> If productive sector employees' demand for goods causes inflation, prices will rise.

I'm not sure what you mean. Prices rising is what we call 'inflation' - one doesn't cause the other. They're the same thing.

Rising demand induces inflation because more money is chasing the same goods.

That might just mean more competition is created as there's a bigger market to chase. Minimum wage has the same risk as the one you mentioned, but also all but guarantees higher prices (particularly on labour-intensive goods such as food) as everyone's wage needs to go up to make the harder/worse jobs worth doing.