It is being determined based on supply and demand.
The more people buy Bitcoin, the higher the price. Since Bitcoin has a limited supply, if the demand increases, we would have to 'fight' (with our cash

) for our share of BTC.
Furthermore, how do different exchanges reach on the consensus for a price?
The exchanges are just platforms that allow people *that are* selling and buying bitcoin to meet each other. If the difference *of BTC in different exchange sites* *is significant *then people from other places will come to the exchange with different price and make trades in a way to balance things out.
Exchange sites are like individual markets. There might be people
selling at a lower price at Market A, and people buying at a
higher price at Market B. But a trader who visits these two markets can instead buy from Market A, and sell high at Market B to earn profits. A simple analogy.

The users determine the price of Bitcoin, Bitcoin is governed by all of us. ^_^