The Relation Between Prices of Factors and Goods in General Equilibrium

In an n x n economy, the relation between commodity prices and factor prices has been presented in terms of finite variations. Using a generalization of the dominant diagonal condition on the Jacobian of the set of unit cost functions, this paper shows that a rise in the price of any commodity will bring about an increase in the earnings of the corresponding factor, making no other factor better off than that factor while the earnings of at least one other factor will not increase. Strengthening the requirement further shows that the earnings of at least one factor will decline.