The short answer is that the price is set by markets.

Bitcoin, like most other currencies, has a floating exchange rate. That means that the value of bitcoin vis-a-vis any other
currency fluctuates according to supply and demand in the various markets where it is traded. For example, the “price” of
bitcoin in US dollars is calculated in each market based on the most recent trade of bitcoin and US dollars. As such, the
price tends to fluctuate minutely several times per second. A pricing service will aggregate the prices from several markets
and calculate a volume-weighted average representing the broad market exchange rate of a currency
pair (e.g., BTC/USD).