Emerald is very expensive and amethyst is not, can you explain why?

When supply is high, prices are low when demand is high prices are high. Emerald, ruby and sapphire are much rarer than amethyst and demand for these gemstones is also much higher therefore the prices of those gemstones are significantly higher than amethyst

Its expensive because, Emeralds are super hard to find today, but Ameythyses are found easly in gemstone mines.