I read (actually re-read) a good description of inflation in Joseph Heath's Enlightenment 2.0. He describes it this way. In periods when a country's "productivity" goes up, salaries increase, companies make more money, the economy (the thing we call the economy is just a way to measure those things) expands. When productivity decreases, what should really happen is that wages should be cut, profits should reduce, etc. But that wouldn't go over well, instead we let inflation decrease everyone's spending power.
My first job out of school several decades ago was as data and programming support for a group or macro economists at an economic consulting company. My background was not economics but math/physics. It became pretty clear to me that trying to explain inflation's causes in a sentence or two misses the mark by a mile. There's more to it than blaming the current politicians in power.
That's not inflation. Inflation is always the expansion of the money supply. The reason the Fed got it wrong, and keeps getting it wrong, is because they learned it wrong in college. That's why we're in the mess we're in.
As the famous economist Milton Friedman famously said, “Inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output.”
You also have a few other facts wrong. If a particular company's productivity goes up and the boss increases their wages because of it, it's because he's able to produce more widgets cheaper. Those savings are passed on to the customer who pays less for the product, not more. Inflation, the printing of money beyond equivalent productivity increases, raises the prices of products. Increased productivity lowers the prices. Companies whose workers are producing less fire their employees or the company goes out of business.
That's what we're going to see soon as the recession hits and the Fed doesn't print to support zombie companies. Marginal companies will fail. No one is going to loan them money or capital as the Fed encourages now with cheap printed money. Unemployment will go up, GDP will go down, stocks will go down, and more workers will be laid off. Assets will deflate. Welcome to the recession and higher prices - stagflation of the 1970s/80s. It's going to get bad pretty soon as the again-to-be-seen free market tries to correct the central planning mess the government has created over the last couple of decades of deficit spending, printing and low-interest rates with attendant debt.