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Bringing the financial system into the 21st century : Comments
By Ken McKay, published 10/2/2009A new international finance system is needed and for that we must have a new Bretton Woods Agreement.
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however see below in dealing with general equilibrium some fundamental mathematical principles apply.
In mathematical terms the number of equations is equal to the number of individual excess demand functions which in turn equals the number of prices to be solved for. By Walras' law if all but one of the excess demands is zero then the last one has to be zero as well. This means that there is one redundant equation and we can normalize one of the prices or a combination of all prices (in other words, only relative prices are determined, not the absolute price level). Having done this, the number of equations equals the number of unknowns and we have a determinate system. However, because the equations are non-linear there is no guarantee of a unique solution. Furthermore, even though reasonable assumptions can guarantee that the individual demand functions are well behaved, these assumptions do not guarantee that the aggregate demand is well behaved as well.
in simple terms unless all demand functions for all markets are linear there is no guarantee of a unique equilibrium point. Real world is that there can be differing equilibrium points, thus different prices to clear markets, thus non-market intervention can lead to a more beneficial outcome.
sorry i forgot the austrian believe in the flat earth and believe mathematics has no place in economics
quite simply it is possible for some goods to be have a linear supply/demand curve and others to be parabolic in shape if the parabola does not intersect the linear function then no equilibria for whole economy can occur.
similar to current situation where nominal negative interests rates are required, as this is not possible market cannot create an equilibrium point