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The fish are generally considered a bonus. It's the vegetables that produce the value.
I imagine most of the documented data is in the commercial realm, not the home AP gardener.
Any home-grown food tends to be more expensive than store-bought food if you calculate in labor costs. Especially at the start. Once a garden is set up and you're down to maintenance, it can compete with store-bought, and it can be far cheaper than organic store-bought. We've run general costs for our AP and our Square Foot gardens, and our payback (compared to regular store-bought food) is about 2-3 years. Compared to organic store-bought food it's about 1 year.
If you've never needed to condition your soil and if you haven't had to buy/rent a tiller to prep the soil or needed to put in lots of labor preparing the beds, you've been very blessed! The soil prep and labor are the bigger expenses in building traditional gardens, while in AP, the expenses are the containers, beds, and equipment. Once done, though, the cost in either is nominal & primarily labor. Our AP system was a little less expensive than our Square-Foot garden to start, but more labor/knowledge intensive.
Re: fish vs veggies, for us, like Bob, veggies are our "main dish" and fish are the "side dish." You will find some people are fish people, though. Regardless, as you calculate the cost of the fish, you have to deduct the value of the veggies. If you don't do that, you'll find your fish are very expensive! :)
In commercial production, they are able to raise a 1.5 lb tilapia for under $0.50 a pound. That normally takes a great deal of economy of scale and scope to accomplish. However for them to insure profitability they must always compare their costs of production to the lowest wholesale value.
For the home however, as you suggest your comparison point is the cost to buy tilapia at a local grocery store vs. growing it yourself. Your calculations would also likely NOT include labor costs for that would make your goals nearly impossible to meet. For example, on average tilapia have a 33% filet ratio. So a production cost of $0.50/lb would translate into a filet cost of $1.50/lb not including processing dollars. This is where one of the often undiscussed advantages of aquaponics comes in, economy of scope.
Economy of scope is where the average total cost of production decreases as a result of increasing the number of different goods produced. If you look at the cost of tilapia alone it will be difficult to achieve your ends on the family scale. However when E of Scope is added in, that means the value to your family of the fruits and vegetables you grow as well as fish, then there is the real possibility that overall individual production costs can be brought down to a reasonable number on the family scale.
This post is getting kind of long and I must run. Lots of really knowledgeable folks in this group who can add additional and different insights to your excellent question.
Cheers
Regarding cost of production. High US costs of production is why most tilapia are farmed overseas and then shipped in. Only in the few farms serving the live markets in Phoenix, LA and back east have been really able to survive. However the recent revelations on how Asian producers are driving their costs down by feeding their fish wastes may change things. Hopefully this will create a new focus on the need for US production facilitated by the economies of scope within aquaponic production helping to decrease US. costs. If you have not read the article from Boomberg last week on Asian production, just click the link here:
From Bloomberg:
Asian Seafood Raised on Pig Feces Approved for U.S. Consumers
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