How does one really compute inflation? I just now quickly looked up how the real GDP was computed. It is using the base year price to multiply the number of products traded. Is that meaningful? Is a ten year inflation computed on the base of the zeroth year price? The change in demand and supply would have made a huge change in the price when there is no inflation. The Motorola flip cell phone price now must be less than 1/100 of the price when it first came out. Does that mean there is severe deflation? On the other hand, the price for it could explode because it could have become a collector item. What about the price of a quantum computer --- the real one, or just something akin to DWave --- when it comes out? Are we going to compare its price against Von Neumann's Maniac or Allan Turing's Bombe or Intel 40386? This is nonsense and absurd. One rescue I can come up with right now, is we divide a finite time interval into multiple periods and computing recursively. We must assume the inflation speed is faster than the change of the supply and demand in each interval. I do not even know if that makes mathematical sense. Is there a proof of legitimacy for this or any other remedies, at least mathematically?
luchonacho has provided some sources below in his answer, particularly hedonic regression, for estimating the inflation. I have expressed my doubt over the efficacy of method. Here I would like to criticize the method further on the technicality.
The hedonic regression does not answer my question for distinguishing the change in supply and demand including that caused by the technological change. It seems the proponents of hedonic regression claim that it could make the distinction. Hedonic regression assumes the price of a good as the linear function of its attributes. Suppose the attributes have not changed over the period under consideration. However, the supply and demand for this good have changed due to, say, technological innovation that either has made the good obsolete or more valued or made useful in completely different ways than before, as well as inflation. Unless one already know extraneous information either on the change in supply and demand or the inflation, there is no way one can distinguish inflation from the change in supply and demand.