Utility is also used as an abstract concept in economics. It signifies how much benefit a person has from owning/buying a thing. To really understand how supply and demand work, you have to first understand utility which is one of the factors determining demand.

One of the first assumptions in economics is that all people (called 'economic subjects') are acting rational. This is defined as everyone trying to maximize the utility (e.g. money, goods, recognition, happiness, ...) he trades in for the limited amount of resources he owns (labor, money, goods, recognition, ...). We will focus now on the consumer, who tries to trades in money for goods. Please note that there are a few constraints and preconditions to the rationality principle, but I will skip these.

Maximizing the utility of bought goods of course means that there must be an order of preference between these goods or, to be more correct, between different bundles of goods (also called consumption bundles). If e.g. a cotton candy(cc) cost \$2, a roller coaster(rc) drive \$3 and you had \$15 to spend on the fair, you could buy the bundle (1cc,4rc,\$1), (2cc,3rc,\$2), (3cc,3rc,\$0), .... or (6cc,1rc,\$0 and some vomiting). You will prefer some of these bundles over others and we assume that these preferences put up a total order between these bundles ('total order' is just a magic word from mathematics saying that there is a '<' relation behaving exactly as you would expect from it :-).

With qi being an arbitrary bundle and Q the set of all bundles we can now define the utility function u: Q -> R+ (i.e. it is a function which assigns to each bundle of goods a positive real number). It is defined using the preference relationship '<' defined above:

u(q1) < u(q2) <=> q1 < q2 (i.e. the utility value of bundle 1 is lower than the utility value of bundle 2 if and only if bundle 1 is less preferred than bundle 2)

Two remarks: First, please note that the first '<' is a comparison between numbers while the second '<' is a comparison of bundles (it's difficult to use different signs for that with HTML). Second, if you know anything about math you are probably already complaining "That is no real definition, how do I calculate u(q)?". Well done, you're correct! We don't know how to calculate the utility function ..... and we don't need to. The only things needed to know are a few of its characteristics:

Ordinality:
The values representing utility can be arbitrarily chosen (within the restrictions given by the above 'definition'). This means that if u(q1)=2*u(q2) you are not allowed to conclude that q2 has the double utility (benefit) than q1. You are only allowed to conclude that it brings more benefit. This also means that you can not compare at all the utility numbers two persons each assign to a bundle of goods. (This is of course the reason why there is no algorithm to calculate u(q))
Insatiability:
The utility function is monotonically increasing. In less mathematical terms this means that getting more of something while at least getting the same of everything else provides you with more utility. So two cotton candies are better than one, and three are better than two, ... and 1001 better than 1000 (uhmm, well, nobody ever claimed economics to be totally realistic).
Decreasing marginal utility:
The second derivative is negative. As you have already seen in the example above the additional utility of every additional unit of a good you get is decreasing. So whereas getting 5 cotton candies as a present while expecting 4 is a nice surprise, getting 2 while expecting 1 is a much nicer surprise. (Please do not start sending in cotton candies now.)

OK, now with these characteristics, what do we gain from having an utility function, which we can not even calculate. Well, we gain two things. First the graphs of the overall utility function u for a single good and of the utility u' of the last added unit of that good (i.e. the derivative of u).

```u /\                                     u' /\
|                    *******              |*
|               *****                     |*
|           ****                          |*
|        ***                              | *
|      **                                 |  *
|    **                                   |   **
|   *                                     |     **
|  *                                      |       ***
| *                                       |          ****
|*                                        |              *****
|*                                        |                   ********
---------------------------->             ----------------------------->
q                                          q```

Now, have a look at the graph for the utility of the last added good (the right one). The more of a good you have, the less you value the latest unit. This looks a lot like the graph of the demand curve which shows that more of a good is demanded by the customers the less it costs (in the standard case). This similarity is not the whole truth (more (in a few days) under demand) but if you just want to understand things on a high level, it is enough to remember that one has to lower the price to create more demand because people value another unit of the same good less than the previous units and therefore pay less for it. You can also stop reading now.

The second thing we gain from the utility function is the ability to determine how combinations of goods behave which a person values the same. We can arrange all equally-valued combinations on a curve which is called indifference curve (for combinations of two goods, for more goods its is less of a curve and more of a hyperplane). You can choose several levels of utility and draw an indifference curve for each of them into one diagram. Normally (!) this will look somehow like the following:

```q1/\
|  *   *   *
|  *   *   *
|  *   *    *
|  *    *    *
|   *    *    **
|    *    *     **
|     *    **     ***** u3
|      **    ***
|        **     ***** u2
|          ***             u1<u2<u3
|             ***** u1
---------------------------->
q2 ```

The indifference curves are not allowed to intersect (due to the transitivity of the preference relation) and higher utility levels will always be found to the right and/or up (due to insatiability) . The above graph also tells you e.g. how much more of good q1 a person wants as a replacement for one unit of good q2. This if further explained under substitution.

To determine demand we will draw the line representing the available money of the person (called budget line) into this curves. The point at which this line touches the highest possible indifference curves determines the demand of the person for these two goods given that nothing changes. Since changes are of course the interesting case (i.e. we want to know how demand for a good changes if its price changes) you should continue to read at demand (in a few days). You will also learn there how to draw the budget line.

Please note that I only minored in economics, that that has been some time ago and that I'm a native German speaker. So the above might contain passages being arbitrary wrong , out-dated or using the wrong phrases. Don't copy this as a homework!

U*til"i*ty (?), n. [OE. utilite, F. utilit'e, L. utilitas, fr. utilis useful. See Utile.]

1.

The quality or state of being useful; usefulness; production of good; profitableness to some valuable end; as, the utility of manure upon land; the utility of the sciences; the utility of medicines.

The utility of the enterprises was, however, so great and obvious that all opposition proved useless. Macaulay.

2. Polit. Econ.

Adaptation to satisfy the desires or wants; intrinsic value. See Note under Value, 2.

Value in use is utility, and nothing else, and in political economy should be called by that name and no other. F. A. Walker.

3.

Happiness; the greatest good, or happiness, of the greatest number, -- the foundation of utilitarianism.

J. S. Mill.

Syn. -- Usefulness; advantageous; benefit; profit; avail; service. -- Utility, Usefulness. Usefulness has an Anglo-Saxon prefix, utility is Latin; and hence the former is used chiefly of things in the concrete, while the latter is employed more in a general and abstract sense. Thus, we speak of the utility of an invention, and the usefulness of the thing invented; of the utility of an institution, and the usefulness of an individual. So beauty and utility (not usefulness) are brought into comparison. Still, the words are often used interchangeably.