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.
