Chapter 8, Why should we accept the preference axioms? Video Solutions, An Introduction to Decision Theory

Problem 1

Your preferences over a set of objects are not cyclic, i.e. it is not the case that there exists some $x$ such that $x>\square$ I $>x$. Does it follow that your preferences satisfy the transitivity axiom?

Manisha Sarker

Numerade Educator

Problem 2

(a) What is a pragmatic argument? (b) What is the money-pump argument?

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02:21

Problem 3

The money-pump argument shows that an agent with cyclic preferences can be money-pumped. It does not entail that anyone who violates transitivity can be money-pumped. (a) Explain why! (b) Can the money-pump argument be strengthened, i.e. can this gap be filled? If so, how?

Kaylee Mcclellan

Numerade Educator

03:21

Problem 4

I prefer $x$ to $y$ and $y$ to $z$, but I have no preference whatsoever between $x$ and $z$. (I regard them to be incommensurable.) (a) Do my preferences violate transitivity? (b) Can I be money-pumped?

Aman Gupta

Numerade Educator

00:50

Problem 5

You will shortly be executed. However, before you are executed you will be given a free meal of your choice. The decision what to eat will be your very last one, and you know this for sure. Just as you are about to tell the prison guard what you would like to eat, you realise that if you were to act on your preferences you could be money-pumped, because your preferences are cyclic. However, for obvious reasons, you know for sure that you will not be money-pumped. Do you now have a reason to revise your preferences?

Joanna Quigley

Numerade Educator

02:58

Problem 6

Why is Samuelson's theory of revealed preferences incompatible with the small improvement argument?

Tommy Nguyen

Numerade Educator

04:32

Problem 7

Consider the decision tree in Section 8.4 once again (Figure 8.1). Imagine that just before you make your choice at the first (leftmost) choice node, a being with perfect predictive powers offers to tell you (for a fee) whether it will rain tomorrow or not, i.e. whether $R$ is true. Would you at this point, at the first choice node, be prepared to pay the being a fee for finding out the truth about $R$ ? If so, how much? (We assume that your utility of money is linear.)

Nicole Powell

Numerade Educator

04:09

Problem 8

You are offered a choice between (i) one left and a right shoe, and (ii) a fifty-fifty chance of getting nothing or ten left shoes. Since the utility of a left shoe in the absence of a right shoe is nil, you prefer (i) to (ii). Does this mean that you are risk averse in the actuarial sense, since you preferred two shoes to five expected shoes?

Heena Haldankar

Numerade Educator

01:02

Problem 9

Karen's utility of money is $u=x^{1 / 2}$ and John's utility of money is $u=x^{1 / 3}$, where $x$ is the current balance in each person's bank account. Who is most averse against actuarial risks, Karen or John, for large amounts of money?

Niamat Khuda

Numerade Educator