Having enjoyed time in the L-29 I can safely say that “low cost” and “jet aircraft” really don’t occur in the same sentence. This is even truer when developing a Personal Jet. While there is argument on the definition, some have termed the more recent VLJ (Very Light Jet), as one with a gross weight under 10,000 pounds. A Personal Jet has a gross weight under 5,500 lb, which is substantially smaller. The L-29, a war bird, isn’t really either one but since it’s less than 12,000# , doesn’t require a type rating.
Many start the design process searching for a low cost solution. The engine out of an L-29 is relatively inexpensive, assuming you can find one that you or anyone else would be willing to sit on top of. There is usually a good reason why the engine is cheap, thus the issue with finding parts, as well as someone qualified to work on it. Further, given the age of the technology, you can figure the thing needs an equivalent of a toilet bowl for a fuel delivery device (the whooshing sound is the fuel dollars being sucked down the drain). It makes the J-79 look efficient.
Then, you need to determine what you want the airplane to do. If you don’t care about range and only wish to bore holes in the sky around your local airport, then you might develop a decent sized airplane, but you’ll never go cross country in it. The rule of thumb for any jet aircraft, in order for it to have anything approaching a realistic range, it must have as a very minimum the same amount of fuel on board in pounds as the engine is rated for static thrust, in pounds also. The L-29 flys only two hours in cruise but anything more strenuous makes it a much shorter flight.
So, assuming you find a 1,200 pound thrust engine, (The L-29 Motorlet engine is 1,800 pounds of thrust) you will need to carry between 1,000 to 1,500 pounds of fuel. If you’re building a Personal Jet, then you may be lucky to achieve a thrust to weight ratio of .25 and while that’s OK, it’s not anything to brag about. A larger engine will require larger fuel tanks and a larger airframe as the design evolves into something ever larger. Then it weighs more and the engine that seemed plenty powerful isn’t so much. Small wonder there’s not too many of them around. The most recent personal jet effort was the ATG Javelin and it was a nice looking little F-18. Unfortunately they went bankrupt in 2008.
If you want a short history, look here . None are in existence but it indicates why VLJ’s, with their range and capability, are more commercially viable. And those aren’t anywhere near what I’d call inexpensive.