Hot answers tagged

6 votes
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 ...
user avatar
3 votes
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^...
user avatar
  • 4,417
3 votes
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 (...
user avatar
  • 4,517
2 votes

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 $u:\mathbb{R}^2_+ \rightarrow \mathbb{R}$ ...
user avatar
  • 4,417
2 votes

Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?

If the commodity space is $\mathbb{R}^2_+$ and the preference is Lexicographic, then with the standard budget sets $B=B(p_X, p_Y, M) = \{(x, y) \in \mathbb{R}^2 | p_Xx + p_Yy \leq M\}$ where $(p_X, ...
user avatar
  • 4,417
2 votes

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 ...
user avatar
  • 4,417
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 $u_1(x_1, y_1) = x_1$...
user avatar
  • 4,417

Only top scored, non community-wiki answers of a minimum length are eligible