Indifference Curve

Indifference curve analysis puts a number on satisfaction for rational agents. Indifference curve analyses are use to analyze human consumption. The reason indifference curve is use to analyze human consumption is because indifference curves analysis assumes people are rational. Indifference curve analysis is a good way to understand satisfaction because it can be translated into bits for computers to understand  Indifference curves can also be combined in the same model with other curves, like the income curve & CCP, to help analyze rational agents. 

Rationality is defined by having two axioms of preferences. The first axiom is completeness, which also includes indifferent. The second axiom is transitivity. An example of completeness is; assume there are two choices A or B. For something to be said to be complete the rational agent either likes A better than B or B better than A. If the rational agent likes equally both options, the agent is said to be indifferent. Completeness could be mathematically written as A ⪰ B when choice A is weakly prefer over B. B ⪰ A when option B is weakly prefer over A. If the agent is indifferent between the two choices is written as A∼ B meaning the rational agent is indifferent between the two choices. Transitivity axiom could be explain by if A is weakly prefer over B and B is weakly prefer over C then A is weakly prefer over C. Mathematically shown by: A ⪰ B  ⪰ C.

The model below shows a typical consumer choice theory model. It shows two indifference curves indicated by the blue lines. The model shows two “restrain of satisfaction” called income lines in consumer choice theory and indicated by the red lines. The model shows the income and substitution effect. In the model below, the income effect is the movement between T and S on the indifference curve I’ and between C and B on the X axis.

The substitution effect is the movement between U and T (U,T) creating a new indifference curve I’. It is also the movement of (A,C) on the X axis.

Assume there are two goods indicated by the X and Y for example apples on the X axis and oranges on the Y axis. The “restrains” income lines represents the amount that can be consume. It also shows the amount of satisfaction the agent can get. Each point on the indifference lines is a combination of apples and oranges, (X,Y), the agent is indifferent. For example on the model below in indifference curve line I’, the agent is indifferent between any point at line I’.

https://www.britannica.com/topic/income-effect/media/284837/1244.