# 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 ...
• 9,190
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^...
• 4,347
1 vote

### Calculating price in a pure exchange economy

Let $\omega_1 = (\omega_{1}^X, \omega_{1}^Y)$, and $\omega_2 = (\omega_{2}^X, \omega_{2}^Y)$ be the endowment of the two consumers, respectively. Also, their utility functions are $u_1(x_1, y_1) = x_1$...
• 4,347

### What is the assumption behind "indifference curve does not cross"?

Consider any utility function $u: \mathbb{R}^2_+ \rightarrow\mathbb{R}$. Indifference curve for satisfaction level $\mu$ is defined as: $\text{IC}(\mu) = \{(x, y)\in\mathbb{R}^2_+|u(x, y) = \mu\}$ I ...
• 4,347

### Convex Preference but Convex Utility

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 $u:\mathbb{R}^2_+ \rightarrow \mathbb{R}$ ...
• 4,347

• 9,190
Accepted

### risk aversion and the law of diminishing marginal utility

If your preferences over lotteries satisfy the vNM-axioms, i.e. if you are an expected utility maximizer, then you cannot be risk averse and at the same time not have diminishing marginal utility of ...
• 4,457
I used to ask my students if they preferred getting \$4 with probability 1 or \$10 with probability 1/2 and \\$0 otherwise. Most students went for the gamble. When I asked for their reasoning they said ...