How much would it cost to privately own and operate a MiG-21?

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This is one of those things where if you have to ask the price you cannot afford it. If I had to state a value I’d benchmark it at around $3.5M-$4M (plus operating costs and maintenance).
As it happens, I

recently started working with a company that trains foreign Air Force pilots to fly in fighter jets. They have some of the largest privately owned fleets of high performance jet and turbo-prop (aka “Warbird”) aircraft on earth.

A student with no past flight experience (who already speaks fluent English) has to go through an Initial Flight Screening (in something like a Cessna 172), Basic Flight Training (in a propeller trainer like a Tucano), and Advanced Jet Training (in a jet trainer like an L-39) before they are even allowed to begin training in a “real fighter” like a MiG-21.
Start to end the curriculum takes ~30 months. Assuming you pass all the classes the first time (the washout rate is ~30%) and you have a couple hundred buddies who also want to get trained they can probably get the cost down to just over ~$2.5M per student.
Out of curiosity, I asked a sales guy what it would cost to buy a fully updated and flightworthy L-39 (because a lot of military aircraft are not sold in flightworthy condition). He said a starting price would likely be around ~$300k depending on the features required by the customer.
So that’s ~$3M (and 2.5 years of full-time training) just to get trained on and aquire an L-39. The L-39 is not nearly as powerful as a MiG-21; which would cost more to purchase. Just like used cars, the actual dollar amount would vary wildly based on things like the aircraft’s condition, the seller’s urgency to sell, the sentimental attachment, etc.
Then you’ll have to pay for jet fuel. Just like a high performance car guzzles gas your high performance jet will have an unquenchable thirst for jet fuel.
You’ll also need a hanger to keep your new jet in, and a certified mechanic on call to help keep it operational. Oh did I mention how it’s almost impossible to get Russian jet fighter parts in the West? You’ll probably have to reverse engineer quite a lot of the parts you need to fix/replace. That means adding significant engineering and fabrication costs to the already high maintenance and operational costs.
As I mentioned at the beginning; if you have to ask the price you cannot afford it.