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This is the subject of the article.

Last I checked, current market rates are about $30 for a typical transaction.

To happen, transactions must be included in a fixed size block in the global block chain. Currently, there is not enough room per block, so space is auctioned off on a per byte basis. The size of a transaction is not related to the number of bitcoins involved, but the number of "utxo" involved. Essentially, if Alice sends you 1BTC and Bob sends you 1BTC, you do not simply have 2BTC, you have 2 utxo's each worth 1BTC. If you want to send more than 1.5BTC in a single transaction, you will need to include both utxo's, which will increase the size and therefore the fee. In contrast, if Carol sent you 2BTC in a single transaction, you can then send 1.5BTC at the same cost as 1BTC because only 1 utxo is involved.

In a world with sufficeint space in a block, you could still need fees because the miners might decide to leave empty space instead of includeing free-rider transactions. This does not actually save them money, but if they control a non-trivial amount of the hashrate, it could encourage people to increase there fees in order to decrease their confirmation time (especially if all the major miners do this).

The vast majority of the compute time is finding the nonce that produces the output hash with the appropriate number of leading zeros. The transaction merkle tree output is an input to that calculation and transactions only need to be computed once per block. The rest of the time is generating hashes with random nonces.

Change address would also take some space

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