By convention, the first transaction in a block is a special transaction that starts a new coin owned by the creator of the block. This adds an incentive for nodes to support the network, and provides a way to initially distribute coins into circulation, since there is no central authority to issue them. The steady addition of a constant of amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.
The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.
The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU proof-of-worker than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.
The fact that new coins are produced means the money supply increases by a planned amount, but this does not necessarily result in inflation. If the supply of money increases at the same rate that the number of people using it increases, prices remain stable. If it does not increase as fast as demand, there will be deflation and early holders of money will see its value increase. Coins have to get initially distributed somehow, and a constant rate seems like the best formula.
If you're having trouble with the inflation issue, it's easy to tweak it for transaction fees instead. It's as simple as this: let the output value from any transaction be 1 cent less than the input value. Either the client software automatically writes transactions for 1 cent more than the intended payment value, or it could come out of the payee's side. The incentive value when a node finds a proof-of-work for a block could be the total of the fees in the block.
There will be transaction fees, so nodes will have an incentive to receive and include all the transactions they can. Nodes will eventually be compensated by transaction fees alone when the total coins created hits the pre-determined ceiling.
Total circulation will be 21,000,000 coins. It'll be distributed to network nodes when they make blocks, with the amount cut in half every 4 years. first 4 years: 10,500,000 coins next 4 years: 5,250,000 coins next 4 years: 2,625,000 coins next 4 years: 1,312,500 coins etc... When that runs out, the system can support transaction fees if needed. It's based on open market competition, and there will probably always be nodes willing to process transactions for free.
It might make sense just to get some in case it catches on. If enough people think the same way, that becomes a self fulfilling prophecy. Once it gets bootstrapped, there are so many applications if you could effortlessly pay a few cents to a website as easily as dropping coins in a vending machine.
You could say coins are issued by the majority. They are issued in a limited, predetermined amount.
To Sepp's question, indeed there is nobody to act as central bank or federal reserve to adjust the money supply as the population of users grows. That would have required a trusted party to determine the value, because I don't know a way for software to know the real world value of things.
In this sense, it's more typical of a precious metal. Instead of the supply changing to keep the value the same, the supply is predetermined and the value changes. As the number of users grows, the value per coin increases. It has the potential for a positive feedback loop; as users increase, the value goes up, which could attract more users to take advantage of the increasing value.
Those coins can never be recovered, and the total circulation is less. Since the effective circulation is reduced, all the remaining coins are worth slightly more. It's the opposite of when a government prints money and the value of existing money goes down.
Eventually at most only 21 million coins for 6.8 billion people in the world if it really gets huge. But don't worry, there are another 6 decimal places that aren't shown, for a total of 8 decimal places internally. It shows 1.00 but internally it's 1.00000000. If there's massive deflation in the future, the software could show more decimal places.
I'm sure that in 20 years there will either be very large transaction volume or no volume.
In a few decades when the reward gets too small, the transaction fee will become the main compensation for nodes.
The price of any commodity tends to gravitate toward the production cost. If the price is below cost, then production slows down. If the price is above cost, profit can be made by generating and selling more. At the same time, the increased production would increase the difficulty, pushing the cost of generating towards the price.
At the moment, generation effort is rapidly increasing, suggesting people are estimating the present value to be higher than the current cost of production.
Lost coins only make everyone else's coins worth slightly more. Think of it as a donation to everyone.
It's the same situation as gold and gold mining. The marginal cost of gold mining tends to stay near the price of gold. Gold mining is a waste, but that waste is far less than the utility of having gold available as a medium of exchange. I think the case will be the same for Bitcoin. The utility of the exchanges made possible by Bitcoin will far exceed the cost of electricity used. Therefore, not having Bitcoin would be the net waste.
Bitcoins have no dividend or potential future dividend, therefore not like a stock. More like a collectible or commodity.