The eventual failure of price fixing schemes

This essay examines the feasibility of a government buffer stock program which attempts to fix a relative price over time. In the model, m risk averse agents with random endowments of two commodities maximize expected utility over an infinite horizon. It is shown that a price fixing scheme will fail with probability 1, regardless of the price set by the government and regardless of the initial level of buffer stocks. The proof of this proposition turns on some well-known properties of random walks.