The petitioner grows sugar cane and beets. It takes the former a whole year to grow while the latter grows in six and a half months. The only available market for the two crops is the sugar company which determines their prices. 

Questions

What type of zakat should be paid on sugar cane and beets—zakat on crops or zakat on money?
Should zakat be paid on the total sum of money received from their sale or should any expenses be deducted from it?

If the case is as mentioned in the question, the implemented opinion for fatwa is that no zakat is paid on sugar cane and beets, but only on the proceeds from their sale regardless of the buyer, provided:

The sum reaches the minimum amount upon which zakat is due [nisab] which is the equivalent value of 85 grams of 21 carat gold.

One lunar year passes upon its possession.

Only debts owed to others, and not expenses, are deducted from the sum upon which zakat is due.

Allah Almighty knows best.