# Tag Info

### Why are utility functions typically assumed to be concave?

I disagree with @bbecon. I agree with @bbecon that concave utility functions present nice mathematical properties which help theorists develop analytical models. If the OP's question was why utility ...

### Is the market price objective?

The market price is the current price at which something may be bought or sold. If a good is not sold or bought at a particular price, then that is not the market price. Whether or not any particular ...

### Is the market price objective?

The vast majority of economists subscribe today to the subjective theory of value that was in economics introduced by Jevons, Walras, and Menger. Subjective theory of value posits that value is ...
Accepted

### Why are utility functions typically assumed to be concave?

More or less, yes. Making the right assumption on the shape of the utility function allows you to prove existence or uniqueness of the equilibrium. The exact assumption you need depends on what ...
Accepted

### For any small perturbation dx, utility cannot change, or else, x* would not be optimal

It is basically a restatement of the first order condition - at an extrema (maxima or minima) of a well-behaved function its first derivative is equal to zero. If you are at the point of maximization, ...

### Visualizing the expenditure minimization problem

I am not sure what you mean - the visualization is essentially the same, only the roles of the goal function and the constraint are switched. Given the appropriate utility and income levels the ...
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 ...
Accepted

### Proving Pareto-efficiency with MRS

One way to check that this allocation is Pareto efficient is using the first welfare theorem. Consider the exchange economy with utility functions \begin{eqnarray*} u_i(x_i, y_i) = \sqrt{x_iy_i}\end{...

### Can any three of the four vNM axioms (of expected utility theory) be satisfied without satisfying the fourth?

(1) Satisfying completeness, independence, and continuity but not transitivity: Take two outcomes, $\{0,1\}$, and the associated lottery space $[0,1]$. Consider the preference relation $\succsim$ ...

### Nonseparable utility across states of nature: an intuitive example

I'm not aware of any intuitive justification for the state-non-separability in Epstein-Zin preference. However, as both @MichaelGreinecker and @afreelunch alluded to, there are micro/behavioral ...
Pairwise MRS The Marginal Rate of Substitution is usually defined as a pairwise thing. E.g., in case of three goods $x,y$ and $z$, you would have $\text{MRS}_{xy}, \text{MRS}_{xz}$ and \$\text{MRS}_{yz}...