Obviously it's fair to say that inflation may be measured more in some prices than others, but you're sort of muddying the waters by referring to housing as both an asset class and a cost-of-living, right?
Perversely, if inflation primarily affects "assets" (i.e. of the investment/speculation type), the premise of the original question here is sort of flawed: if increasing the money supply increases the price of assets, those with savings get richer—exactly the opposite of the ordinary understanding of "inflation!"
