On the survival of poor peasants

Previously, in underdeveloped countries, people tried to keep the prices of food products artificially low, in order to help the poor to buy their food. But it became soon clear that such system, although helpful for the city poor, was disastrous for the peasants (who usually are even poorer), so that hunger increased, instead of decreasing. More recently, thus, higher prices have been imposed. But a high-price system does not solve the problems. It helps, indeed, a peasant to buy in the city non-edible products, but not to buy (more expensive) food products from other peasants. The question is discussed here in more detail starting from the simplest conceivable case of two peasants producing each a different food product (bread and cheese, say), then generalizing to several food items and to any number of peasants producing a given food item j. Like in every economic system which wants to be sustainable, or able to reproduce itself in a stationary state at least, prices are determined by the necessity of exchanging "means of production" among "industries", except that here industriesare replaced by working peasants and means of production are replaced by food. It is found that prices must obey certain inequalities related to the minimal amount of each food item necessary for survival. Inequalities may be rewritten as equations and, in an important special case, such equations give rise to a simple version of the matrix equation used by famous authors to describe the economy.