Housing shortage and its impact on the society has been one of the most discussed topics during the past decade. The aim of this thesis was to explore the possible effects the introduction of market rents could have on rental housing. We observe an existing free market which can be seen as a close substitute to the rental market today, namely the market of tenant owned apartments and estimate the possible market rents based on that. Three Swedish cities have been studied. The results showed that there are possible increases and decreases in rents, variation between and within cities as well as variation between the time periods.