DECENTRALIZED REOURCE ALLOCATION WITH A MODICUM OF INCREASING RETURNS

The problem explored in this essay is the possibility of decentralizing the allocation of inputs among many producers, endowed by nature with ifferent production functions, in order t mximie he output of a single commodity. The results described extend in some respect the range of technologies to which decentralized allocation procedures can, at least conceptually,bpplied. The particular decentralized alloca tion scheme explored is a formaized version of the Lange-Lerner algithm, in which the ministry of production announces a trail price for each input and producers demand quantities of inputs to maximize shadow profits at the announced trial price vecotr. The vector is revised by changing its components in proportion to the excess de mands (that is, total demands minus supplies) resulting from profit maximization at the announced prices. The process is repeated in the hope of reaching a price vector which is an equilibrium set of prices in the sense that the m of producers' profit-maximizing demands just equals supplies, so that every producer is at a position from which he has neither incentive nor need to move; for such an equilibrium always represents an optimal allocation of inputs. (Author)