Advanced Micro: Graphing a Utility Function with Domain Restrictiions

[math4me]

Hello,
I need help getting started on this question. Can someone please take a crack at this and explain their thought process? What are the functions on the right? On the left? Seriously what am I looking at here? I don't have much of a background in this so just....pretend you're explaining it to a five year old who for whatever reason wants to follow along and to know the names of everything. Cheers.

 

[Deleted member 4993]

Hello,
I need help getting started on this question. Can someone please take a crack at this and explain their thought process? What are the functions on the right? On the left? Seriously what am I looking at here? I don't have much of a background in this so just....pretend you're explaining it to a five year old who for whatever reason wants to follow along and to know the names of everything. Cheers.

Which textbook are you following in this "class"?

What is the name of this "class"? What is/are the pre-reqs for the class?

It can be explained to a five year old - who has not completed the prereq for this class - but it will take about 15 years to complete!!

 

[JeffM]

Hello,
I need help getting started on this question. Can someone please take a crack at this and explain their thought process? What are the functions on the right? On the left? Seriously what am I looking at here? I don't have much of a background in this so just....pretend you're explaining it to a five year old who for whatever reason wants to follow along and to know the names of everything. Cheers.

It is almost impossible to read that tiny thumbnail clearly. This is economics presented purely in the language of abstract mathematics. It has only the most tenuous relationship with anything possible in the real world.

$\displaystyle X = R_+^2$ means that X is the set of all possible ordered pairs of positive real numbers, including pairs that exist in physical reality such as (2, 4) and those that exist solely in the imagination of mathematicians and theoretical economists such as

$\displaystyle \left ( \dfrac{\pi}{e^2},\ \dfrac{\sqrt{2}}{\sqrt{3}} \right ).$

To make this concrete, think of 2 chocolate bars and 4 brussel sprouts.

He then gives utility functions that define all pairs that have equal perceived value to some imaginary individual. So for example, what is being supposed is that this imaginary individual finds it equally satisfactory to have 1 chocolate bar and 2 brussel sprouts or alternatively 2 chocolate bars and 1 brussel sprout because 1 * 2 = 2 * 1 = 2 < 3.

He then wants you to draw curves representing certain levels of utility for this imaginary individual on a Cartesian plane, including the curve with a utility of zero. This will be impossible to do mathematically because none of the given functions imposed on the designated set can give a resultant of zero.

After that, I find nothing that I can read. If you want to read this kind of economics, you need to have a thorough understanding of mathematical notation and sufficient suspension of disbelief to induce you to write to Santa Claus.

 

[math4me]

It is definitely very abstract, almost unbearably so.

As for the problem though, I'm more worried about what I should be writing down?/ Whether I am "reading" the problem correctly.
we have "u(x1x2)= {x1x2, if x1x2<3
{3 if 3<x1x2< 10
{x1x2-7 if x1x2>10.
at utility levels 0, 3 and 6"

We have three utility levels given to us--0,3,6. So we just make the graph according to conditions that apply to those levels, right? I.e. at utility level 0, since that's less than 3, we fill in the x1x2 curve that's equal to 0. Repeat for 3 and 6, and fill in the area in between (and label it as utility of 3) because those apply to this condition: 3<x1x2< 10. For the last utility function, first you set it equal to 0,3,6, in turn to see for which value the function is greater than 10. It's only true for 6 so we graph the utility function at x1x2= 13. , and that becomes u=6.