Cities produce in Traders and barbarians of Catan
When it says you will receive only 1 resource for the city, it is talking about the initial resources that you start the game with, NOT the resources produced by the city whenever the adjacent numbers are rolled. 

From the rules under Setup:


  Set up as outlined in the Catan base Settlers game, except that your second settlement is replaced by a city. You still only receive 1 resource for each terrain hex adjacent to your city.


Note that this is specifically talking about the setup; in normal Catan you start the game with 1 resource for each terrain hex adjacent to your second settlement; this rule is just clarifying that you still only start with 1 per hex even though it is a city instead of a settlement. The city acts the same as any other normal city throughout the game.