Econophysics of precious stones

The importance of the power law has been well realized in econophysics over the last decade. For instance, the distribution of the rate of stock price variation and of personal assets show the power law. While these results reveal the striking scale invariance of financial markets, the behaviour of price in real economy is less known in spite of its extreme importance. As an example of markets in real economy, here we take up the price of precious stones which increases with size while the amount of their production rapidly decreases with size. We show for the first time that the price of natural precious stones (quartz crystal ball, gemstones such as diamond, emerald, and sapphire) as a function of weight obeys the power law. This indicates that the price is determined by the same evaluation measure for different sizes. Our results demonstrate that not only the distribution of an economical observable but also the price itself obeys the power law. We anticipate our findings to be a starting point for the quantitative study of scale invariance in real economy. While the Black--Sholes model provided the framework for optimal pricing in financial markets, our method of analysis prvides a new framework that characterizes the market in real economy.