The price of cryptocurrencies basically follows the rules of demand and supply. As the coin becomes scares it becomes more valuable and hence the price increases.
it is not the law of supply! it is called the supply AND demand. which means having scarce supply doesn't change anything. a coin may have only 1000 total coins and still be worth nothing!
it is the demand along with supply that can change things. with a limited supply and increasing demand (like bitcoin) the price goes up. in other words that increasing demand is important.
also the type of demand is important. if it is pure speculative demand by traders then it won't have any future but if it is real demand like bitcoin as a currency in real world then the rise will be strong and it can last.