No.
Economics rents (not strictly the same as the money paid in rent. It is the return above costs that accrue to the supplier rather than renter of the property. The net problem is the combination of the two phenomena David Ricardo noted:
1. The iron law of wages: wages tend toward subsistence level. https://en.m.wikipedia.org/wiki/Iron_law_of_wages
2. The law of rent: the rent of a land site is equal to the economic advantage obtained by using the site in its most productive use. https://en.m.wikipedia.org/wiki/Law_of_rent
Given the latter, rent is determined by economic benefit, not by the cost of provision. A land tax, set to the difference between the value of utilisation and the cost of using the land, secures that surplus value to the state. (You'd want to leave "normal economic profits" to the landlord.)
The effect of this is to introduce a carrying cost, to the landlord, on the value of the land. The price of the rent itself is bound by the beneficial use (say, 30% of prevailing wages). If someone cannot afford to pay that amount, they will seek alternative accommodations, or move out of the area. Any landlord charging more than that amount will have no takers (rational actors, long term), if the number of units on a property isn't sufficient for the landlord, the alternative is to increase density (build higher, smaller, or occupy more of the land space).
Meantime, the tax revenues go to fund urban services.
In much the same way, raising wages does not increase prices, but rather secures more of the manufacturing profit to labour rather than owners, as prices are established by the overall market (net of imports from elsewhere).
That's the principle of Georgism.
https://en.m.wikipedia.org/wiki/Georgism
More generally: if you go back to the classical economists (Smith, Marx, Ricardo, Malthus, Mill), you find a number of distinct classes of goods being transacted. Generally (and adding a few):
1. Commodities.
2. Labour.
3. Capital.
4. Rents (monopolies).
5. Interest (and risk).
6. Investment assets.
8. Natural resources.
8. Public goods.
(Subject to possible consolidation / reordering, though that's the gist of it.)
Quite significantly, each of these has specific behaviours in terms of pricing, most specifically as to the relationships of the true economic cost of production (cost), the true economic value (value, for which I don't follow Bentham's Utility theory), and exchange price (price).
The ideal, as Smith notes, is for price to approach the long-term true economic cost, but in the case of the goods classes listed, that's frequently not the case (also noted by Smith). Marginal analysis describes this in terms of market function, though that misses critical elements, including market failures and distortions.