In previous questions I understood that printing money and injecting it in the economy generates inflation because there is a bigger demand for the same offer (please correct me if I'm wrong) so it's not a good idea. After thinking this, a new question arose. Why can't goverments print money to fund the productive sector? In that way, it can get money in circulation while generating more offer so there is no inflation. I can't understand what prevents goverments to do that.
Government usually do not have control of the money supply because historically it is a very bad idea. They have a tendency to print a lot of money and cause hyperinflation. That's why most countries have an independent central bank that controls the money supply.
In a way, government will subsidize productive/protected sector through subsidies like rice farming in Japan. However, it is just not through newly printed money but through tax funding.
Now if you are asking why can't central banks print money to fund productive sectors like manufacturing. That's call helicopter money. Many people are contemplating it now as global growth is slow and inflation is dangerously low. It is possible and historically it has been done. However, currently it is illegal for central bank to directly give out money to the economy through newly printed money. Perhaps in the near future it will be done.
The first thing to be aware of is that money is continuously being created and destroyed through the process of fractional reserve banking (which according to the Bank of England and others is incorrectly explained in most textbooks). Under this system there can be periods in which, in the absence of central bank intervention, there will be a fall in the money supply and deflation. In these periods there would be little risk of inflation if the government printed money for whatever purpose they liked. Indeed some economists have advocated direct money printing instead of QE.
With regard to the idea that creating money for productive purposes causes less inflation because more is produced - I know that this is something that Prof. Richard Werner has emphasised in the past, though I don't have a specific reference for that to hand.