It depends on what is around the city as a whole and what you have access to work....
The plain desert tile is crap... BUT.... if your city is on a river you likely have plenty of Flood plains.
Flood plains farmed with Civil Service = 4 food Which will support the citizen farming the Flood Plain and 1 more.
The question is what to do with your "bonus" citizen from the flood plain yield.
You can put a farm on the desert tile to make the citizen self sustaining (after fertilizer), Which will allow for a larger city and those "hidden" bonuses that Wodan mentioned.
Also remember that any tile improvement is going to contribute to your tile improvement maintenance cost...
To support a city that works all 36 Tiles and has
ALL the
BASIC specialist buildings with their specialist slots filled (4 Engineers, 4 Merchants, 4 Scientists) you need a city of 48 Citizens, which is 96 Food. From 36 tiles.
You need to average 2 2/3 food per tile to achieve this. Now almost no one places cities 6 hexes apart to achieve the 36 tile yield unless they are going REALLY tall. Plus 48 citizen cities take a long time to get going.
So here are your options:
- Farm = 1 extra citizen = 1 beaker + a bit more gold in trade. + Unhappiness + Tile improvement cost
- Trading Post = 1-3 Gold & 0-1 Science depending on technology / social policies.
- GP Improvement = Varies
- Nothing / Use citizen as a Specialist (with free slot):
Engineer = 2 hammers + GP Points
Merchant = 2 gold + GP Points
Scientist = 3 beakers + GP Points
You have to decide how you are going to place GP tile improvements, which for the most part means Academies not Customs Houses or Manufactories.
You can place your Academies on Grasslands which will make them self sustaining but you loose 1 food for not having the grassland farmed.
If you place your Academies on a desert you loose 2 food because it takes a citizen to work the tile and no food is produced.
My conclusion on desert tiles is that if there are NO specialist slots to be filled in the city and I can't build a building to hold one and I have ALL other tiles worked then I will build a Trading Post and work it. I don't put GP tile improvements on Desert tiles anymore. I use grasslands or hills but not plains.
Finally remember that you now have a citizen working a desert tile and this citizen does contribute to your empires over all unhappiness. You probably should have checked "Avoid Growth" in this city before that citizen appeared to allow for more citizens in other cities with better tiles or free specialist slots for the the same level of unhappiness.