How much does an air data module cost?
For airliners, a lot of money, in the tens of thousands or more. Thales Aerospace is one of the manufacturers of AOA's for transport and military aircraft -- the word "cheap" does not exist in their vocabulary and "inexpensive" is a matter of opinion. For GA aircraft they are significantly less expensive, about US\$2000 or less. For aircraft with other than standard airworthiness certificates (experimental, homebuilt, etc.) the cost falls well under US\$1000. Sometimes manufacturers don't call them AOA's, and instead refer to them as "Lift Reserve System." For a general idea of the cost of GA AOA systems, check Aircraft Spruce and search for "AOA".