This is not how supply and demand should work in a functioning economy. Higher demand will up the price at first, but then some market player should be able to step in and make it work for less (thus upping the supply), until the market has found a new steady state (which, as long as supply isn't restricted, should be around the same price as before or lower because of a higher scale).

Now obviously, if what you have isn't actually a free market but an oligopoly with government protections, price fixings etc., this won't work. You'll have some of these problems in some markets, but that would just have to be next thing to concentrate on.