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).
[...] In fact this bundle requires her to have an income (m') of: 10*15,81+158,1=158,1*2=316,2=m' So, for Lea to keep the same utility with the price increase, her income has to go up by ₤216,2. That will not happen, so Lea has to reduce her consumption so that her total spending on both good does not exceed (and because she wants to maximise her utility it will be equal to The new conditions are thus: 10Px+Y=100 knowing that X=m/2Px and Y=m/2. That gives us and Y(B)=50. [...]
[...] 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. [...]
[...] The opportunity cost of an action is the best forgone alternative Parkin, Economics p.G-13 The Hicksian demand curve is also called compensated demand curve because the consumer's income is ‘compensated' in a way so that the consumer can keep his utility constant. 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. [...]
[...] This is the definition of a giffen good[?] To conclude, we can say that both income and substitution effects play an important role in the consumer's decision to change his consumption following the change in a good's price. We have also seen that Marshallian demand curves for goods usually slope down except in the case of a giffen good where it slopes up. Preferences are represented by indifference curves, the utility on a indifference curve is everywhere the same. That means that the consumer equally ‘enjoys' all the possible consumption bundles that are on that line. [...]
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