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I'm not sure how you expect that to work. How would expiring bitcoins increase circulation?
"You will have 10 BTC expire next month" So you spend it. Also, once the BTC expire, they don't disappear. They are made available for mining. This is possible because the block chain has full history.
For instance, let's say I wait until the literally last minute to spend my expiring bitcoins. I want to exchange my almost-expiring 10 BTC for $100. Would you accept this offer, knowing that those 10 BTC will vanish shortly after you accept them?