Frederich the Great raised three `light infantry regiments` (or `Freiregimenter`) in 1786, each of 10 companies. This name was a throw-back to the 7 Years` War, when skirmishing in the Prussian army was the task of the Frei-Korps, which were disbanded when that conflict ended.
In 1787, Friedrich Wilhelm II used these units, some Grenadier Battalions and some garrison battalions to form 20 independent battalions, called `Fuesilier` Battalions, each of 4 companies. These were the regiments 33, 35-49 and 51-55. They were trained to fight in extended order and were armed with shorter, smoothbore, muskets than musketier regiments. NCOs and the sharpshooters (there were 10 sharpshooters in each company from 1787 - 1808) were armed with shorter, rifled weapons, sighted up to 300 paces.
(We will now descend into an interminable debate as to how long a pace in the Prussian army of 1787 was).
I have found nothing to say that Fusilier battalions were any cheaper - or dearer - than musketiers.
In the campaign of 1806, the lack of sufficient light infantry in the Prussian army was keenly felt.
In the post-1806 reorganization of the Prussian army, the independent fusilier units were disbanded and each line infantry regiment was now made up of two musketier and one fusilier battalion.