Need Help With a A Simple Query That's Not So Simple

I think this should be easy, but I can't seem to put the SQL together
correctly and would appreciate any help. (I'm using Pg 8.4 in CentOS
5.5, if that matters.)

I have a table of Farms and a table of crops in a 1:M relationship of
Farms : Crops. There are lots of different crops to choose form but for
now I'm only interested in two crops; corn and soybeans. Some farms grow
only corn and some grow only soybeans, and some grow both. What I'd like
to know is, which Farms and how many are growing only corn, which and
how many are growing soybeans and which and how many are growing both? I
can easily get all the corn growers with:

SELECT a.*
FROM farms a
JOIN crops b
ON a.farm_id=b.farm_id
WHERE crop_cd='0041'

I can do the same with soybeans (crop_cd= '0081') and then I could
subtract the sum of these from the total of all farms that grow either
corn or soybeans to get the number of farms growing both, but having to
do all those queries sounds very time consuming and inefficient. Is
there a better way to get the farm counts or data by categories like
farms growing only corn, farms growing only soybeans, farms growing
both? I'm also interested in possibly expanding to a general case where
I could select more than two crops. and get counts of the permutations.

Here's a sketch of the relevant pieces of the data base.

*Tables:*
farms crops
======= =======
farm_id bigint (pkey) crop_id (pkey)
type farm_id foreign key to farms
size crop_cd 0041 = corn 0081=soybeans
... year
...

Any help would be much appreciated.

TIA,

- Bill Thoen