Inflation is a side effect of monetary and fiscal policy; central banks are now quite good at adjusting interest rates to keep inflation in the 0-2% band.

> In direct response to large classes of workers demanding more pay & benefits, companies will raise their prices to pay for those increases, again totally regardless of whether a stock market exists.

How well this works is down to the "tightness" of the labour market. Central bank policy affects this: raise interest rates -> decrease investment -> increase unemployment above the "NAIRU" ("non-accelerating inflation rate of unemployment") -> workers are unable to demand pay increases as they may be replaced by eager cheaper workers from the pool of unemployed.