1.0. Introduction to Economics

Syllabus Content

  • Economics as a social science
  • Concepts of scarcity, choice and opportunity cost
  • Central themes of the course

Task 1: View the introductory video on Economics below and write down five words, which in your opinion, you will encounter throughout the IB Economics course

Task 2: The following is an excerpt from the book 'Black Box Thinking' (2015, p.39)

'Bomber aircraft in Europe were being asked to take huge risks. For certain periods of the conflict, the probability of a pilot surviving a tour of duty was little than fifty-fifty. Kevin Wilson, the military historian, described these remarkable and brave men as 'ghosts already'. The wartime leaders realised that they needed to reinforce the planes with armour. This would help protect them from gunfire from the ground and the air. The problem is that they could not armour the entire surface area because the planes would become too heavy to fly, and lose manoeuvrability. Wald was brought in to prioritise the areas that needed armour most.

He had lots of data to work from. To their credit the air force had taken the trouble to examine returning aircraft to assess the extent of the damage, and how they might respond to it. This was black box style behaviour. They were examining the data from adverse events in order to work out how to improve the safety of the aircraft

To the relief of the air force command, the pattern seemed clear. Many of the planes were riddled with gunfire all over the wings and fuselage. But they were not being hit in the cockpit and tail. The longer the incident reporting continued, the clearer the pattern became. You can see the pattern in the diagram below:

  • Question: if you were in charge of reinforcing the armour on planes, but could only cover one-fifth of its surface, what parts of the plane would you reinforce with additional armour?

Task 3: Watch the music clips, Bruce Springsteen's The Working Life & 'Fastcar' by Tracey Chapman below. Try and ascertain the major economic issues mentioned in the songs and how they can have major ramifications for society

Task 4: What connections do you see between your respective graphic and the subject of Economics?

Microeconomics

Economics is the scientific study of the ownership, use, and exchange of scarce resources - often shortened to the science of scarcity. Economics is regarded as a social science because it uses scientific methods to build theories that can help explain the behaviour of individuals, groups and organizations. Economics attempts to explain economic behaviour, which arises when scarce resources are exchanged.

In terms of methodology, economists, like other social scientists, are not able to undertake controlled experiments in the way that chemists and biologists are. Hence, economists have to employ different methods, based primarily on observation and deduction and the construction of abstract models.

As the social sciences have evolved over the last 100 years, they have become increasingly specialized. This is true for economics, as witnessed by the development of many different strands of investigation including micro and macro-economics, pure and applied economics, and industrial and financial economics. What links them all is the attempt to understand how and why exchange takes place, and how exchange creates benefits and costs for the participants.

The study of economics

The study of economics involves three related investigations.

1. Why scarce resources are exchanged?

2. How consumers and producers behave as they interact with each other in markets, in their attempt to achieve mutually beneficial exchange?

3. The role of government in compensating for the limitations of markets in achieving mutually beneficial exchange?

The methods used by economists

Economists use scientific observation and deduction in their investigations. To achieve this they:

Describe and measure the exchanges they observe

Economists describe changes in economic variables, and measure these changes over time. For example, economists describe and measure how interaction in markets determines the prices of such diverse products as motor-cars, houses, haircuts, and computer software. Measurement in economics can take many forms, including measuring absolute and relative quantities and values. When measuring relative values it is common to use index numbers.

Explain how interactions arise and create costs and benefits

Economists try to explain the effects, or results, of economic transactions. For example, economists can explain why, despite bubbles and crashes, the long-run trend in house prices in the UK has been upwards over the last 30 years, and can identify those who have been affected positively and negatively by this increase. Of course, economists also try to explain the short-term movements in prices, and how they also have costs and benefits.

Propose hypotheses, construct, and apply ‘models’ to test these hypotheses.

Like all scientists, economists develop hypotheses to explain why economic behaviour takes place, and then construct models to test these hypotheses. For example, economists may propose that price rises are caused by excess demand, and then attempt to construct a model of price that explains how excess demand can raise price. Economists frequently use versions of the demand and supply model to help explain events such as house price trends and movements. Economic models usually employ graphical and mathematical analysis to help explain and illustrate such economic processes.

Gather data to put into the model

Models must be tested against the real world, which means gathering statistical data about real events. In this way, a model can be improved and revised when necessary.

Predict behaviour based on these models.

The ultimate goal of the economist is to predict future behaviour. For example, by using a demand and supply model and by inputting real data about the housing market, economists can show that even a small fall in bank lending can trigger behaviour that leads to a significant fall in house prices in the short run. The ultimate value of an economic model is that it can accurately predict the onset and the effect of an economic event. The better the model is, the more useful it is in helping economists make predictions.

Economists assume that economic events and phenomena do not occur at random, but are determined by underlying and understandable causes. Unlike the pure scientist, economists cannot undertake controlled experiments, so they must test their models in different ways. Statistical analysis of actual economic data can provide a flow of information from which to build models and test hypotheses. For example, by gathering data about changes in house prices it is possible to deduce factors that cause house prices to go up or down, and by how much. Economists use index numbers to help make comparisons between countries and over time.

Correlation analysis can help determine the strength of particular causal relationships so that strong and weak relationships can be identified. For example, it might be possible to demonstrate that, of all the factors that have contributed to falling house prices, the reduced availability of credit is the single biggest factor.

The role of the professional economist

Professional economists apply their skills of description, analysis, model building, and prediction to generate knowledge and, from this, provide advice to private firms, to governments and other organisations.

Providing knowledge

1. The first function of the economist is to provide information, called economic intelligence, from which decisions can be made. For firms to survive and succeed, they need to take many decisions, but each decision carries with it a risk. The professional economist can help reduce such risks by gathering and analysing economic intelligence. This economic intelligence is only useful when it can be put into an economic model, and then applied to the decisions that need to be taken.

2. The second function of the professional economist is to interpret the data that has been gathered and provide informed advice to firms, organisations, and governments about the likely costs and benefits of the decisions they make.

In providing advice, the economist will always make an assessment of the other options that could have been chosen. For example, a large petrol refiner and retailer may be faced with a significant rise in the costs of crude oil – should it now raise price? After having made an assessment of all the pricing options, and having taken account of the likely response of rivals, the firm’s chief economist may advise it to hold price constant – perhaps the least ‘common sense’ answer.

See - Why this Nobel Prize confers ‘misleading authority’ - http://www.scmp.com/business/article/2039527/why-nobel-prize-confers-misleading-authority

Task 5: Classify each of the following topics as relating to microeconomics or macroeconomics.

(a) A family’s decision about how much income to save.

(b) The effect of government regulations on auto emissions

(c) The impact of higher national saving on economic growth.

(d) A firm’s decision about how many workers to hire

(e) The relationship between the inflation rate and changes in the quantity of money.

Positive and normative economics

As a social science, economics attempts to use the principles and methods of science to explain economic behaviour. This involves making positive statements about the economic world.

Positive statements are those that can be verified, and are factual, such as:

‘.. House prices have fallen by 15% over the last year...’

In contrast, normative statements are based on opinion and value judgement. Statements suggesting that something ‘ought to’ happen, or that something is ‘unfair’, are normative because they are matters of opinion.

For example, ‘..the recent fall in house prices is unfair to the rich..’.

This statement cannot be tested because it not based on anything testable. If there is an agreed definition of fairness, and it can be measured, then it might be possible to test the effect of the change in house prices on the degree of fairness experienced by a certain identifiable group of people defined as rich. Therefore, this statement is normative, impossible to verify, and based on opinion rather than fact.

Task 6: Classify each of the following statements as positive or normative.

(a) Society faces a trade-off between inflation and unemployment.

(b) A reduction in the rate of growth of money will reduce the rate of inflation.

(c) The European Central Bank (ECB) should raise the rate of inflation

(d) Society ought to require social security recipients to look for jobs.

(e) Lower tax rates encourage more work and more saving.

Task 7: If you were Chief Executive of Hong Kong SAR would you be more interested in your economic advisors’ positive statements or normative statements? Why?

The ceteris paribus rule

Economics is a social science, and, unlike the physical sciences, cannot engage in controlled experimentation to demonstrate how variables are connected.

In the real world, economic variables such as price and income, are constantly changing, and this creates a problem in demonstrating the relationship between variables. For example, a fall in price is likely to lead to a rise in consumer demand if we assume nothing else changes.

Of course, for independent reasons, income could also fall while demand does not rise. The fall in price could have been counteracted by a fall in income. The ceteris paribus rule, that all other things remain the same, is used whenever attempting to demonstrate the link between economic variables.

TOK: Cold fusion: A case study for scientific (mis)behavior - https://undsci.berkeley.edu/article/cold_fusion_01

Economic Exchange

Economic behaviour involves the exchange of one scarce resource for another. When people engage in paid work, they exchange their scarce time, effort, and skill for income, and, when people make purchases, they exchange their scarce income for scarce goods and services. Economic activity is driven by the need to exchange.

Wants and needs

The need to exchange has its roots in human biology. All humans are born with basic needs, including the need to eat and drink, the need to keep warm, and the need to be protected. These result in a sustained demand for food, drink, clothing, and shelter.

In addition, the human species has wants, which also have a strong influence on behaviour. DVDs, computers and foreign holidays are all examples of wants. As incomes rise the relative importance of wants increases in relation to needs. In a modern and affluent economy, the satisfaction of wants frequently dominates economic activity, while in less developed economies the satisfaction of basic needs remain the overwhelming goal.

Consumption

The process of satisfying needs and wants is called consumption. The need and desire to consume is, clearly, what drives individual economic actions and provides the motive for engaging in an exchange of scarce resources. To be able to consume, individuals need to exchange their skill and effort, or their enterprise, land or capital, for an income. They can then exchange this income for the scarce products they need or want. Through exchange, consumption is satisfied by a process called production.

Factors of production

Production involves the creation of goods and services by using scarce resources. Producers must exchange the income they earn for the scarce resources they need to enable them to produce. Therefore, both parties, producers and consumers, must exchange something they have for something others want.

There are four types of scarce resource used in the process of production.

1. Land and natural resources

This includes the land on which production is located as well as the resources contained within the land, such as metals, minerals, and oil. The environment - the air, sea, rivers, and forests – is also a scarce resource.

2. Human capital

This includes the value of human skill and physical effort that is available to an economy, and is more commonly referred to as labour.

3. Real capital

This includes all man-made assets which have been created to help produce goods and services, such as machinery and equipment. It also includes stocks of raw materials waiting to be used before they become goods and serves. The creation of capital is called investment.

4. Enterprise

Enterprise is supplied by the entrepreneur who has two crucial roles:

1. Combining the other factors in such a way that goods and services can be produced in the most efficient way.

2. Taking risks associated with the potential loss of assets or with making commercial losses.

Scarce resources are also called factors of production. All production requires the input of scarce resources.

Types of Production

Production is undertaken by firms, also known as enterprises, or businesses. There are three stages of production:

1. Primary production, which involves the extraction of resources from the earth, such as agriculture, fishing, and mining. Land and natural resources are the main resources used in primary production.

2. Secondary, which involves the manufacture of semi-finished and finished consumer goods, such as computers, motor vehicles, and clothing. Labour and capital are the main resources used in the secondary sector.

3. Tertiary production involves the distribution of products and the creation of services, such as road haulage, financial services, and healthcare. Human capital is usually the most essential resource used in tertiary production. The tertiary sector is sometimes sub-divided into tertiary, quaternary and quinary sectors. The quarternary sector of an economy includes the infrastructure of information technology and knowledge that enables an economy to produce successfully. The quinary sector is defined at the not-for-profit aspect of the economic, political and social infrastructure which supports economic activitiy, including universities, charities and government activity. Sophisticated quaternary and quinary sectors are commonly viewed as essential to economic development in a globalised economy.

The role of money in exchange

Money occupies a central role in market economies because it acts as a medium of exchange. The advent of money replaced the need for exchange through barter and enabled producers and factor owners to specialise. For example, without money, a hairdresser would have to accept another good or service as direct payment for a haircut. However, if the hairdresser is paid in potatoes, it means that he must pay for his assistant in potatoes, as well as pay himself in potatoes, and his suppliers. However, what if another client wants to pay in rice, and yet another in wheat? What is a haircut worth in terms of rice or wheat? Exchange through barter is very complex, and barter economies tend to remain highly undeveloped because direct trade is extremely difficult.

Money allows complex trade and exchange

Money is any asset that is acceptable in the settlement of a debt incurred in an exchange. For an asset to be widely used as money, it must have certain properties, including that the asset is portable, divisible, durable and stable in value. Some assets fulfill the role of money much better than other ones. Potatoes, for example, would not make a good medium of exchange because they are not durable, nor do they have a stable value. Throughout history, gold and silver have frequently been used as money, given their divisibility into bars and coins. The introduction of paper money by the Chinese in the 9th Century AD marked a significant development in the evolution of money, especially given the ease with which different denominations could be created, and the portability of paper money in comparison with gold or coinage. It is said that the Chinese invented paper money because there was a shortage of metal to make coins.

It is clear that the evolution of money as a medium of exchange, and as a store of wealth, had a considerable impact on the development of modern commerce, international trade, and global prosperity.

Task 8: Your roommate is a better cook than you are, but you can clean more quickly than your roommate can. If your roommate did all of the cooking and you did all of the cleaning, would the work take you more or less time than if you divided each task evenly? Explain.

The Basic Economic Problem

All societies face the economic problem, which is the problem of how to make the best use of limited, or scarce, resources. The economic problem exists because, although the needs and wants of people are endless, the resources available to satisfy needs and wants are limited.

Limited resources

Resources are limited in two essential ways:

1. Limited in physical quantity, as in the case of land, which has a finite quantity.

2. Limited in use, as in the case of labour and machinery, which can only be used for one purpose at any one time.

Choice and opportunity cost

Choice and opportunity cost are two fundamental concepts in economics. Given that resources are limited, producers and consumers have to make choices between competing alternatives. All economic decisions involve making choices. Individuals must choose how best to use their skill and effort, firms must choose how best to use their workers and machinery, and governments must choose how best to use taxpayer's money.

Making an economic choice creates a sacrifice because alternatives must be given up, which results in the loss of benefit that the alternative would have provided. For example, if an individual has £10 to spend, and if books are £10 each and downloaded music tracks are £1 each, buying a book means the loss of the benefit that would have been gained from the 10 downloaded tracks. Similarly, land and other resources, which have been used to build a new school could have been used to build a new factory. The loss of the next best option represents the real sacrifice and is referred to as opportunity cost. The opportunity cost of choosing the school is the loss of the factory, and what could have been produced.

It is necessary to appreciate that opportunity cost relates to the loss of the next best alternative, and not just any alternative. The true cost of any decision is always the closest option not chosen.

Task 9: Basic economic problem - Watch the YouTube clips below (People Face Trade-offs & The cost of something is what you give up to get it) and identify the connection between trade-offs and the basic economic problem (scarcity, choice & opportunity cost)

Questions related to the video 'People face Trade-offs'

A number of definitions of economics were given in the video clip notably the following three:

  1. Economics is about the allocation of scarce resources
  2. Economics is the study of how societies manage their resources; and
  3. 'Economics is the study of mankind in the ordinary business of life' (Alfred Marshall)
  • In your opinion which of the three definitions is closest to your understanding of what Economics is?
  • In the video, Mankiw spoke about the classic trade-off example of 'Guns vs Butter'. He also made reference to the purported trade-off between the environment and employment (coal industry in USA). Do you believe that this trade-off is similarly evident in Hong Kong?
  • Questions related to the video 'The cost of something is what you give up to get it'
  • This video is about the economic principle of 'opportunity cost'. Opportunity cost is defined as the value of the next best alternative forgone. In the video, Mankiw refers to not just the explicit costs of going to college (tuition fees; accommodation and living expenses) but also the implicit cost of the lost wages you could have earned if you were working instead. If attendance at university generates an opportunity cost, why do young people still attend college?

Task 10: Describe the tradeoffs (decisions that lead to an opportunity cost) that could have been experienced with the following – what is scarce; what could be the choice and what the opportunity cost is:

(a) A family decides to purchase a new car.

(b) Members of LegCo decide that more of the HRSAR Budget will be spent on the maintenance of national parks.

(c) A company’s board of directors decides to close their subsidiary in Ma on Shan, New Territories

(d) A professor decides to miss lunch in order to prepare for his economics lecture.

Task 11: Economic incentives - investigate how incentives drive economic activity. View the YouTube clip below and complete the tasks that follow:

Questions related to the video 'People respond to incentives'

  • Having watched the video, take note of three different ways in which incentives modify human behaviour.
  • Government policy can sometimes have unintended consequences of altering people's behaviour by altering private incentives. How do the examples of safety belts in cars and the provision of government pensions generate such consequences?

Task 12: The social security system in Europe provides income for people over age 65. If a recipient of Social Security decides to work and earn some income, the amount he or she receives in Social Security benefits is typically reduced.

(a) How does the provision of Social Security affect people’s incentive to save while working?

(b) How does the reduction in benefits associated with higher earnings affect people’s incentive to work past the age of 65?

Principle of Marginalism/marginal analysis - people think at the margin

Marginal analysis

Economic decisions are taken in a marginal way, which means that decisions to produce, or consume, are made one at a time.

For example, a typical consumer does not decide to drink four cans of cola at the beginning of each day, rather they make four individual decisions, one at a time. Similarly, a baker does not decide to produce 5,000 loaves of bread in a year, but decides each day or week what to produce. Economic decisions are marginal because conditions are constantly changing, and consumers and producers would be highly irrational if they did not consider this. Hence, each production or consumption decision is assumed to be made one at a time so that changing conditions can be assessed.

Task 13: Question related to the video 'Rational People think at the margin'

  • In your own words, describe what 'making decisions at the margin' actually means.

Task 14:

(a) You are trying to decide whether to take a holiday. Most of the costs of the holiday (airfare, hotel, and forgone wages) are measured in Hong Kong $, but the benefits of the holiday are psychological. How can you compare the benefits to the costs?

(b) Three managers of the Magic Potion Company are discussing a possible increase in production. Each suggests a way to make this decision.

Harry: We should examine whether our company’s productivity- litres of potion per worker- would rise or fall.

Ron: We should examine whether our average cost – cost per worker – would rise or fall.

Hermione: We should examine whether the extra revenue from selling the additional potion would be greater or smaller than the extra costs.

Who do you think is right? Why?

The principle of marginalism is embedded in the following two laws: The Law of Diminishing Marginal Utility and the Law of Diminishing Marginal Returns. Watch the two videos below to understand what these laws are.

Marginal and Total Utility

The Law of Diminishing Marginal returns

TOK: Which of the following signs would be more effective in ensuring medical professionals wash their hands? Can we apply the concept of marginalism here?

Samuelson's three questions

America’s first Nobel Prize winner for economics, the late Paul Samuelson, is often credited with providing the first clear and simple explanation of the economic problem - namely, that in order to solve the problem of scarcity all societies, no matter how big or small, developed or not, must endeavour to answer three basic questions.

What to produce?

Societies have to decide the best combination of goods and services to meet their needs. For example, how many resources should be allocated to consumer goods, and many resources to capital goods, or how many resources should go to schools, and how many to defence, and so on.

How to produce?

Societies also have to decide the best combination of factors to create the desired output of goods and services. For example, precisely how much land, labour, and capital should be used produce consumer goods such as computers and motor cars.

For whom to produce?

Finally, all societies need to decide who will get the output from the country’s economic activity, and how much they will get. For example, who will get the computers and cars that have been produced? This is often called the problem of distribution.

Production Possibility Frontiers

An opportunity cost will usually arise whenever an economic agent chooses between alternative ways of allocating scarce resources. The opportunity cost of such a decision is the value of the next best alternative use of scarce resources. Opportunity cost can be illustrated by using production possibility frontiers (PPFs), which provide a simple, yet powerful tool to illustrate the effects of making an economic choice.

A PPF shows all the possible combinations of two goods, or two options available at one point in time.

Production possibilities

Mythica, which is a hypothetical economy, produces only two goods - textbooks and computers. When it uses all of its resources, it can produce five million computers and fifty five million textbooks. In fact, it can produce all the following combinations of computers and books.

These combinations can also be shown graphically, the result being a production possibility frontier.

Interpreting PPFs

Firstly, we can describe the opportunity cost to Mythica of producing a given output of computers or textbooks. For example, If Mythica produces 3m computers; the opportunity cost is 5m textbooks. This is the difference between the maximum output of textbooks that can be produced if no computers are produced (which is 70m) and the number of textbooks that can be produced if 3m computers are produced (which is 65m). Similarly, the opportunity cost of producing 7m computers is 31m textbooks - which is 70 - 39.

PPFs can also illustrate the opportunity cost of a change in the quantity produced of one good. For example, suppose Mythica currently produces 3 million computers and 65m textbooks. We can calculate the opportunity cost to Mythica if it decides to increase production from 3 million computers to 7 million, shown on the PPF as a movement from point A to point B and textbooks is shown here.

The result is a loss of output of 26 million textbooks (from 65 to 39m). Hence, the opportunity cost to Mythica of this decision can be expressed as 26m textbooks.

Pareto efficiency

Any point on a PPF, such as points 'A' and 'B', is said to be efficient and indicates that an economy’s scarce resources are being fully employed. This is also called Pareto efficiency, after Italian economist Vilfredo Pareto. Any point inside the PPF, such as point 'X' is said to be inefficient because output could be greater from the economy’s existing resources.

Any point outside the PPF, such as point 'Z', is impossible with the economy’s current scarce resources, but it may be an objective for the future. Pareto efficiency can be looked at in another way - when the only way to make someone better off is to make someone else worse off. In other words, Pareto efficiency means an economy is operating at its full potential, and no more output can be produced from its existing resources.

Pareto efficiency is unlikely to be achieved in the real world because of various rigidities and imperfections. For example, it is unlikely that all resources can be fully employed at any given point in time because some workers may be in the process of training, or in the process of searching for a new job. While searching for work, or being trained, they are unproductive. Similarly, an entrepreneur may have wound-up one business venture, and be in the process of setting-up a new one, but during this period, they are unproductive. Despite this, Pareto efficiency is still an extremely useful concept.

It is a useful concept for two reasons:

1. It can be an objective for an economy because it can set a direction towards which an economy can move.

2. It can help highlight the imperfections and rigidities that exist in an economy and prevent Pareto efficiency being achieved.

Increasing opportunity cost

Opportunity cost can be thought of in terms of how decisions to increase the production of an extra, marginal, unit of one good leads to a decrease in the production of another good.

According to economic theory, successive increases in the production of one good will lead to an increasing sacrifice in terms of a reduction in the other good. For example, as an economy tries to increase the production of good X , such as cameras, it must sacrifice more of the other good, Y, such as mobile phones.

This explains why the PPF is concave to the origin, meaning its is bowed outwards. For example, if an economy initially produces at A, with 8m phones and 10m cameras, and then increases output of cameras by 10m (to 20m), it must sacrifice 1m phones, and it moves to point B.

If it now wishes to increase output of cameras by a further 10m (to 30m) it must sacrifice 4m phones, rather than 1m, and it moves to point C; hence, opportunity cost increases the more a good is produced.

The gradient of the PPF gets steeper as more cameras are produced, indicating a greater sacrifice in terms of mobile phones foregone.

Task 15 : Shifts in Production Possibilities Curves/Frontiers

PPCs/PPFs will shift when there is a change in the quantity and/or quality of the factors of production.

Using the following graphics, determine how the Chinese economy's PPC/PPF would be expected to change in the long-term

Scarcity, Opportunity Cost and the PPC

PPF and Opportunity Cost

Shifting the PPC

Revision video on Production Possibilities

Task 16: The following table illustrates the production possibilities of a factory producing medicines. Graph the following production points on a PPF. Vaccines should be on the horizontal axis, while Tablets should be on the vertical axis.

(a) Plot the points H and G. H is an inefficient level of production while G is currently unattainable given the current configuration of resources.

(b) Calculate the opportunity of vaccines in terms of tablets forgone. Do the same for tablets in terms of vaccines forgone.

(c) How would the PPF change if the company bought a new machine that increased the number of vaccines a worker could produce but had no effect on the number of tablets that that a worker could produce.

(d) What factors would increase the productive capacity of this factory?


Task 17: Imagine a society that produces military goods and consumer goods, which we’ll call “guns” and “butter”.

(a) Draw a production possibilities frontier for guns and butter. Explain why it most likely has a bowed-out shape.

(b) Show a point that is impossible for the economy to achieve. Show a point that is feasible but inefficient.

(c) Imagine that the society has two political parties, called the Hawks (who want a strong military) and the Doves (who want a smaller military). Show a point on your production possibilities frontier that the Hawks might choose and a point the Doves might choose.

(d) Imagine that an aggressive neighbouring country reduces the size of its military. As a result, both the Hawks and Doves reduce their desired production of guns by the same amount. Which party would get the bigger “peace dividend” measured by the increase in butter production?

Files to download

Copy of 1.0 Foundations of Economics.pptx