How many catnip fields are worth the catnips they require?
Solution 1:
Catnip fields give infinite catnip. Therefor more fields is better. At least, that is my philosophy. I have 47 fields right now, and the next costs 2057. During spring I have no farmers and +1.5 catnip. During summer and autumn I need 1 or 2 farmers, depending on the amount of catnip I have to survive winter. During winter, I have most of the time negative catnip production, but I have a buffer (that was a tip from a previous question) so that does not matter very much. My buffer is now 3500, after a warm summer.
It's not mathematical my answer, but I try to upgrade my field when my buffer is more than twice as much as the price of the new field. In that way I still can survive winter and have as least as kittens possible on the farm.
Solution 2:
If you want to calculate if a new Catnip field is worth the investment use:
Price/ProductionRate = Seconds Till Profit
Example, if a new field costs 10K
10000/0.63 = 15873 seconds
Convert seconds to hours
15873/3600 = 4.4 Hours
A field that costs 10K will start paying you back in about 4.4 hours
Of course the modifiers and seasons change this payback rate, generally the payoff time will be much better, this simple math can help provide a baseline.