Describe a utility function.

Our preferences allow us to make comparisons between different consumption bundles and
choose the preferred bundles. We could, for example, determine the rank ordering of a whole
set of bundles based on our preferences. A utility function is a mathematical function that
ranks bundles of consumption goods by assigning a number to each where larger numbers
indicate preferred bundles. Utility functions have the properties we identified in Module 1
regarding preferences. That is: they are able to order bundles, they are complete and
transitive, more is preferred to less and, in relevant cases, mixed bundles are better.

The number that the utility function assigns to a specific bundle is known as utility, the
satisfaction a consumer gets from a specific bundle. The utility number for each bundle does
not mean anything in absolute terms; there is no uniform scale against which we measure
satisfaction. Is only purpose is in relative terms: we can use utility to determine which
bundles are preferred to others.

If the utility from bundle A is higher than the utility from bundle B, it is equivalent to saying
that a consumer prefers bundle A to bundle B. Utility functions therefore rank consumer
preferences by assigning a number to each bundle. We can use a utility function to draw the
indifference curve maps described in Module 1. Since all bundles on the same indifference
curve provide the same satisfaction, and therefore none is preferred, each bundle has the
same utility. We can therefore draw an indifference curve by determining all the bundles that
return the same number from the utility function.

Economists say that utility functions are ordinal rather than cardinal. Ordinal means that
utility functions only rank bundles – they only indicate which one is better, not how much
better it is than another bundle. Suppose, for example, that one utility function indicates that
bundle A returns 10 utils and bundle B 20 utils. We do not say that bundle B is twice as
good, or 10 utils better, only that the consumer prefers bundle B. For example, suppose a
friend entered a race and told you she came in third. This information is ordinal: You know
she was faster than the fourth place finisher and slower than the second place finisher. You
only know the order in which runners finished. The individual times are cardinal: If the first
place finisher ran the race in exactly one hour and your friend finished in on hour and six
minutes, you know your friend was exactly 10% slower than the fastest runner. because
utility functions are ordinal many different utility functions can represent the same
preferences. This is true as long as the ordering is preserved.

Take for example the utility function U that describes preferences over bundles of goods A
and B: U(A,B). We can apply any positive monotonic transformation to this function (which
means, essentially, that we do not change the ordering) and the new function we have created
will represent the same preferences. For example, we could multiply a positive constant, α ,
or add a positive or a negative constant, β . So αU(A,B)+β represents exactly the same
preferences as U(A,B) because it will order the bundles in exactly the same way.  This fact is
quite useful because sometimes applying a positive monotonic transformation of a utility
function makes it easier to solve problems.

OR Utility function
Utility is the ‘satisfaction’ we get from using, owning or doing something. It is what allows
us to choose between options. This can be plotted on a chart.

A preference function therefore assigns values to the ranking of a set of choices. This is

useful as it allows us to see consumer behaviour as a maximisation problem: faced with a set
of options and a budget constraint, we will choose what satisfies us most. Utility functions
are often expressed as U(x1,x2,x3…) which means that U, our utility, is a function of the
quantities of x1, x2 and so on. If A is a basket of goods, and  , then U(A)>U(B). That is, if
we prefer A to B it is because we derive greater utility from it.

Utility functions follow the same code of conduct, the same axioms, as preferences, because
they are simply numerical representations of them. That is, they are transitive, complete,
continuous and convex, for the same reasons. Being continuous allows us to differentiate
them, and being insatiable allows us to say that:

This means that the more, the better, which is the same as saying that utility functions grow
with quantity.

The most important thing to point out is perhaps the fact that utility functions do not assign a
numerical value to our preferences. They simply indicate order and magnitude of preference,
that is, what we like more and by how much

OR

In economics, utility function  measures preferences over a set of goods and services. Utility
represents the satisfaction that consumers receive for choosing and consuming a product or
service.
Utility is measured in units called utils but calculating the benefit or satisfaction that
consumers receive from is abstract and difficult to pinpoint. As a result, economists measure
utility in terms of revealed preferences by observing consumers' choices. From there,
economists create an ordering of consumption baskets from least desired to the most
preferred.

Understanding Utility Function

In economics, the utility function measures the welfare or satisfaction of a consumer as a
function of consumption of real goods such as food or clothing. Utility function is widely
used in the rational choice theory to analyze human behaviour.

When economists measure the preferences of consumers, it's referred to ordinal utility. In
other words, the order in which consumers choose one product over another can establish that
consumers assign a higher value to the first product. Ordinal utility measures how consumers
rank one product versus another.

Economists take the utility-function concept one step farther by assigning a numerical value
to the products that consumers choose or choose not to consume. Assigning a value of utility
is called cardinal utility, and the metric used to it is called utils.

For example, in certain situations, tea and coffee can be considered

perfect substitutes for each other, and the appropriate utility function must reflect such
preferences with a utility form of u(c, t) = c + t, where "u" denotes the utility function and "c"
and "t" denote coffee and tea. Economists might conclude that a consumer who consumes
one pound of coffee and no tea derives a utility of 1 util. 

KEY POINTS

 In economics, utility function is an important concept that measures preferences over

a set of goods and services.
 Utility represents the satisfaction that consumers receive for choosing and consuming
a product or service.
 Economists track consumer choices to ascertain the utility of one product versus
another and assign a numerical value to that utility.
 Company executives research consumers' utility to guide the company's advertising,
sales, and new product offerings.
Applying Utility Function
Let's say a consumer is shopping for a new car and has narrowed the choice down to two
cars. The cars are nearly identical except that the second car has enhanced safety features and
as a result, costs $2,000 more than the first car.

Economists might conclude that the consumer prefers the added safety features and thus,
assigns a higher value to car two versus car one. The utility or satisfaction derived from car
two could be represented numerically as the $2,000 price difference in the two cars. In other
words, the consumer is receiving $2,000 in utility from car two.

Let's take say that 100,000 consumers throughout the economy preferred car two to car one.
Economists can infer that consumers overall received $200,000,000 million worth of utility
from the safety features of car two or (100,000 * $2,000 ). The utility is derived from the
belief by consumers that they're likely to have fewer accidents by choosing the added safety
features of car two.

Limitations and Benefits of Utility Function

Of course, in reality, economists can't assign a true numerical value to a consumer's level of
satisfaction from a preference or choice. Also, pinpointing the reason for the purchase can be
difficult if there are many variables being considered. In our simple example, the two cars
were nearly identical. In reality, there might be several features or differences between the
two cars. As a result, assigning a value to a consumer's preference can be challenging since
one consumer might prefer the safety features while another might prefer something else.

However, tracking and assigning values to utility can still be useful to economists. Over time,
choices and preferences can indicate changes in spending patterns and in utility.
Understanding the logic behind consumer choices and the level of satisfaction is not only
important to economists but companies as well. Company executives can use utility to track
how consumers view their products. Also, the findings from studying consumers' utility can
guide a company's advertising, sales, and new product offerings or upgrades.