Advanced Microeconomics Problem Set 1: Preference & Choice (Master Level)

Solution:

1.      (a). Rationality in preference and choice means that people would prefer to the thing which makes them satisfied instead of other things. It also can be said that these people are likely choosing goods and services in a rational way. When people make a decision, they will consider many factors which can maximize their satisfaction, compare them with the other and also use several information that they have and believe it would make the best decision and choice. There are two properties to describe it further:

1)  Completeness, assumes that there is one thing which would be chosen instead of other things. If there are two goods, let say xand y, people are going to choose x instead of y or vice versa.

2)  Transitivity is a consistent comparison and behaviour by people toward the goods or choices. For example, a student prefers to study instead of work and he is more likely to work than going long vacation, so therefore this student definitely likes to study instead of going long vacation.

(b). Example from everyday life that violates the property:

       - Completeness: If someone has to choose between the two very similar things, then each thing cannot be better off the other, because these are almost indifferent things for him. For example, croissant from bakery A and bakery B are at price, taste, quality, size and other indicators which could be regarded as indifferent, or are just slightly different. When someone is facing either choosing croissant from bakery A or bakery B, he is unable to make a decision quickly because he does not know what his real preference is, due to the “extremely slightly difference” of the choices.

       - Transitivity: It will be happened if the people are being to be inconsistent. For instance, someone like to eat bread with cheese instead of milk and he will use milk instead of chocolate, but he will choose chocolate instead of cheese, because he prefer to eat bread with a chocolate more than cheese.

So that, violation defines the inconsistent and irrational behaviour of the people (or in this case, the consumer).

Solution:

Solution:

3.      (a). There is choice structure (B, C₂(·)) and also there are two choice sets. In first nonempty set which is C₂({x,y,z}) = {x,y}, it has y ≥* x, y ≥* z, x ≥* y and x ≥* z. But in second nonempty set which is C₂({x,y,}) = {x}, only xis revealed preferred to y(x ≥* y). Consequently, the choice structure (B,C₂) violates the Weak Axiom of Revealed Preference (WARP).

Example1: 

Today you went to a bakery, and all of the breads are in your budget set (because breads are quite affordable). And your budget set B= {Croissant, Cakes, Berliner}, then you bought a croissant. According to the choice rule, you have a preference on croissant over cakes and Berliner, which is C(B)= {croissant}. 

The other day, you went to the same bakery again, but you didn’t buy the croissant, instead, a cake, because you feel boring to buy the same bread as yesterday. Then it does not fit the properties of the rational preference relation, but very reasonable in daily life by the way.

Example 2: 

You go out to a bar with your friends. The pub offers several kinds of drink, like beer, cola, red wine, champagne. You could afford beer, cola and red wine, so your budget set is B = {beer, cola, red wine}. Then you bought yourself a beer first, so we could say that you have a preference on beer over other drinks, C(B)= {beer}. After drinking all your beer, you ordered a cola. In this situation, the fact violates the previous preference relation, which seems irrational but in fact very rational.

Therefore, it could be explained that people have different preference at different time, and preference could be influenced by the past events, environment, etc.

(b). The revealed preference relation, ≥*, is defined by

  

It explains that xis revealed at least as good as y, or it also can be said that xis revealed preferred to y. So xis ever chosen over y, then it can restate the WARP as: “if x is revealed at least as good as y, then ycannot be revealed preferred to x”.

 Solution:

4.      It’s given C({x,y}) = {x}, which means xis revealed at least as good as y, and x is preferred to be chose over y. 

It’s also given that C({y,z}) = {z}, which means y is revealed at least as good as z, and y is preferred to be chose over z.

According to the WARP, two properties completeness and transitivity have to be satisfied. Which means, while x is preferred over y, and y is preferred over z, then x has to be preferred over z, related to the transitivity of WARP.

However, it is given by the quiz that C({x,z}) = {z}, which means zis revealed at least as good as x. Then zis preferred to be chose over x. This result violates the WARP by both the two required properties.

Source: My Solution for Problem Set #1 in Tutorial Class of Advanced Microeconomics Course at Master of Economics, University of Tuebingen, 2017.