There are many typical commodity pairs in which the commodities are linked together by a fundamental production relationship. A typical example is the burning of fossil fuel to produce energy. The dynamics of the commodities influence each other, which results in certain feedback effects and affects the spread dynamics of the two commodities. In this paper, we use a simple model to study the joint dynamics of a driving commodity and a driven one and obtain explicit formulas for the terminal variances of the commodities and their spread. We apply the model to real-world data and study the dynamics of coal-power, gas-power and oil-gas oil pairs.