Under rent control, the demand for housing changes in both axes. It increases because those who previously would not have sought their own home will see it as an attractive option given the artificially low prices. It also decreases because those in housing that is now too large (children have moved out, or the elderly no longer accesses the upstairs) feel no need to downscale. There is no incentive to do so without the saving of money. Smaller housing might be even more expensive. The result is that the demand can become stagnant as the natural turn-over ceases.