I'm skeptical you could hit that sort of range for anywhere near $10K. Forget the electronics, you need an engine powerful enough to lift a few hundred pounds for that distance. Unless you want it detected immediately by early warning radar you need it to fly at a low altitude, like a hundred feet or less. Unless you want it to take forever and be susceptible to infantry with small arms it needs to be traveling fast, in the hundreds of miles an hour. That's simply not possible with an electric system with today's technology, and a rocket engine won't provide the endurance or efficiency you need. That leaves a jet engine or pistol engine. Plus, flying at that speed and altitude means you need an effective autopilot system that uses terrain-following radar. You'll also need some nice guidance packages that allow the shooter to set multiple waypoints, so the missile doesn't have to just fly a direct course. And a 50 lb payload of high explosive just isn't that helpful. There aren't a ton of targets where you only need 50lb of explosives to defeat them, that are also going to stay in the same exact GPS position long enough for your missile to travel a few hundred miles. So you'll want a different terminal guidance method, either some sort of radar sensor or infrared.
I don't think you could get an engine capable of getting you hundreds of miles at that speed and altitude, much less the sensors and guidance system.
A lot of the cost in defense contracts is paying for guaranteed domestic supply in the event of a war. If you buy COTS parts and outsource your machining I see $10k as very achievable, the majority of that being metal and explosives. The electronics are nearly trivial, but some of the IR tracking is embargoed and hard to get outside the US.
Hydro-formed "Escopette"-style valveless pulsejet?
They run as efficiently as a turbojet (w.r.t. specific fuel consumption), and Mach 0.7 is way beyond your "couple hundred miles an hour".
It will be burnt up by the time it runs out of fuel, though.
For a good one it has to be hydro-formed out of seamless pipe, which is likely hot-stretched (like wire drawing, but using an induction heating coil in place of the die, and independently controlling the feed-rate and the pull-rate) in advance to retain consistent wall thickness in the engine despite being cross-section after hydro-forming. Also probably incremental hydro-forming with grain-structure-fixing re-heating between stages.
The hard part is just that most of the work is in making the hydro-forming dies/tools, not then using them to cheaply produce more engines.
Fascinating, haven't heard of this. Some googling suggested there is some active research in this area, and at least some active use by hobbyists and by the military in target drones. Seems like a promising angle for a cheaper cruise missile, at least on the engine front.
You're going to have serious troubles implementing a cruise missile with a range in the hundreds of miles with a solid rocket engine. While most cruise missiles use a solid booster to launch the missile and get it up to the proper speed and altitude, you need an engine to sustain flight. You also need a propulsion mechanism that allows you to control thrust, which a solid engine wouldn't. To my knowledge there is no cruise missile in existence that uses just a solid rocket engine. In theory you could get into the hundreds of miles with just a booster if you use it to get up to a significant altitude and glide the rest of the way. But that largely defeats the purpose of a cruise missile: traveling at low altitude to avoid enemy radar.
Of course, you can definitely make a BALLISTIC missile with a couple hundred mile range using a solid rocket engine, and probably for fairly cheap (especially if you don't particularly care about accuracy)
Also: Scud missiles are comparable, made outside western cost inflation, and still ~$1M each. So I'm guessing you can't get a ballistic missile anywhere near $10k (at least, not one that isn't more likely to kill its owner).
I think they can bring the price down a bit, but not to $10K, even with a smaller size payload. Also I should mention the V1 was barely accurate enough to target a city the size of London. Not that adding modern GPS guidance would necessarily cost that much, of course.
So you use a solid rocket booster or maybe make it air-launched and have it glide to the target? So that is definitely a thing, an example I can think of is the US small diameter bomb (https://en.wikipedia.org/wiki/GBU-53/B_StormBreaker ) or the JSOW (https://en.wikipedia.org/wiki/AGM-154_Joint_Standoff_Weapon ). Though those aren't in the "hundreds of miles" that OP originally proposed, they are in the 50-75 mile range. Those also technically aren't cruise missiles, and don't have the primary advantage of a cruise missile: the ability to travel at low altitudes to evade enemy radars and air defenses.
That said, you could probably make a glide bomb for pretty cheap. The two examples I gave above are in the hundreds of thousands, but I bet if you sacrificed some of the accuracy and payload, and you were really optimizing for cost, you could get that into the tens of thousands
I don't think you could get an engine capable of getting you hundreds of miles at that speed and altitude, much less the sensors and guidance system.