What is inflation?
Let's stick with the simple definition of inflation as a decline in purchasing power over time.
What are the roots of inflation?
This is still an open question but on one hand, the mainstream answer given by the Keynesian schools, which is the most spread among universities, politicians and policy makers, is that: inflation occurs when we have a scenario where aggregate demand for final goods and services exceeds the aggregate supply at full (or nearly full) employment level. It can also happen when the aggregate supply is not capable of meeting the aggregate demand, forcing the producers to raise the price of goods. In other words, for the mainstream economics, any imbalance between supply and demand can possibly generate inflation and therefore we need the merciful central banks to equalize the inequalities of the market. Simply put, if the price of food rises, it is because people are either demanding more food or the producers are selling less food and therefore the central banks should come in and charge their expensive fees to be part of the solution. But, in any case, whatever happens, they are NEVER part of the problem and their models don't even consider that.
I guess that the only question remaining is: if the current model is working and the only goals of the central banks are control of inflation and employment rates, how can we have so much inflation now? I will let Jerome Powell, chairman of the FED, answer this one:
On the other hand, the Austrian School economists explain that inflation is always caused by the increase of the money supply from governments (who are the ones that control the currency). If the price of food rises, it is because we have more money circulating in the economy for the same quantity of food.
While it is pretty obvious that increasing the money supply directly increases the level of prices, most policy makers across the globe continue doing it and expecting to have low inflation rates.
This was a just a brief introduction to say that the focus of this work is 100% on the supply side of the currency, which is calculating the amount of XMR circulating in the economy.
Monero supply curve
Let's start with the theoretical supply curve of Monero, which you can see in the graph below. We can simply sum the amount contained in each block mined and see if it is following the emission rules previously agreed by the network consensus. If a miner wants to add a block with a reward value bigger than the expected reward, it will be denied by the network consensus and the block will not be validated. Although it is pretty easy to verify if the new creation of XMR is playing according the rules, it is not sufficient to prove that an unexpected creation of XMR (also named as inflation) happened. Due to the strong privacy preserving schemes in Monero, it is not trivial to evaluate if the transactions are obeying the equation Inputs = Outputs + Fees and an imbalance in this equation could lead to an inflation bug.