# 3. Preferences (2016)

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 Universidad Universidad Pompeu Fabra (UPF) Grado International Business Economics - 1º curso Asignatura Microeconomics I Año del apunte 2016 Páginas 7 Fecha de subida 27/04/2016 Descargas 8 Puntuación media Subido por avillagrasa

### Descripción

Resumen del libro completado con apuntes de clase.

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avillagrasa 1st year IBE - 3rd Term Microeconomics I III. Preferences Index Consumer preferences ..................................................................................................... 2 Strict preferences ......................................................................................................... 2 Indifferences ................................................................................................................. 2 Weak preferences......................................................................................................... 2 Assumptions/Axioms ........................................................................................................ 2 Indifference curves ........................................................................................................... 3 Perfect substitutes ........................................................................................................ 3 Perfect complements ................................................................................................... 4 Bads .............................................................................................................................. 4 Neutrals ........................................................................................................................ 4 Satiation ........................................................................................................................ 5 Well-behaved preferences ............................................................................................... 6 Marginal rate of substitution (MRS) ................................................................................. 6 Other interpretations ................................................................................................... 7 Behaviour...................................................................................................................... 7 Summary ........................................................................................................................... 7 1 avillagrasa 1st year IBE - 3rd Term Microeconomics I Consumer preferences Consumption bundles (X): goods and services involved in our choice problem. We use x1 and x2 to denote the quantity of good 1 and good 2. Instead of writing (x 1, x2) we can simply denote it by X.
A very important assumption we are making is that people know which are their preferences. However, this is not always true, since nowadays there’s too much information to be able to really evaluate it. Under this assumption we know that people is always going to choose the bundle they like the most.
Strict preferences We use “>”. It means that we will always prefer one bundle to another. If Coca-Cola > Pepsi I’m never going to drink Pepsi.
Indifferences We use “~”. It means that we don’t care which bundle we are getting. If Coca-Cola ~ Pepsi I think Coca-Cola is as good as Pepsi, so I don’t care which one I drink.
Weak preferences We use “≥”. It means that one bundle 1 is at least as good as the other. If Coca-Cola ≥ Pepsi I will ask for Coca-Cola but if they only have Pepsi I’m fine too.
Assumptions/Axioms We assume three things over preferences: 1. Complete: we can always compare them.
2. Reflexive: the bundle is always at least as good as itself. It means X ≥ X, which is very logic.
3. Transitive: we are logic with our preferences.
o If X>Y and Y>Z, then X>Z o If X~Y and Y~Z, then X~Z We need the transitive assumption because if not there would be a set of bundles (X, Y, Z) with no best option.
2 avillagrasa 1st year IBE - 3rd Term Microeconomics I Indifference curves They are a graphical representation of preferences. They indicate which set of bundles makes us equally happy (give the best utility).
All the bundles that give us a higher utility form the preferred set, while the boundary of it is the indifference curve (X~Y~Z).
Note that well-behaved indifference curves can’t cross. All the points at the right of the indifference curve are, at least, as good as the points in the line. This means that we will always prefer bundles at the right of the indifference curve.
How to construct the line? He have to see how much units of good 1 we have to give in order to renounce to one unit of good 2 (substitution).
We will do this to have different points and be able to plot the line. In the general case we will obtain a convex curve with negative slope. This is because when we have a lot of good 1 we are more willing to give up one unit in order to get more good 2.
We can have infinite indifference curves, and the more to the right, the better.
However, there are other types of goods, which give us different shapes.
Perfect substitutes This is when we can always exchange one good for the other for a constant rate (note that before the slope/substitution rate) was changing along the curve.
The indifference curve is a straight line with constant negative slope.
In the book they refer to the case where the slope is -1. This is when one unit of good one can be substituted with one unit of good 2.
3 avillagrasa 1st year IBE - 3rd Term Microeconomics I Perfect complements They are goods that must be used together to give us any use. Because of this they have an L shape, meaning that we only care about the vertex combination because having more of good 1 without good 2 doesn’t give us any additional utility.
They can have a proportion 1-1 (we need the same quantity of both) like left and right shoes or any other proportion (like in our example).
In either case the preferred indifference curves are the ones that have the same proportion.
To draw them we can draw a line with the slope equal to the quantities we need (dotted line) and draw the L curves along it.
Note that in this case we are indifferent between the bundle (2, 1) and (2, 100), because we consume, in both cases, 2 coffee spoons and 1 cup of milk.
Bads They are something we don’t like. Because of this, the slope is positive. One of the goods is a bad, so we have to be compensated we something we like.
For example I want a flat and I want it quiet and with lots of light. Then, to accept a flat with noise I have to be compensated with more light. The preferred bundles are to the right of it, as we get more light for the same noise.
Neutrals We have neutral goods when we only consume one of them. The indifference curves can be horizontal or vertical.
4 avillagrasa 1st year IBE - 3rd Term Microeconomics I We only want good 1: We don’t care how much sugar we have if we don’t put sugar in the coffee.
Therefore, we are indifferent between the bundle (1, 0) and (1, 100). Our preferred bundles are the ones that give us more coffee (to the right).
We only want good 2: We don’t care how much sugar we have if we don’t put sugar in the coffee. Therefore, we are indifferent between the bundle (0, 1) and (100, 1). Our preferred bundles are the ones that give us more coffee (up).
Satiation The consumer has a point that makes him better off, he can’t obtain anymore satisfaction. The point where we are satiated is called satiation point or bliss point.
The closer we are to that point, the better, and the furthest, the worst. It looks like this: The indifference curve has negative slope when we have too little or too much of both goods, and the slope is positive when we have too much of only one of the goods.
We have been assuming that the goods were continuous (we could have fractions of them) because it is easier to work like this. However, a lot of goods are discrete (we can only have an enter unit) and then the indifference curve will be a set of points joined by a dashed line.
5 avillagrasa 1st year IBE - 3rd Term Microeconomics I Well-behaved preferences They have 2 features: a) Monotonicity: this means that the more, the better1. We always want more.
Because of this, we will always prefer a bundle where we have more of one of the goods. It implies negative slope. This is, obviously only true before the satiation point and with goods.
b) Convexity: we prefer averages rather than extremes. For example, we prefer going 5 times to Paris and 5 times to London rather than going 10 times to Paris. We talk about strict convexity for strict preferences, when the average is strictly preferred to the extreme. Note that perfect substitutes are convex but not strictly convex. Preferences are not convex when we prefer the extremes. A situation where this happens is in the labour market, where the employer prefers an expert (extreme) rather than someone who knows about everything but is not specialized.
As we see in the picture, with convex preferences the average (central point in the line) lies more to the right than the extremes. With the others the average is below the indifference line, so it is a worst option.
Marginal rate of substitution (MRS) It is the slope of the indifference curve. It says for how much the consumer is willing to trade one unit of good 1 to obtain one unit of good 2. In other words, how much do I have to give him of good 1 to be able to subtract one unit of good 2. The rate at which the consumer is willing to substitute one good for the other is Δx1/ Δx2. The MRS is computed when changes are small (both the denominator and the numerator are small numbers) and it is a negative number.
1 There’s an exception with bads, which make us happy when we have less.
6 avillagrasa 1st year IBE - 3rd Term Microeconomics I Other interpretations The slope of the indifference curve can also be interpreted as the marginal willingness to pay. This is logic when we are assuming that the good 2 is actually all the other goods measured in dollars2. This is because we can interpret it as measuring the amount of good 2 we are willing to pay to have more of good 1, as the money spent in one good can’t be spent in the other.
Behaviour Perfect substitutes: the line has a constant and negative MRS Neutrals: the MRS is infinite (or 0) everywhere Perfect complements: the MRS is 0 at the horizontal part and infinite in the vertical part.
The MRS is always negative because of monotonoicity, as we have to reduce the consumption of one good to obtain more of the other. Also, when preferences are described by a convex curve the MRS decreases as we increase the quantity of one of the goods. This is called diminishing marginal rate of substitution. This is because if I already have a lot of one of the goods I’m more willing to exchange part of it to get some of the other good.
Summary     2 We assume that the consumer can rank bundles according to his preferences.
Indifference curves can have different shapes depending on the characteristics of the goods (complements, substitutes, bads...).
Well-behaved preferences are monotonic (more is better) and convex (average is better than extremes).
Marginal rate of substitution (MRS) is the slope of the indifference curve.
See “two goods are enough” from chapter 2 7 ...