Descriptive or normative Theories
Descriptive: how people in fact make decisions
Normative: how people should make decisions
—>theories can also be both (descriptive and normative)
Exercise 1.1 : Descriptive vs. normative
a) On average, people save less than 10 percent of their income for retirement (Rente).
b) People do not save as much for retirement as they should.
c) Very often, people regret not saving more for retirement.
a) descriptive
b) normative
c) descriptive
Standard Theory
normative
rational
no assumptions about preferences
often axiomatic
Behavioral Economics
empirically motivated decision Theory
Descriptive (positive) Theory
irrational
preferences
links decision making to psychology
Exercise 1.3 Numeracy
In a recent study on financial decision making, people´s answers to three quick maths questions were strong predictors of their wealth: households where both spouses answered all three questions correctly were more than eigth times as wealthy as households where neither spouse answered any questions correctly. So if you have ever struggled wirh math, be glad that you did. You can try answering the three questions for yourself:
a) If the chance of getting a disease is 10 percent, how many people out of 1000 would be expected to get the disease?
b) If five people all have the winning numbers in the lottery and the prize is 2 million dollars, how much will euach of them get?
c) Let us say you have 200 Dollars in a savings account. The account earns 10 percent interest per year. How much would you have in the account at the end of two years?
a) 1000*0,1= 100
b) 2.000.000/5 =400.000
c) 200*1,1=220 220*1,1=242
Which of these statements are normative/positive?
− One should be honest.
− Honesty pays.
− Most people are honest.
Which of the following decisions are collective, risky, intertemporal, strategic?
− Chose Stammessen today.
− Choice of the party location on Saturday.
Preferences
Preference = relation
Examples for binary relations (=relation between two entities):
Alf is older than Max.
France is bigger than Norway.
Bill is worried he may not do as well on the exam as Jennifer.
Example ternary relation (=involves three entities)
Mom stand between Bill and Bob.
Exercise 2.1 Relations
Assume that f denotes France and n denotes Norway, and that B meand “is bigger than”.
How would you write that…
a) France is bigger than Norway.
b) Norway is bigger than France.
c) Norway is bigger than Norway.
a) fBn
b) nBf
c) nBn
Exercise 2.2 The universe
Suppose we are talking about all countries that are members of the united nations. How should that be written?
{Afghanistan, Albania, Algeria, Andorra,…}
Exercise 2.3: Preferences
Suppose d denotes “enjoying a cool drink on a hot day” and r denotes “getting roasted over an open fire”.
How would you..
a) state your preference over these two options.
b) express a masochist´s preference over these two options.
a) d≽r
b) r≽d
rational prefence relation
= transitive and complete
Exercise 2.7
Assuming the universe is a set the of all people - past, present and future - are the following relations transitive? Are they complete?
a) “is the mother of”
b) “is an ancestor (Vorfahre) of”
c) “is the sister of”
d) “detests (verabscheut)”
e) “weighs more than”
f) “has the same first name as”
g) “is taller than”
a) intransitive, incomplete (weil: Wenn A Mutter von B und B Mutter von C, müsste auch A Mutter von C sein)
b) transitive, incomplete
c) transitivity depends whether we consider half-siblings; either way it is incomplete
d) intransitive, incomplete
e) transitive, incomplete
f) transitive, incomplete
g) transitive, incomplete
Exercise 2.8: The enemy of the enemy
Suppose it is true, as people say, that the enemy of your enemy is your friend. What does this mean for the transitivity of “is the enemy of”? (Assume there are no true frenemies: people who are simultaneously friends and enemies.)
If the enemy of your enemy is not your enemy, then “is the enemy of” is intransitive.
Ich>Feind
Feind>Eventuell Freund
Ich > Eventuell Freund —>somit wäre der eventuell Freund auch mein enemy
Exercise 2.9: Assuming the universe is the set of all natural numbers, meaning U={1,2,3,4,…}, are the following relations transitive? Are they complete?
a) “is at least as great as” (≽)
b) is equal to (=)
c) “is strictly greater than” (≻)
d) “is divisible by” (|)
a) Transitive, complete (3≽2, 2≽1, 3≽1)
c) transitive, incomplete
d) transitive, incomplete
Exercise 2.10: Preferences and the universe
Use your understanding of transitivity and completeness to answer the following questions.
a) If the universe is {apple, banana, starvation} what does the transitivity of the preference realtion entail?
b) If the universe is {apple, banana} what does the completeness of the preference realtion entail?
a) Transitivity implies that if apples are at least as good as bananas, and bananas are at least as good as starvation, then apples are at least as good as starvation. That if starvation is at least as good as bananas, and bananas are at least as good as apples then starvation is at least as good as apples an so on.
b) Completeness implies that either apples are at least as good as bananas or bananas are at least as good as apples but also that apples are at least as good apples and that bananas are at least as good as bananas.
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