Because we 'know' that the tfitonnement, in its presentation as a set of simultaneous autonomous differential equations for the multimarket system, will lead globally asymptotically to an equilibrium if Walras' law
holds, if the system is continuously differentiable, and homogeneous in prices and income, and gross substitutability prevails, it is hard to disconnect Allais' argument from later proofs.
But, this event allows us to attack the issue of whether it is possible to produce an alternative to Walras' Law
, which has some similarity in appearance, but which produces much different results in application.
The present article provides an approach based on Walras' Law
, which is in the same time a rigorous and easy to understand method.
He also estimated the value of one variable from what is called Walras' Law
. In the end, he had 2m+2n-1 independent equations and variables.
is an example of a law that is true by definition: the total payments made to factors of production will equal the total value of the goods sold.
," in The New Palgrave: A Dictionary of Economics.
"Free Banking, the Real-Balance Effect, and Walras' Law
," available at http://papers.ssrn.com/abstract=1274385.
From the budget constraint equations (2), by rearranging terms and summing across consumers, we get the so-called Walras' Law
, that is:
Since there is only one other market, the resource market, it must also clear by Walras' law
. If the model were generalized to contain k resource goods, k - 1 resource prices would have to be determined by tatonnement so as to clear all markets.
Correspondingly, there are two dependent relationships since Walras' law
holds both for the transactions during the period and for the transactions with payments at the end of the period.
A fortiori, Walras' law
will not be satisfied by effective demand." (Emphasis in the original.) Thus, Walras's law is essentially discarded in fixprice theory.
The only way that Walras' Law
could hold under such an assumption would be for the IS and LB curves to be coincident, implying that the economy has no stable equilibrium [Patinkin, 1965, pp.