Rent control keeps the price below equilibrium (at R1) – it can’t rise to the equilibrium rent of R0 because of the rent control rules. The lower rent makes renting more attractive relative to owning your own home. Some people would find it cheaper or more convenient to be a renter at this lower rent, so the quantity of rental housing demanded increases (to QD1). However, the lower rents make rental housing a less attractive investment for landlords. Perhaps they convert that rental housing into commercial rentals instead (e.g. offices) or maybe they choose to live there themselves (the opportunity cost of living in the house is now lower). Either way, the quantity of rental housing supplied decreases (to QS1). The difference between QD1 and QS1 represents the excess demand for rental housing at the controlled rent – there are fewer houses available than the quantity people want to rent.
Why does that lead to lower quality housing? Excess demand means that there are many more prospective tenants available than there are rental housing units. That gives landlords a lot of power. They can be choosy about tenants, but tenants can't afford to be choosy about rental properties because they may miss out. And landlords know that tenants can't be choosy. So, if you're a landlord why would you go to the expense of maintaining your property to a high quality, when if the tenant doesn't like it they can leave and it is easy to find a new tenant? You wouldn't.
Coming back to Tabarrok's blog post, that's exactly what he described:
Walking around Mumbai it’s common to see some lovely, older buildings (circa 1920s perhaps) that are rent control in a great state of disrepair. A well maintained building can last for hundreds of years so why are these buildings falling apart? The answer is rent control. Bombay passed a rent control act in 1947 that froze rents at 1940 levels.
More than fifty years later, rents remained frozen at 1940 levels. It wasn’t until 1999 that the Act was modified slightly to lift controls on some new construction and to allow rent increases of 4% per year. After a fifty two year freeze, however, a 4% increase was a pittance. Thus, even today there are thousands of flats where tenants are paying rents of 400-500 rupees a month (that’s $6 to $8 a month!)–far, far below market rates.
The rent control law meant that there was virtually no construction of rental housing (WP) for decades and a slowly dilapidating housing stock. (Ironically, the only free market in rental housing is in the slums.)
The nominal landlords have neither the incentive nor the funds to maintain the buildings so every year during monsoon season some of the buildings collapse and people die.So, not only to rent controls create deadweight losses (see here), they can have very real and very harmful consequences.