# Tag Info

### Under what condition is a cost function strictly concave in prices?

No function that is homogeneous of degree one, is at the same time strictly concave in its arguments. If the function is differentiable (or non-differentiable at a finite number of points), then the ...
• 3,371

• 1,745
Accepted

### Can I assume utility functions strictly increasing?

You have to show that something does not hold universally true. To show this, you just have to show that there is at least one exception- a counterexample. For this counterexample, you can make any ...
• 13.3k

### Representing a Lexicographic Preference in a Natural X Natural Choice Space With Utility Function

Take a strictly increasing mapping $f:\mathbb{N} \to [0,1)$, such as $$f(y) = 1 - \frac{1}{y+1}.$$ Then $$U(x,y) = x + f(y)$$ represents the Lexicographic preference in the $\mathbb{N}^2$ choice ...
• 29.3k
Accepted

### Does x ≽ y imply x > y or x ~ y in preferences?

The usual definition of $x \succeq y$ is that either $x \sim y$ or $x \succ y$ hold. Your proof and the assumption of completeness are not necessary. One could also start from $\succeq$ and $\sim$ ...
• 29.3k
Accepted

### How do you establish uniqueness of a rational preference relation?

Assume that, towards a contradiction, that both $\succeq$ and $\succeq^\ast$ rationalise the choice function and that they are different. The fact that $\succeq$ and $\succeq^\ast$ are different means ...
• 12.4k
Accepted

### Proof of Expected utility theorem with three outcomes

In order to do that, you need to define $u(·)$ as a utility function on "sure things" rather than on lotteries. In your example, you need to think in terms of the set of possible prizes to the ...
• 721