If you have at least three luxuries, marketplaces also make citizens happier. As I recall, the Civilopedia details how much extra happiness the marketplace gives for each extra luxury. As I recall, it works precisely like this: Let M stand for marketplace, and accordingly M(x) indicate the amount of extra contentedness one gets from x luxuries via the marketplace. Then,
M(1)=0
M(2)=0
M(3)=1
M(4)=2 (one for the 3rd luxury and one on top of that for the 4th luxury)
M(5)=4 (two for the 5th luxury)
M(6)=6
M(7)=9 (three for the 7th luxury)
M(8)=12
If I recall correctly, you can derive this from the happy faces on the city screen. The first happy face on the same line as the luxury indicates increased happiness/contentedness from the luxury itself. All other happy faces indicate extra happiness/contentedness gained from the marketplace. So, with a marketplace, the number of happy faces H seen next to the xth luxury goes
H(1)=1
H(2)=1
H(3)=2
H(4)=2
H(5)=3
H(6)=3
H(7)=4
H(8)=4
So, M(x)=M(x-1)+H(x)-1, with M(1)=0. Thus,
M(2)=M(1)+H(2)-1=0+1-1=0
M(3)=M(2)+H(3)-1=0+2-1=1
M(4)=M(3)+H(4)-1=1+2-1=2
M(5)=M(4)+H(5)-1=2+3-1=4
M(6)=M(5)+H(6)-1=4+3-1=6
M(7)=M(6)+H(7)-1=6+4-1=9
M(8)=M(7)+H(8)-1=9+4-1=12