Equilibrium adjustment of disequilibrium prices

We consider an exchange economy in which price rigidities are present. An always converging price and quantity adjustment process for such an economy is presented that is based on a discrete algorithmic procedure rather than on more traditional adjustment processes, which are based on difference or differential equations. In the short run, all non-numeraire commodities have a flexible price level with respect to the numeraire commodity but their relative prices are mutually fixed. In the long run, prices are assumed to be completely flexible. The adjustment process starts with a trivial equilibrium with a low enough price level and complete demand rationing on all markets. Along the path followed by the adjustment process, initially all relative prices of the non-numeraire commodities are kept fixed and the price level is increased. Rationing schemes are adjusted to keep markets in equilibrium. In doing so, the process reaches a short-run equilibrium with only demand rationing and no rationing on the numeraire and at least one of the other commodities. In the long run, the process allows for a downward price adjustment of unrationed non-numeraire commodities and eventually reaches a Walrasian equilibrium.