ECON6001/6701 Microeconomic Analysis 1
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Problem Set 1
ECON6001/6701 Microeconomic Analysis 1
* Several of the following are taken from Rubinstein's text.
Exercise 1. In each part of this question below, I describe a choice rule. In each case, verify whether the choice rule statisfies Axiom a, Axiom β .
1) For any given set choice set B , the decision maker's (DM) choices C (B) consist of those alternatives that maximize another person's suffering. Hint: Just as you have a preference
relation in standard consumer theory to describes tastes, instead now let denote the “suffering” relation of the other person. That is x y means x causes at least as much suffering as y etc.
2) A DM has two children, each of them have a well-defined utility functions over the set of
alternatives. The DM's choice is aimed to maximize the average utility of his two children.
3) DM has a well-defined strict ranking over the finite set of alternatives X = {a ; b ; c ; d ; e}. Without loss of generality, assume a>b>c>d>e. His choice rule picks the median ranked alternative whenever the choice set B has an odd number of elements.
4) The decision maker has an ideal point in mind and chooses the alternative that is closest to it.
Exercise 2. Consider a decision maker who, for each alternative x evaluates its “moral” value m(x) and his selfish satisfaction u(x). For any B eR, she first identifies x* = argmaxx2B u(x). If m(x*) > c* , some exogenously fixed constant c, she chooses x* . Otherwise, she chooses y* = argmaxx2B m(x). Show by example, that is, give a set X of alternatives, two functions m and u defined on it etc. to show that the above procedure violates Axiom a.
2023-08-19