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A function expresses a relationship between two or more variables. The demand function is the first we'll encounter.

One need to understand what demand depends upon. What determines the quantity demanded of a good over a particular period of time? Certainly the price of the product is important, thus one can show the quantity demanded of good x as a function of its own price

QDx = f(Px)

QDx is the quantity demanded of good x, Px is the price of good x. Any study of consumer buying behaviour shows that the price of a product is one of the most important determinants of demand. However, it is not the only determinant. Many factors affect the total demand for a product - when these change, the demand curve can shift.

A movement along the curve -- a change in quantity demanded -- occurs following a change in the price of the good itself, everything else held constant (known as the ceteris paribus assumption, more on this later). A change in demand means that the quantity demanded has changed at each and every price level. This occurs if one of the conditions of demand changes.

Consider the factors that cause an increase or a decrease in demand for a good or service, these factors are also called the conditions of demand.

• Change in the price of a substitute
  Substitutes are goods or services in competitive demand and acts as replacements for another product. For example, a rise in the price of BP petrol should cause a substitution effect away from BP towards GapCo or other competing brands. Consumers will tend to switch to the cheaper brand or service provider.
• Change in the price of a complement
  A complement tends to be bought together with another good. Two complements are said to be in joint demand. Examples include: printers and computers; DVD players and DVD discs; success and hard work; and so on. A rise in the price of a complement to good x should cause a fall in the demand of that very good or service.
  For example a decrease in the cost of flights from London Heathrow to New York would cause an increase in the demand for hotel rooms in New York and London, in addition to an increase in the demand for taxi services both in London and New York.
• Change in disposable income
  Most of the things we buy are classified as normal goods, that is, more is bought when income rises. When an individual's real income (money income adjusted for inflation) goes up, their ability to purchase goods and services increases, and this causes an outward shift in the demand curve. When income fall, there will be a decrease in the demand for most goods.

  However, for a few goods and services, demand may fall as income rise. These are called inferior goods which doesn't mean that there's anything wrong with the goods. Inferior goods differ in different societies and at different times, thus in many developed economies the motor car has been a normal good and buses and trains inferior goods. In developing economies rice is more likely to give way to more expensive substitutes of fish and meat, making rice an inferior good as income rises. If household income falls, the family may be forced to give up meat and resort to rice.

• Change in tastes and preferences
  Tastes can often be volatile leading to a change in demand. Particularly affected are the clothing trades, but industries producing furniture, food and beverages are also subject to changes in tastes and fashion. Advertising is designed to change the tastes and preferences of consumers and thereby causes a change in demand.
• The availability of credit
  Many goods are bought on credit using borrowed money and therefore the demand for them may be sensitive to the rate of interest charged by the lender. Examples of goods sensitive to interest include household appliances, electronic goods, new furniture and motor vehicles. The demand for new homes is affected by changes in mortgage interest rates.
• Changes in population size and structure
  An increase in the size of the population will increase demand for most goods and services. Changes in the age and gender structure of a population will have obvious impacts on age/gender sensitive products.

Ceteris paribus
Means other things remaining equal. If we wanted to see the effects of changing one variable upon quantity demanded how can the other variables be prevented from changing? They cannot. So in discussing economic theory one assume that everything is held constant or remains unchanged save from the variable we are changing be it price, income or population.