Some good answers here, but missing some critical points, so I'll add my own answer.
First of all, when you think about an economy and a currency, the question is, why does the currency have value? Our currency used to be gold-backed. Now it's basically valuable because (a) the gov't says people must accept it in payment of debts, and (b) you can pay your taxes with it. Still, the central bank's job is to make sure to match the money supply to the value of real physical wealth in the country, but increase it by around 2% per year inflation (I won't get into the reasons for that). The gov't and central bank have some quite complicated ways of managing the money supply, the simplest way being to print or destroy money, but there is also the money multiplier effect of banks to take into account.
In this movie, the currency has value because you have a device implanted in your arm that will kill you if you run out.
Also, it naturally drains down at one second per second times the population (over 25). The central bank can just keep increasing the virtual time at the same rate, since it's all just data being moved around. Some of this is created by "gifting" the 1 year to each 25-year-old. The rest has to be added, typically through debt, but in this movie I think the government just creates it. That's how the government gets money instead of taxes. They create "time" and give it to you for working, which allows you to live. 852
It's absolute slavery, and very evil.
Note that you can also pay rent and buy food, etc., with time, so the central bank also needs to add time to circulation to match the growing wealth of the country, or else you get crazy inflation or deflation. Note that they show a scene in the movie where prices suddenly inflate. That typically means either a whole bunch of wealth was destroyed, or a whole bunch of money was created.
In fact, in the scene just before, thugs looted a bank and stole time. You would think this would add more time to the money supply, but it's questionable. In the bank, it's subject to the money multiplier because they can loan it out, so taking it out of the bank and putting it in your "pocket" actually reduces the money supply. In the movie, the government is seen raising prices as a punishment, so I guess this means it's a government controlled market, not a free market for these goods. It does kind of make sense that if the amount of goods for sale (coffee, etc.) is fixed and you dumped a whole bunch of cash on the local population, you'd expect prices to rise in the short term. Across the whole economy, I don't think that's the case. You'd see a slow-down in spending on capital items like cars/houses because the bank would reduce loans. 852