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4 votes
1 answer
178 views

Why does $\varepsilon_{x,p_x}^H =-s_y \sigma $?

Suppose I have two goods $x$ and $y$ and their associated prices $p_x$ and $p_y$. Income $m$. $x^H$ is Hicksian demand and $x^M$ is Marshallian demand. Slutsky Equation: $$\frac{\partial x^M}{\...
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3 votes
2 answers
573 views

Does there always exist a consumption bundle at which the indirect utility function is the inverse of the expenditure function?

Two questions: Given $v(\vec{p},m)$ and $e(\vec{p},\bar{U})$, is there only a single point at which these are inverses of each other? Does an inverse always exist for a given price vector $\vec{p}$,...
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