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## Explanation & Answer

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Running Head: Preferences and Utility

Preferences and utility

First name, last name

Institution, affiliation

Preferences and Utility

If we observe a consumer choosing ( x1 , x2) when ( y1 , y2) is available one time, are

we justified in concluding that ( x1 , x2) ≻ ( y1 , y2) ?

We are not justified to say that x1, x2 is greatly preferred to y1, y2 because the consumer might

have been indifferent to y1, y2. However we can say that x1, x2 is weakly preferred to y1, y2.

1. Consider a group of people A, B, C and the relation “at least as tall as,” as in “A is at

least as tall as B.” Is this relation transitive? Is it complete?

2

Preferences and Utility

2

The relation is transitive. Suppose and individual in group A is at least as tall as an individual in

group B and the individual in group B is at least as tall as the individual in group C.

Consequently, the individual in A will be at least as tall as the individual in C therefore the

relation satisfies transitivity.

The relation is complete, this is because if an individual in group A is at least as tall as an

individual in group B, The reverse is also true – the individual in group B is at least as tall as the

individual in group A. Therefore the relation satisfies completeness.

2. Take the same group of people and consider the relation “strictly taller than.” Is this

relation transitive? Is it reflexive? Is it complete?

The relation is transitive. Consider an individual in A is strictly tall...