You can verify your assumption by looking at the offers at the vendor of your choosing.
Traditionally, SMF optics used to be a lot more expensive than MMF ones due to the laser/detector technologies involved and tighter margins, but for reasonably priced original and 3rd-party modules there isn't so much difference any more (say 20-50%) for the most popular link rates (1-25 Gbit/s).
A rather obvious driver for cost is the need for increasing power demands over long distances - MMF is used for short distance <1 km, SMF for 5-100 km.
In combination with data rates in the multi-gigabit/s range that that power will need to be modulated with, longer distances and higher rates generally increase cost.
While 100BASE-FX works fine with a very cheap LED driver, 1000BASE-SX and 10GBASE-SR (MMF) require a (rather simple) VCSEL laser. 1000BASE-LX and 10GBASE-LR (SMF) need a Fabry-Pérot or even a DFB laser. Faster rates or longer ranges require externally modulated (EM) lasers. Each technology step increases cost. Those cost steps used to be quite high but have significantly dropped over the last decade due to economy of scale.