Yes, aggregate demand is increased but aggregate savings, which are the source of investment, are decreased. Those assets of the minority, we're assuming, are also productive. So the prices of the assets purchased by those with 'significant income' go down. So this might manifest as increased prices on low-end staple goods and decreased prices on durable assets. Still doesn't imply general inflation. (Of course, this is a major bone of contention of the whole Monetarist vs Keynesian debate, so if you think the Keynesian account is more convincing, then that's a sticking point.)