Walras' Law states that summation of pi Ei(p) = 0 for all pi. We define Ei(p) = xi(p) - qi(p) - Ri. What are the next steps that I should take?
What's the most straight-forward way to prove Walras's Law?
4
$\begingroup$
economics
-
0@Patience the most straightforward proof of Walras' Law requires one to assume LNS preferences and little more (it is implicit in Zermelo's answer). – 2011-11-16
1 Answers
2
Let $i$ denote an agent; $j$ denote the good.
Walras' law: $p.e(p)=0$ for all $p$.
Start with the budget constraint:
$\sum_{j} p_j.x_{ij}=\sum_{j} p_j.w_{ij}$ where $w_{ij}$ is $i$'s endowment of good $j$, $x_{ij}$ is $i$'s consumption of good $j$.
In other words, $\sum_{j} p_{j}.e_{ij}=0$, where $e_{ij}=x_{ij}-w_{ij}$.
Now just add over all agents $i$. You get $\sum_{j}p_j.e_j=0$, where $e_j=\sum_i e_{ij}$ for each $j$. This is Walras' Law. Note that this applies to ALL $p$ - regardless of whether it's the equilibrium price.
-
0by the way, for your specific question (where there is production too) replce $w_j$ for every good $j$ by $w_j+R_j$ – 2011-11-15