possibly greater, as there is less duplication in R&D. GlaxoSmithKline, a pharmaceutical company, uses this argument to justify monopolies on certain drugs, such as the anti-depressant Seroxat. However, on balance the lack of competition means that the minimised incentive to innovate reduces dynamic efficiency overall, especially considering the often short-term goals of firms executives.

Moreover, there is a line of argument that suggests that monopolies bring with them productive inefficiencies. As with dynamic inefficiencies, a lack of competition is pivotal. This leads to poor motivation and performance, decreasing productivity. Furthermore, inelastic demand coupled with a monopoly holder’s power to control supply, means that in order to obtain a higher profit margin firms lower output, despite this meaning that the firm doesn’t operate at the lowest possible average cost.

However, monopolies can also result in increased productive efficiency. Economies of scale can occur, in which larger firms can reduce average cost because of their size (specialisation; technical, managerial, financial and network economies of scale). Monopolistic firms also avoid costs of competition. They have more bargaining power with their suppliers for example, also this has the associated problem of exploiting their suppliers. However, conversely the size of monopolistic firms can also lead to diseconomies of scale.

The existence of a monopoly in a market is, despite potentially having positive aspects, considered a market failure. They can actually improve choice for consumers. Furthermore, they can result in economies of scale or act as in incentive for R&D, which results in future improvements in productivity. However, they are regarded as a market failure because more often than not, they reduce choice for consumers, result in a decrease of economic welfare via higher prices and can reduce both dynamic and productive efficiency.

‘The Curious Incident of the Dog in the Night Time’

Another article on a book, this time on ‘The Curious Incident of the Dog in the Night Time.’

Mark Haddon’s novel is in principle fairly standard. A young detective stumbles upon a mystery, and attempts to solve it. Unlike most novels of this kind, however, the young detective who narrates the tale has an unusual view of life. Christopher Boone suffers from an intense form of autism and, by his own admission, ‘cannot tell jokes’ and cannot read facial expressions. Through his ‘detecting,’ truths that had been kept hidden from him begin to unravel and a sense of dramatic irony lingers throughout the novel. Only long after we discover something, due to his condition, does he catch on.

Christopher is extremely organised and methodical. He thinks very logically, but without emotion. For example, the majority may feel that it’s perfectly reasonable to ask someone to be quiet. Christopher, however, is confused by this request and asks ‘for how long,’ when his mother asks Christopher to be quiet. And he’s got a point. How do we know how long we should be quiet for? By judging the mood of the person who has told us to be quiet, something Christopher is unable to do.

He often compares humans to computers. For example he says that when he closes his eyes it ‘is like pressing CTRL+ALT+DEL and shutting down.’ Unable to see the emotion in anything, he compares humans to computers, something he feels comfortable, and at home with.

Despite, or perhaps because of, his logical outset, he struggles-being autistic-to communicate with others, making ‘a noise like a dog barking’ on three separate occasions when someone touches him. The striking thing is that on none of the occasions he does he treat this behaviour as out of the norm, nor does he note the reaction of the person he has barked at. If someone barked at you, I’m sure you would respond with a look of bafflement, and quite possibly worry, over the person’s mental state. He has absolutely no idea of other people’s thoughts, or emotions, and is unable to interpret the responses of the people around him

Christopher insists ‘this will not be a funny book.’ However, because of this, it is. His ability to treat any sarcastic comment, or joke, seriously, means that he writes down in his book a particular person’s attempt at wit as a legitimate comment. For example, a man at the till sarcastically calls an A to Z map a ‘sodding crocodile.’ Instead of laughing, or discarding the comment as off hand, Christopher wonders whether ‘I had heard him wrongly’ because ‘it wasn’t a crocodile.’ The shop owner’s comment isn’t exactly hilarious by itself, but it is Christopher’s incomprehension that makes the sequence funny. It is ironic that the element that makes the book funny is Christopher’s lack, rather than abundance, of humour.

Although the novel is reasonably funny, the novel is also deeply frustrating. As he unravels more clues, he damages the lives of everyone close to him. His parents split up because ‘of the arguments’ they were having over him. When he discovers his dad killed Wellington, the dog whose death he was investigating, he decides to live with his mother and her new partner. Not for a moment does he consider the impact it will have on the couple. After a few weeks the couple split, because of Christopher. Even when Mr Shears, his mother’s new partner, stumbles into Christopher’s room late one night, and asks ‘Don’t you ever, ever think about other people,’ he doesn’t realise the stress and anguish he gives people looking after.

He even says ‘everything was O.K’ as ‘the doctor gave her [Mother} pills to stop her feeling sad,’ not considering for a moment why she was sad. It’s enough to make you really dislike Christopher. That’s why the book is, in my opinion, so masterfully written. The whole point of autism is that the suffers of the syndrome find it difficult to relate to ‘normal’ people, and vice versa. We aren’t meant to feel sympathy for him, but for the people around him. At least, that is what I feel, more than anything else.

He ‘groans’ whenever there is too much noise-‘information’-around him. As he notices much more than the majority (for example he notices ’19 crows’ whereas most people would just notice that there are crows) a crowded space means he gets ‘confused’ with all the information and groans to create ‘white noise,’ which reassures him. However, again, he is self-orientated, not caring how this behaviour may anger, irritate or worry people around him, but only about how it benefits himself.

However, Christopher Boone’s unique perspective shows us that everyone’s opinions on life are subjective. He serves to show us the diversity of human opinion by representing the rational, rather than emotional, extreme of human perspective. His thought processes are ruled entirely by his head, rather than his heart.

‘Cry Freedom’

An article I wrote after reading ‘Cry Freedom’

Cry Freedom, based from the 1987 film of the same title, describes the true story of South Africa journalist, Donald Wood, and his dangerous relationship with Steve Biko, a prominent black activist during the South African apartheid. Wood had published several articles, as a newspaper editor, which criticised Biko, but upon a meeting between the two, a friendship was forged, and Wood became increasing sympathetic towards the plight of black South Africans. Due to his influential position as a newspaper editor, he begun to attract the attentions of the South African authorities, after publishing several pro-black articles, culminating in the Wood family escaping from South Africa. Most culpable in forcing Wood out of the country was his determination to expose the police’s complicity in the death of Steve Biko, who died in suspicious circumstances while under government custody.

The book outlines a key reason the apartheid was allowed to flourish for as long as it did. Although many white South Africans were uncomfortable with the inequality present, with blacks consigned to live in crowded townships, in which many houses had no access to electricity, they accepted it due to their cosy live style. The overcrowded black settlements meant that white South Africans usually had large houses with large gardens, and a black servant was not limited to the wealthy, but was in actual fact almost the norm. Furthermore, censorship ensured the white population were not fully aware of the plight of the black population. Any anti-apartheid citizens were ‘banned.’ These citizens were barred from leaving their banning zone, and were not allowed to be quoted, in publications for example, nullifying the ability of the anti-apartheid message being spread. Some of the white population actually believed they were being generous-even kind-to the blacks of South Africa, by offering employment, as a servant, for example.

Steve Biko, who was considered a major black political voice by the tender age of 25, was a leader of the Black consciousness movement (BCM). The BCM were critical of the views of white liberalists, who were sympathetic towards black South Africans, dismissing them as ‘condescending.’ Black consciousness can be described as an awareness among blacks that their identity is based on the fact they are black. It accepts that they have a culture and history which is separate to that of white South Africans. Members no longer accepted being judged according to white values and norms, thus liberating themselves from the slave mentality created by institutionalized racism. As such, the movement wanted a society in which blacks and whites had equal opportunity to forge a future for themselves, uninhibited by the racist views of the apartheid government. As such, it’s aim could be described as to achieve something similar to peaceful co-existence (in which Khrushchev, then leader of the Soviet Union, outlined his wish for communism and capitalism to exist peacefully alongside each other, during the Cold war) in that the whites and blacks of South Africa could live alongside each other in a peaceful manner, despite their differing histories and customs.

On a more personal, and human level, Cry Freedom illustrates the ability of people to stand firm, in the face of adversity. It portrays the loyalty that can be created due to the presence of oppression. In the aftermath of Biko’s death, Wood was determined to expose police involvement, despite the huge risk he places not only on himself, but his entire family. So loyal is he to a friend, he is willing to leave his whole live behind, so as to realise the ideology Biko had preached so fervently. However, on the flip side of the coin, it also exposes the cruelty, and the ability to ignore atrocities, humans can display, for the sake of self-preservation. These qualities are exhibited by Jimmy Kruger, the South African minister for justice. He ignores Wood’s plea to expose police involvement in Biko’s death, and sends men to harass Wood due to his friendship with Biko. In short, he is willing to ignore the horrific treatment of someone who has done nothing wrong apart from voicing their political views, so as to keep the blacks oppressed, allowing him to keep his huge estate, vast wealth, and extravagant lifestyle.

The apartheid ended in 1994, thanks in part to Nelson Mandela and Frederik de Klerk, who won a joint Nobel peace prize the year before. So that discrimination does not facilitate such catastrophic consequences in the future, such as the 46 years of oppression the South African Apartheid resulted in for South African blacks, novels, and other forms of communication such as this one must be spread. It is importance to remember the brutal consequences of discrimination, such as the Holocaust for one, so that the mistakes of the past are not repeated in the future.

Why Does Antarctica Matter

This the essay I wrote for the young geographer of the year award.

The Antarctic treaty was signed on the 1^st December 1959 by 12 separate governments (Argentina, Australia, Belgium, Chile, France, Japan, New Zealand, Norway, South Africa, USSR, United States, United Kingdom, South Africa). It was preceded by the International Geophysical Year (IGY), the first major multi-nation research project in Antarctica. Of the twelve nations (same as above) involved in the project, nine made territorial claims. Therefore, so their differing political agendas would not handicap research programs in Antarctica, the Antarctic Treaty was drawn up immediately after the IGY ended. The treaty made territorial claims impossible, and put clear jurisdiction laws in place. Furthermore, the treaty ensured that Antarctica would remain a non-military zone, the only continent on Earth which can lay stake to that claim. In Article I it is stated ‘there shall be prohibited, inter alia, any measure of a military nature.’ Removed from political and military asides, work on the continent could be focused on scientific discovery. Article II of the Antarctic treaty established ‘freedom of scientific investigation,’ while Article III of the same referred to a number of clauses so as to ‘promote international cooperation in scientific investigation,’ including that ‘information regarding plans for scientific programs in Antarctica shall be exchanged.’ As such, the Antarctic treaty has set a precedent for scientific discovery and cooperation between different states. Moreover, the treaty reinforced the importance of the conservation of plants and animals native to Antarctica. Since its formation, the Antarctic treaty has gathered momentum, with 46 signatures currently, each from a different independent state. It has largely been branded a success, as an example of how governments with political differences can work together. Indeed, the treaty’s terms have allowed Antarctic to become, as the Antarctic parties call it, ‘a nature reserve, devoted to peace and science,’ which is one reason why Antarctica does matter.

The Antarctic treaty, due to its reference to freedom of scientific investigation and cooperation between nations, relating to scientific work in Antarctica, has caused ground breaking scientific work to develop in Antarctica. One illustration of how Antarctica has seen cooperation between major political powers is the third International Polar Year (IPY), of 2007-08. In this project scientists from more than 60 nations collaborated so as to increase scientific knowledge and understanding of polar areas. It is an example of information sharing between usually separate scientific entities, which sped up development, in various fields, due to the wider range of scientific information available to each individual. More specifically, the setting up of weather and research stations in the Antarctica have led to a much improved understanding of weather patterns, climate change and the ozone layer. In particular, relating to the ozone layer, three scientists working in Antarctica named Joseph Farman, Brian Gardiner and Jonathan Shanklin discovered a recurring springtime ozone hole above Antarctica. The discovery of the above problem has allowed preventative measures to be taken to ensure the problem of the Antarctic ozone hole does not augment. The discovery, made due to access to the Antarctic, highlights the importance of the Antarctic. In addition, the landscape of Antarctica is predominantly white, which has meant that it is one of the better places on Earth for meteorites to be discovered, due to the contrast between Antarctica’s white landscape and meteorite’s dark (often black) colour. The meteorites can then be analysed, aiding scientific research, and providing yet another factor displaying why Antarctica does indeed matter.

The Antarctica is home to a unique landscape which, due to its status as the only continent on Earth without a native human population, is home to wildlife which has remained undisturbed for centuries. The importance of conserving Antarctica’s biodiversity cannot be under estimated. There are 21 species of penguin that call Antarctica their home. The number of penguins in Antarctica have dropped alarmingly over the past 40 years (see Figure 1), emphasizing the

figure 1

importance of conservation work in Antarctica. In addition, if even one species on Antarctica becomes extinct the whole Antarctic food web will become unbalanced, potentially leading to the extinction of some species and mass over population of another. Possibly, the species which experience population growth could carry a disease harmful to humans, or be malign in another fashion. Thus, the importance of the Antarctic ecosystem remaining stable is conceivably a matter of life or death. Other than penguins (including the Emperor, Gentoo, King and Macaroni penguins), Albatrosses can be found in Antarctica, with wing spans of up to 3 metres. Among the wildlife present in Antarctica are several species of Whale, including the killer and fourtooth Whales. On top of that dolphins and seals can also be found in the icy waters of Antarctica. There are six species of seal resident in the Antarctic. These include the Weddell, Ross and Leopard seals. Seals are extraordinary in how well they are adapted to their environment (see figure 2).

figure 2

They have a layer of blubber up to four inches thick to protect themselves from the biting cold. As well as this, they have slits for nostrils that close upon entering water, shutting even tighter when under higher water pressure. Additionally, some species of seal can breathe under water for up to two hours. Seals can even eat their prey while underwater without drinking sea water, as a result of their unique mouths and larynx’. Feeding these animals are krill (a Norwegian word meaning ‘wale food’) who live in phenomenally dense swarms which usually consist of around 10,000 krill per each cubic metre. Fascinating plants, which exhibit ingenious adaptations to allow survival in the harsh Antarctic conditions they live in, can also be found. One example is the Pearlwort. This plant grows in close clusters so as to resist the cold of the Antarctic.

igure 3

Playing host to such an exhilarating array of wildlife, Antarctica has the ability to inspire and excite generation after generation of people. Tourism to Antarctica has become more and more popular in recent years- as figure 3 shows. This rise in tourism in Antarctica can be attributed to the rise in extreme tourism, which is defined as a niche in the tourism industry, involving travel to physically challenging places by people wishing for a challenge, and something to do that no one else they know has done before. In this respect, Antarctica is important in that it provides people with a tourist outlet in which they can challenge themselves in an unfamiliar environment-although to describe this as Antarctica’s only, or principle reason for importance wold be grossly unfair. Of course, the growth of tourism isn’t just beneficial for the tourists. It has also allowed chances for opportunistic entrepreneurs to grow businesses exploiting the growth of tourism in Antarctica, as a result creating jobs in the tourist sector.

Perhaps most important in illustrating the Antarctic really does matter, is the major role it plays regulating the Earth’s global climate system. It has two main functions, in ocean circulation and in heat balance. Almost completely covered in ice and snow, Antarctica is a white area. As such, it is a good reflector, reflecting much of the solar energy that hits its surface back into space. As a result, Antarctica acts as the main region-along with the arctic-of heat loss from Earth to space. However, when global warming causes ice to melt, it means less solar energy is reflected back into space, causing further warming- a system of positive feedback if you will. In order to explain Antarctica’s role in ocean circulation, I must first take you through some preliminary explanations. When sea water freezes, the salt present in the water cannot be accommodated in the newly forming water crystals. As such, the salt is ‘pushed’ out. This causes high salinity levels in the regions of water near the frozen sea water. This extra salt causes the sea water to become denser. As a result it sinks, pushing deep water to one side, causing current to flow. Therefore, the freezing and melting of thousands of square kilometres of ice from winter to summer in the Antarctic plays a significant role in ocean circulation due to the currents created.

In conclusion, due to the reasons I have illustrated, you would be hard pressed to argue the Antarctica doesn’t matter. For one, the scientific discoveries relating to Antarctica-such as the discovery of the Antarctic ozone hole-have enabled more widespread problems to be tackled due to an increase in knowledge, therefore having globally beneficial consequences. Moreover, the Antarctic treaty is recognized as an exemplary case of different nations working together successfully for the benefit of all. Furthermore, the continent is home to a unique and breathe taking landscape and ecosystem, which will surely inspire awe in visitors for generations to come. Finally, of course, Antarctica is a major component of the Earth’s global climate system, making it important in maintaining the very existence of the human race. Were a large enough portion of the ice covering Antarctica to melt, heat loss from Earth would be severely restricted, leading to temperatures which could, very possibly, lead to human deaths and-although unlikely-extinction.

How a fall in investment could effect the UK economy

Investment is the part of current output devoted to further production, i.e. the creation of capital (a good which is used to create more goods) and the cost of maintaining existing capital. The UK economy is judged on how well it achieves its goals of steady economic growth, low unemployment and inflation (around 2%) and trade stability. In the UK, interest rates are very low (at 0.5%) and have been since March 2009, in the aftermath of the financial crash. This is an attempt to boost investment due to negative affects low investment expenditure can cause. The link between interest rates and investment is shown via the MEC curve. However, the UK’s ultra-low interest rates haven’t boosted investment as it was expected to.

Two measures of the strength of the economy are the aggregate demand and supply curves. Aggregate demand (AD) is the total expenditure by all consumers, businesses, the government and individuals and firms abroad. It can represented by the following equation:

Aggregate Demand= Consumer expenditure + Investment + Government Spending + Net Exports

A change in any of the factors in the equation will change aggregate demand. There are two types of Aggregate supply (which is the volume of goods and services produced each year). Short Run Aggregate Supply (SRAS) shows planned output when prices can change but prices and productivity of factors of production are constant. Long Run Aggregate Supply (LRAS), which investment directly effects, is a measure of a country’s potential output. Both supply and demand will be effected by a fall in investment.

As a component of AD, a significant fall in investment will lead to an inwards shift of the AD curve. This could lead real output to decrease, and could therefore increase unemployment. Furthermore, the negative multiplier effect could cause the economy to suffer further. The increase in unemployment could lead to a fall in consumer spending, shifting the AD curve further inwards, and further reducing real output and unemployment levels. However, the fall in investment could be offset by another factor of AD, particularly government spending, which could rise in a deliberate effort to offset the fall in investment. Moreover, the size of the multiplier (defined as the number of times by which the rise in national income exceeds the rise in injections of demand that caused it) will affect the impact a fall in investment has on the economy. The larger the multiplier is, the larger the negative impact a fall in investment will have on spending and unemployment. In UK the multiplier is very low, at 0.5, so the impact of a fall in investment will be more subdued.

A fall in investment could lead to a fall in productivity. For example, computers may not be updated, or machinery may fall into disrepair. This in turn increases costs of production, and would lead to an inwards shift in SRAS, which would decrease real output and slow down economic growth.

A reduction in investment could also lead to a decrease in international competitiveness. This could lead to problems with the UK’s balance of payments. Exports may fall, while imports rise. This would cause an inwards shift in AD. This could cause deflation. Deflation is a serious problem for several reasons. Firstly, it discourages consumer spending, a component of AD, who wait in anticipation of cheaper goods in the future. Therefore AD further retracts. Secondly, it increases real interest rates, therefore further reducing investment and shifting AD further inwards. Furthermore, it leads to increases in real wage. This causes real wage unemployment (when wages are become so high supply of labour becomes greater than demand), and unemployment therefore increases.

In the longer term, a significant fall in investment could lead to a decrease in productivity. Thus, the LRAS shifts inwards, causing trend growth rate to decrease from its current rate of 2.5% a year in the UK. Therefore, a short term increase in AD could reduce the output gap significantly enough to lead to rapid inflation. As a result of this, interest rates could be risen to reduce inflation. This increase in interest rates would further decrease investment, and subsequently slow down economic growth. Of course, if the output gap was sufficiently wide to start with, even a sharp increase in AD might not be enough to trigger rapid inflation. Less investment could also have positive benefits. Less may be invested into developing, and manufacturing technology. This could lead to a higher demand for labour, and a decrease in unemployment. Lower unemployment could lead to an increase in consumer and government (less money spent on benefits for the unemployed) spending, resulting in an outwards shift for AD.

Furthermore, the rise of emerging markets such as China and India may offset falls in domestic investment as they look to invest in European markets. For example, The Chinese, including state-owned China National Nuclear Corporation (CNNC), are investing in a nuclear power station at Hinkley point, Somerset. Therefore, foreign investment may simply slowly replace domestic investment and the impact on the economy will be limited.

In conclusion, a fall in investment will have negative effects both in the long term and the short term. In the short term, AD will fall, leading in stagnating economic growth, and rising unemployment. SRAS will also fall, due to higher costs of production. In the long term, a fall in investment will cause a shift inwards of LRAS, leading to a slowdown in economic growth. The impact of a fall in investment would depend on the size of the multiplier effect, the extent of foreign investment and to what extent other components of AD changed.

James I’s financial problems

Were they his fault?

Upon James accession to the throne in 1603, the treasury had a surplus of £90,000, with debts of £400,000 cancelled out by outstanding debts owed by France and the Dutch and by an uncollected subsidy vote by parliament. By 1606, James had amassed a debt worth £816,000. This was in part due to James extravagance, and ill-advised financial ventures. However, blame can also be attached to the legacy left behind by Elizabeth and the nature of the patronage system. Furthermore, rapid population increase, coupled with a decline in trade, added to financial difficulties. Finally, structural problems with the taxation system-and the exploitation of these faults-further served to enhance the financial issues faced by James. James must take a large portion of the blame. However, the sum of factors outside James control (e.g. population change, Elizabeth’s legacy) was more influential than James in causing the financial difficulties he faced during his reign.

James’ extravagance was certainly important in causing financial problems. James, excited by the new wealth available to him as king of England (comparing his move from Scotland to England he described it as being “like a poor man wandering about forty years in a wilderness and barren soil, and now arrived at the land of promise”) he vastly overspent. In 1510, he spent £35,765 on his son Henry. The Wardrobe account averaged £36,377 in the first five years of James’ reign, compared with £9,535 in the last 4 years of Elizabeth’s reign. £6,467 was spent on Prince Charles debut in the tiltyard in 1621. In 1603 fees and annuities to courtiers amounted to £27,270. By 1605 this figure had risen to £47,783.All these figures point to ridiculous expenditure on James part, leading us to believe James did indeed cause his financial difficulties. In part, he did. However, court had to impress foreign envoys, hence extravagant spending was partly justified. Court festivities, for example, was considered a valuable political investment. One reason for the step-up in household spending from Elizabeth to James was that, unlike Elizabeth, James had a family to look after. Furthermore, courtiers and office holders had very low official salaries, and therefore relied on grants from the crown and other forms of patronage. Courtiers took advantage of James generosity, squeezing more ‘fees and annuities’ out of James than they could Elizabeth. However, despite these minor explanations for James expenditure, James’ extravagance must be considered a major reason for the financial reasons he faced.

Secondly, Elizabeth’s legacy helped create financial problems for James. Linking back to James’ spending on patronage, the scale of it can be blamed, in part, on Elizabeth. During her reign, Elizabeth had been reluctant to hand out forms of patronage, anxious as she was to avoid running into deficit. This meant that by the time of James’ accession, there was enormous demand from disillusioned courtiers. As a foreign king who had to ensure loyalty, it was inevitable James would have to concede to the courtiers, and hand out more patronage than Elizabeth had. Elizabeth’s policy of cutting expenditure (a short term fix to financial problems) rather than increasing revenue (a long-term fix) caused difficulties for James. She sold crown lands, which served to raise quick cash, but that also had the knock-on effect of impoverishing the crown in the future. Furthermore, she made no attempt to exploit the crowns land, and thus increase revenue. Long term leases on crown owned land were agreed, which meant that towards the end of the lease’s timespan, the annual rent of the household was vastly less expensive than the lands actual value. For example, a 50 year lease on crown property in Bermondsey was agreed in 1587 at a rent of £68 a year. In 1636, when the lease fell in, the property was found to be worth £1,071 a year. These long term lease’s restricted James’ ability to exploit crown lands, thus worsening his financial situation. Moreover, James inherited a war with Spain, a huge drain on finances. However, as the war was concluded following the Treaty of London in 1604, just one year after James’ accession to the throne, it could be argued that the Anglo-Spanish war he inherited was not a major factor in causing financial tumult. Despite this, Elizabeth’s legacy was partly to blame for James unstable financial position. Clearly then, not all blame for financial difficulties can be placed on James.

Several other reasons can be seen to have helped to cause financial difficulties for James. For one, the dramatic increase in population size England saw during the period. From 1500 to 1603 the population increased from 2.5 million to over 4 million. However, agricultural development could not grow at the same rate. This impoverished the nation, as there was insufficient industry, and as a result unemployment increased. The consequence for James was that the poorer England was, the less tax he could levy, thus placing his finances under strain. However, taxation-related problems didn’t end there for James. Parliamentary subsidies were based on land valuations. These land valuations were the responsibility of the local elite. As such, they shamelessly undervalued the worth of their, and their neighbour’s properties, so they wouldn’t have to pay as much tax. Therefore, even with inflation (which was itself a problem as goods became more expensive for the crown) each subsidy was worth only £55,000 in 1628, compared with £130,000 in the mid-sixteenth century. Furthermore, trade was on the decline at the time. Wool, England’s main export, was becoming less and less popular as Europeans became less fond of the rough, undyed wool England specialised in. As a duty was paid to the crown on every exported good, this decline reduced James’ revenue. However, the decline of the English wool trade can be partly blamed on James, in the form of the Cockayne project. Cockayne, a city merchant, argued England should export a more finished cloth to revive its popularity in Europe. In 1614, James was then persuaded by Cockayne to take the monopoly on cloth away from Merchant Adventurers, an established company, and hand it to Cockayne’s new company, the King’s Merchant Adventurers. However, the company was poorly financed, and lacked the expertise required. By 1618, the cloth trade had collapsed, and never reached the levels of 1614 again. So, although several factors outside his control did harm royal finances did negatively affect royal finances, he could perhaps have done more to rescue the situation he found himself in. For example, he could have forced changes in the taxation system, although that would have admittedly have been difficult with the uncooperative parliament he found himself with. Furthermore, his decision to approve the Cockayne project was undoubtedly a poor decision. Even factors causing financial problems which seem at first glance unrelated to James, can on further inspection be considered to be partially problems of James’ own making.

In conclusion, Elizabeth’s legacy James’ extravagance served to severely hamper finances. Furthermore, although trade and taxation were problems independent of James, his actions arguably worsened the negative effects they caused for the crowns finances. However, Elizabeth’s legacy (including her stance on patronage, and her ongoing war on Spain) coupled with population growth and inflation had a larger effect on the poor state of James finances than James’ admittedly inept management of the crowns finances. Without population growth, inflation, war, taxation flaws and issues with patronage James I’s financial problems would arguably have been comparatively minor. James I financial problems were, to a large extent, of his own making. However, a larger extent of the blame must be attached to factors outside of James’ control.

Solar Power

 

How it creates energy

There are two main types of solar power, solar thermal and photovoltaic (PV). Solar thermal solar panels use the sun’s energy to heat up water, which can then be used in washing and heating.

A PV panel is made up of a semiconducting material sandwiched between two electrical contacts. To generate as much electricity as possible PV panels need to spend as much time as possible in direct sunlight. When sunlight strikes the panel and is absorbed, it knocks loose electrons from some of the atoms that make up the semiconductor. The semiconductor is positively charged on one side and negatively charged on the other side, which encourages all these loose electrons to travel in the same direction, creating an electric current. The contacts capture this current in an electrical circuit.

Contribution of energy production

Solar PV and solar thermal amounted to 3.3% of total renewable energy in 2013. This equates to 0.49% of total energy use in 2013. Globally, it as of 2015 accounts for 1% of all global electricity demand. China, Japan and the USA are the main drivers of solar instillations, with the Asia Pacific region reported to install 505 of all solar capacity in 2015. India has set a massive 100GW target by 2022.

Where is solar power used and why

Despite having less solar power available than other areas in the world, Europe has the highest capacity of solar PV power. Out of the top ten countries with the highest installed capacity for solar PV power, 6 are European. This is because of the wealth of Europe, and subsidises provided by European governments. Countries with more solar energy available tend to be poorer- the majority of Africa. China, Japan, Australia and the USA are also in the top ten and Middle Eastern countries are increasingly looking at solar power. In 2012, Saudi Arabia announced it was raising funds to spend $109 billion on solar energy.

Advantages of use / exploitation

-Solar energy consists of a one-time payment. After the equipment is installed the energy is free.

-Solar power is a renewable energy source, and is not a pollutant.

-Solar energy can be used in remote areas where it is too expensive to extend the electricity power grid.

-It requires little maintenance.

-It is a silent energy producer.

Disadvantages of use / exploitation

-As solar energy requires sunny conditions, it can be an unreliable energy source in climates such as the UK, when sunny conditions can be sporadic.

-The equipment needed in harnessing solar power is still very expensive, although prices are dropping.

-Large areas of land are required for solar panels.

-Solar panels cannot function at night. Also, solar panels function best when the sun is directly facing them. Therefore, panels in a fixed position will see a reduced energy production when the sun is not at the optimal angle.

Landmead, Oxfordshire

It is the largest windfarm in the UK. The 46MW farm was built on low-grade farmland used for grazing sheep. In 2014 the wind farm was connected to the national grid and will be capable for providing power for as many as 14,000 homes in the UK. No solar farms had been connected.

Walpolenz Solar Park

It is a 52MW PV power station in Germany. It cost 130 million euros to build and takes up 544 acres in total. Construction finished in 2011, and it now provides close to 16,000 homes with electricity in the eastern German townships of Brandis and Bennewitz. Germany has a higher capacity of PV solar power than any other country.

OIL-The Price Drop 2015

Over the last 12 months the Brent Index, which measures the price of oil, has fallen sharply, over 50% from $100 in the September of last year to $47.97 on the 9^th September. On the 24 of August, the price was $42.69, a six year low. Over the past year the price of oil has suffered two rapid falls in price, as the chart shows us. These two major falls in price sandwich a period of relative stability in prices. In the four months leading to January 2015 the WTI index fell by approximately $40. Throughout the following 5 months, oil prices stabilised, with prices not falling below, or rising above, a range of $13. However, between July and September fell a further 35% to $42. This decrease was partially offset by an increase in the WTI index, up to $47.79 per barrel on the 9^th August.

One reason oil prices have dropped this year is due to the strong dollar. As the Brent Index is measured in dollars, a strengthening dollar leads to a drop in the Brent Index because the same amount of dollars buys you more oil. A recent expansion in supply has also resulted in oil prices plummeting. Over the last six years oil production in the United States has almost doubled, which has pushed oil imports out of the country. Oil from exporters such as Saudi Arabia and Nigeria which was exported to the United States is now being send into Asian markets. As a result of this increased competition in asian markets, oil producers are being forced to lower oil prices so as to remain competitive in the market.

Weakening economies in Europe and in developing countries such as India are affecting demand. China, who are the world’s biggest oil importer, devalued the yuan on successive days in August, suggesting their economy is struggling. A struggling economy will import less oil, keeping demand down. Another factor keeping demand down is that vehicles are becoming increasingly energy-efficient, requiring less and less fuel to travel the same distance.

Contributing further to the drop in oil prices is the absence of OPEC (the organisation of petroleum exporting countries), which has before intervened and hauled oil prices back up, by reducing production (and therefore supply). On this occasion, OPEC has declined to reduce production. Although some members of OPEC do wish to reduce production, members including Saudi Arabia and the United Arab Emirates refuse to do so. Saudi Arabia site a loss of market shares, and that it’ll benefit their competitors, as reasons to not cut production so as to increase prices.