user911: I noticed that there are exchange rates for Bitcoin to other given currencies. How are these rates established?

user916: The MtGox exchange rate for bitcoin to USD is established in a 24/7 free market where bids meet offers to generate a last trade price. The bid/offer spread represents the distance that market participants are willing to buy or sell their bitcoin. This is no different than any other free market or any other free-market exchange-determined commodity price. See; http://mtgoxlive.com/orders

user563: It is established by people posting buy and sell orders.

user984: The simple answer is that it is the price at which a seller and a buyer of the currency agreed on a price for it; i.e. the price at which the market clears.  The sold currency is, after all, a commodity.
It may help you to strip away any superfluous notions to think of it as a pound of coffee or somesuch.  Seller Sally has coffee but wants dollars.  Buyer Bob has dollars and wants coffee.  Sally will not part with her coffee for less than $4.  And Bob will not buy coffee for more than $3 dollars.  The market fails to clear at these prices.  A new seller, Sam enters the market and is willing to sell his coffee for $3.50.  And a new buyer, Bill, enters and is willing to buy coffee for $3.50.  Sam and Bill exchange coffee for dollars.  This fact is published to the rest of the market participants; who are thereby able to conclude that at some point in the recent past that two participants were able to transact at the price of $3.50.  As an entrant to the market, are you guaranteed to find another buyer or seller at that price?  No.  But it's a useful piece of data.
If you really want to know how this -- and economy in general -- works, you'll have to do a little reading.  As a start, I recommend:
Murray Rothbard, Man, Economy, and State
http://mises.org/rothbard/mes.asp
Ludwig von Mises, The Theory of Money and Credit
http://mises.org/books/Theory_Money_Credit/Contents.aspx

user441: Most exchanges use the double-auction market system for price discovery. Read more at
http://www.investopedia.com/terms/a/auctionmarket.asp
In economics-speak, the auction market converges where supply and demand intersect.

user323: 
You have people that have BTC or currency already in their accounts.
Those people can claim: "I will buy/sell X amount of Bitcoins for Y amount of currency". If you divide one by the other, you have the exchange rate for that particular transaction.
If a buy and sell transaction overlap, they are executed and removed from the system.
After all such transactions are removed, you have a gap between the exchange rate at which people want to buy Bitcoins, and that at which people want to sell Bitcoins.
Average the closest buy-sell pair of transactions and you have the exchange rate, halfway between those two, or the price of the last trade may be used. In both cases, it's only an estimate of the price that the next trade will take place at.


911: <p>I noticed that there are exchange rates for Bitcoin to other given currencies. How are these rates established?</p>
 916: <p>The MtGox exchange rate for bitcoin to USD is established in a 24/7 free market where bids meet offers to generate a last trade price. The bid/offer spread represents the distance that market participants are willing to buy or sell their bitcoin. This is no different than any other free market or any other free-market exchange-determined commodity price. See; <a href="http://mtgoxlive.com/orders" rel="nofollow">http://mtgoxlive.com/orders</a></p>
 563: <p>It is established by people posting buy and sell orders.</p>
 984: <p>The simple answer is that it is the price at which a seller and a buyer of the currency agreed on a price for it; i.e. the price at which the market clears.  The sold currency is, after all, a commodity.</p>

<p>It may help you to strip away any superfluous notions to think of it as a pound of coffee or somesuch.  Seller Sally has coffee but wants dollars.  Buyer Bob has dollars and wants coffee.  Sally will not part with her coffee for less than $4.  And Bob will not buy coffee for more than $3 dollars.  The market fails to clear at these prices.  A new seller, Sam enters the market and is willing to sell his coffee for $3.50.  And a new buyer, Bill, enters and is willing to buy coffee for $3.50.  Sam and Bill exchange coffee for dollars.  This fact is published to the rest of the market participants; who are thereby able to conclude that at some point in the recent past that two participants were able to transact at the price of $3.50.  As an entrant to the market, are you guaranteed to find another buyer or seller at that price?  No.  But it's a useful piece of data.</p>

<p>If you really want to know how this -- and economy in general -- works, you'll have to do a little reading.  As a start, I recommend:</p>

<p>Murray Rothbard, <em>Man, Economy, and State</em></p>

<p><a href="http://mises.org/rothbard/mes.asp" rel="noreferrer">http://mises.org/rothbard/mes.asp</a></p>

<p>Ludwig von Mises, <em>The Theory of Money and Credit</em></p>

<p><a href="http://mises.org/books/Theory_Money_Credit/Contents.aspx" rel="noreferrer">http://mises.org/books/Theory_Money_Credit/Contents.aspx</a></p>
 441: <p>Most exchanges use the double-auction market system for price discovery. Read more at
<a href="http://www.investopedia.com/terms/a/auctionmarket.asp">http://www.investopedia.com/terms/a/auctionmarket.asp</a></p>

<p>In economics-speak, the auction market converges where supply and demand intersect.</p>
 323: <ol>
<li>You have people that have BTC or currency already in their accounts.</li>
<li>Those people can claim: "I will buy/sell X amount of Bitcoins for Y amount of currency". If you divide one by the other, you have the exchange rate for that particular transaction.</li>
<li>If a buy and sell transaction overlap, they are executed and removed from the system.</li>
<li>After all such transactions are removed, you have a gap between the exchange rate at which people want to buy Bitcoins, and that at which people want to sell Bitcoins.</li>
<li>Average the closest buy-sell pair of transactions and you have the exchange rate, halfway between those two, or the price of the last trade may be used. In both cases, it's only an estimate of the price that the next trade will take place at.</li>
</ol>
