If they could produce more they already would.

The only way of fixing this is decreasing demand by reducing the population numbers.

Why would they produce more if they could? It must meet the demand at the current price point. More money goes to poor people, more demand for food at the current price. That will increase the price, which will increase production. Short term the price might go up a lot, but then new production will come online, and the prices will fall back to today+delta.