How can the change in demand following an increase in the price of goods can be broken into a substitution effect and an income effect?

Résumé du document

We expect people to change their consuming behaviour when the price of a good change, but on what is this change going to be based on? Preferences are determined by the tastes of a person, so they do not depend on the person's real income. If the price of a good changes, the person will make a new choice according to her preferences. That means that she will take the best solution according to her preferences but that is feasible for her regarding new budget constraints. That is the basic idea of breaking down the change in price into a substitution effect and an income effect : the change in price drives the person to readjust her consumption first in function of her preferences, with holding her real income fixed so that she can keep the same utility, and then in function of her real income (which has been modified by this price change).

Extraits

[...] That means that as a price goes down the consumer will want more of it. [...]

[...] Before I start, I need to make clear what utility and real income are. Utility can be said to the level of ‘enjoyment' that a person gets from buying a specific bundle of goods. Real income is the quantity of good that a consumer ca buy according to its nominal income. So real income has nothing to do with the number of 1 pound coins that you possess but it is, for example, how many umbrellas that you can buy with all these 1 pound coins. [...]

[...] Let us now see how we can ‘translate' the substitution and income effect in mathematics. Here we have: And 5X+Y=100 We know that at a tangency point We can replace the value of Y in the budget constraint, which gives us: Which is the demand function. To find Y we replace what we just found for X in PxX+PyY=m which gives In this case, since Py equals the equation will be simplified: This result is not surprising, Lea likes as much shoes as money so she uses half of her income for each good. [...]

[...] So, after the price increase that gives us: 10/1=Y/X, rearranged that gives us 10X=Y If we plug it into the utility function : X(C)10X(C)=10X²(C)=500 And 500=Y*√50 so So the increase in the price of X has led Lea to decrease her consumption of X by approximately 3 units and she has increased that of Y by approximately 21. So she has been substituting shoes for money because the relative price of shoes (i.e. the opportunity cost[?] of shoes) had increased. [...]

[...] This compensating variation is represented by distance on the vertical axis between the first budget constraint (BC1) and the third budget constraint where income is compensated (BC3). This variation is the amount of money that the consumer needs to keep his utility constant with the new price. A giffen good is a type of inferior good where the income effect outweigts the substituion effect. For inferiror goods, the income effect and substitution effect are always in the opposite direction, but in the case of a regular inferior good, the law of demand is respected. [...]