There are no known relations between mattress cost and sleep quality. In fact, there are no standards to recommend a particular bedding system over another.
No benchmark standards presently exist for recommending bedding systems, whether for the purpose of alleviating pain-related sleep disturbance, stress, or for the purpose of enhancing sleep quality. Recommendations of medium-firm mattresses, hard beds, or suggesting that no difference exist between sleep surfaces add to the confusion. Indeed, the ideal mattress is yet to be determined and likely depends on many variables illustrating the need for additional research. It may be overly optimistic to conclude that one type of mattress fits all individuals because of the range of varied anthropometric characteristics of the human body.
--Changes in back pain, sleep quality, and perceived stress after introduction of new bedding systems
However, using a new mattress (possibly medium-firm) will result in better sleep, less back ache and less stress, than sleeping in an older bed:
In the present study, [new] medium-firm bedding systems reduced back pain by approximately 48% (37.1 [pre mean] − 19.3 [post mean week 1-4] = 17.8/37.1 = .48) and improved sleep quality by 55% (43.5 [pre mean] − 21.0 [post mean week 1-4] = 22.5/43.5 = .52)