# Tag Info

Accepted

### Does Debreu's representation theorem of ordinal utility require Hausdorff topology?

No. However, the problem can be reduced to representing preferences on a Hausdorff space. Instead of trying to represent a complete preorder on a set, one can try to represent linear orders on the ...
• 9,330
Accepted

### Constrained optimization to find utility maximizing allocation

I think you are trying to find a feasible allocation that maximises the sum of the utilities of the two individuals. So we can write the objective function as: \begin{eqnarray*} \max_{x,y} & \ xy^...
• 4,417
Accepted

### Constant relative risk aversion for wealth spanning from negative to positive

I'm afraid the answer is no. Let's take any continuous and strictly increasing utility function $U(W)$ which is twice differentiable almost everywhere on the reals. Constant relative risk aversion (...
• 4,517
Example given by Herr K. is perfect. Let me give another example of a dis-continuous utility function which is quasi-concave, but not concave. Consider $u:\mathbb{R}^2_+ \rightarrow \mathbb{R}$ ...