It is impossible to give a cost without knowing the size and the types of
materiel you want to use but we have just constructed a covered patio and i
can tell you the costs we had. ( My husband is a building contractor so this
is for the materiels only and he and I did all the labor). Our patio
consists of a 12 x 10 concrete slab, The uprights to hold the roof are
treated 4x4 and there are 8 in total. The bands are constructed of 2 x 6
rought ceder and run length wise (6 peices of lumber to make a band at the
front , center and back. The cover is made of 2x2 rough cedar peices spaced
3 inchs apart. In addition there is a post and rail fence made of 2x2 rough
cedar around 3 sides. We recon on materiels we spent in the region of $1400
dollars ( that includes the concrete slab). It is certanly not cheap as the
price of lumber is high partically here in the Texas Panhandle and this can
vary with location. It would have been a little cheaper to have constructed
it all out of treated lumber and cost alone prevented us from making it all
out of rough cedar. If my husband was charging a customer for this it would
have been in the region of $2000. The cost of labor in your area may also
differ.
I'm not sure if this is of any help but that is our experience, and now it
is finished we just love it as it is a shady retreat to chill out in and
plan our next projects.