Exchanges determine price by matching bids and asks.

The modern processes for this are called Auctionmarket and Level 2.

Bitcoin itself does not provide a "price" (Some people prefer the expression "Moscow Time"). The multiple exchanges around the world do. You can trust this process since if the price was misquoted or suppressed at one exchange there would be an arbitrage situation that would balance itself out.

You can also assume that there isn't a conspiracy by exchanges to suppress the true value of Bitcoin in fiat because that would mean that are lot's of unmatched bids & asks somewhere - then any local Bitcoin meetup behind your favorite pizzaria in town would trade at vastly different levels. The market ... always finds a way like a drop of water to the ocean.

Finally, exchanges do not have to be decentralized like some shitcoiners pretend to need. Bitcoin is a decentralized world - the access to it can not be guaranteed to be decentralized like Diagon Alley is the access to the magical world in Harry Potter - but isn't the magical world itself. (I hope that metaphor makes sense). The market itself is decentralized every time you buy/sell/work in Bitcoin in the real world or every time you exchange Bitcoin in your local Bitcoin meetup behind your cities pizzarias - capitalism , markets and arbitrage do their magic on their own.

Where is the authoritative source for the Bitcoin price?

Well, there isn't one.

So differences in price for bitcoin occur at different marketplaces ... just as the price of a tomato is different at different grocery markets.

There are various methods that attempt to consider various marketplaces to come up with a more sane, commonly available price.

For instance, Coindesk has their "Bitcoin Price Index", which they suggest the symbol XBP, and the method it is calculated is shown here:

CoinDesks's BPI is used by a number of financial media (e.g., Bloomberg/WJS) and trading products.

There's also the BraveNewCoin's BItcoin Liquid Index (BLX):

The BLX is used by NASDAQ.

The CME has its own "prices", BRR (Bitcoin Reference Rate) -- the "closing price" used for daily settlements, and BRTI (Bitcoin Real-time Index):

MVIS:

TradeBlock (XBX):

BitcoinAverage:

CoinTelegraph:

CoinMarketCap:

Messari OnChainFX:

Nomics:

Winkdex:

NYSE (NYXBT):

Others:

Charts:

Basket / Altcoin indexes:

Related:

i do.

No central authority determines price. Instead each owner individually assigns a value in fiat shitcoin he'd be willing to sell.

Several owners would put Bitcoin price very high, in the millions, or tens of millions of USD. These are currently called HODLERS.

Satoshi decides the price.

So basically, on exchanges, you can put a bid for Bitcoin. If someone accepts your bid at the price you put, that becomes the new Bitcoin price. If you then put up a bid to sell Bitcoin, and someone buys it for the price you put, then that becomes the Bitcoin price instead.