# Tag Info

Accepted

### If utility function is homogenous of order 1, then partial derivatives of demand function are equal

For ease of notation, let's take the setting of two goods $x_1$ and $x_2$. The case is similar when there are more than two goods. If utility is homogeneous, the demand functions are homogeneous of ...
Accepted

### If utility function is convex, what can be said about preference relation?

Concave utility functions are quasiconcave while convex utility functions are quasiconvex. If $U()$ is convex then $-U()$ is concave and represents the 'opposite' preferences, so if you believe the ...

### Showing UMP and EMP do not exhibit duality if the assumption of local non-satiation is absent

A counterexample would work as well. Consider the utility function $U(x) = 0$, and the budget constraint $1 \cdot x \leq 1$. The solution $x^* = 1$ is feasible and maximizes utility, but it does not ...

### Understanding consumption units normalisation by $u^\prime (c)$

The derivative $u'(c)$ is defined as the limit of fractions of the form $\frac{\Delta u}{\Delta c}$, so $\frac{u(c)}{u'(c)}$ is of the form $\frac{u\,\Delta c}{\Delta u}$, which in terms of units ...
For the good in question, let $d^m(p,m)$ denote the Marshallian demand and let $d^h(p,u)$ denote the Hicksian demand, where $p$ is the price vector, $m$ is income, and $u$ is utility. Since the good ...