- +1-530-264-8006
- info@tutorsglobe.com

18,76,764

Questions

Asked

21,311

Experts

9,67,568

Questions

Answered

Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!

Submit Assignment2015 © Tutors Globe. All rights reserved.

## Utility and Utility Functions

Utility and Utility Functions:In the last section we talked a lot about consumers’ preferences and defined this concept as simply the rankings of consumption bundles from less desirable to more desirable. However, it would be nice if we could express these rankings in terms of some numerical index instead of being given a long (possibly infinite) list of rankings of bundles. For historical reasons, such an index is called a utility function.

Let’s assume that we ask our consumer to compare three bundles and that she expresses the following ranking. A ≥ B & B ≥ C. If we had fed these bundles into her utility function we would have gotten some numbers with the following relationship among each other:

U(A) ≥ U(B) ≥ U(C),i.e., the utility number associated with bundle A is greater than or equal to the utility number associated with bundles B etc. Hence, the utility numbers preserve the rankings expressed by the consumer. It is important to note that the actual utility number has no meaning. This also means that we can play around with our utility function; e.g. we can add a constant to all numbers (the same constant) without changing the ranking, we can also multiply our original utility function by a constant, or take the square (or the square- root) of it, and it still is a viable utility function since it will not change the consumer’s ranking of the bundles.

Example:

Let’s assume that we have two goods (1 and 2) and three bundles: A = {3, 3} , B = {3, 2} and C = {2, 2} . If the consumer is not satiated with either good her preferences will be: A > B > C, and we want our utility function to produce numbers such that: U(A) > U(B) > U(C). Consider the following function, for example,

U(Q) = Q1 . Q2,

Where Q

_{i}is the quantity consumed of good i. In our example we would have that,U(A) = 3 . 3 = 9

U(B) = 3 . 2 = 6

U(C) = 2 . 2 = 4,

This does produce the required ranking. Consider now adding a constant, K = 5, so that our new utility function is, V (Q) = K + U(Q). Well, it is obvious that it would also rank the bundles in the correct way (The new utility numbers would be: V (A) = 14, V (B) = 11 and V (C) = 9.) We can also consider the following transformed functions: W(Q) = K+bU(Q), (b >0), Z(Q) = √U(Q), or Y (Q) = (U(Q))

^{2}. If you apply these transformations to U(Q) you’ll find that all the new utility functions preserve the rankings of the bundles.The point of this example is to underscore the important fact that utility numbers in themselves have no meaning, and we can transform the utility function in many ways as long as the transformation preserves the underlying rankings (a so called positive monotonic transformation). We also require some other things of our utility function, for example, if the consumer has monotonic preferences an increase in one good without a decrease in the other, should yield an increase in the utility number (since the consumer would now rank the new bundle higher than the original one). This brings us to the concept of marginal utility, and the marginal utility function.

Latest technology based Economics Online Tutoring AssistanceTutors, at the

www.tutorsglobe.com, take pledge to provide full satisfaction and assurance inIntermediate Microeconomics homework helpviaonline tutoring. Students are getting 100% satisfaction byonline tutorsacross the globe. Here you can get homework help for Intermediate Microeconomics, project ideas and tutorials. We provide email basedIntermediate Microeconomics homework help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Intermediate Microeconomics. ThroughOnline Tutoring, you would be able to complete your homework or assignments at your home. Tutors at theTutorsGlobeare committed to provide the best qualityonline tutoringassistance forEconomics homework helpandassignment helpservices. They use their experience, as they have solved thousands of the Economics assignments, which may help you to solve your complex issues of Intermediate Microeconomics.TutorsGlobeassure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide thehomework helpas per the deadline or given instruction by the student, we refund the money of the student without any delay.