Synopsis :To forecast iron source demand, the Intensity of Use hypothesis, which assumes that material consumption per capita is a function of GDP per capita, is the most dominant theory in existing studies. However, this hypothesis is not effective for a world one-region model of iron sources. Therefore, we focused our attention on utility, and we suppose that economic growth is a major driver to increase the utility. As the utility of steel sustains for ages after purchase, we formulate the Utility of Stock hypothesis, which assumes that the in-use steel stock is a function of GDP. In this study, the world steel stock was computed and the Utility of Stock hypothesis was tested. Clear correlation is found between the steel stock and the GDP. It leads to the estimation that the world demand for iron ore depends not on the volume of GDP but on the variation of GDP. For the first time with total world figures, the result enables us to rationalize the recent decoupling between the world growth of iron source demand and the economic growth.