: Why is a violin so hard to amplify? Why are electric violins so expensive compared to an electric guitar, why is a guitar pickup so relatively easy and cheap to produce compared to an electric violin's pickup?

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At the time of writing this answer, there are roughly two ranges of electric violins available on the market. Inexpensive instruments in the 0 - 0 USD range, and better quality instruments starting around 0 USD and ranging up into the thousands.

The build and physics of the violin create some technical issues that an electric guitar does not have, causing more expense in the manufacture.

Some things that affect the price of manufacture and selling:

Pickup choice and manufacturing
Tone reproduction considerations
Market demand

One of the main issues with amplifying the violin is that it is difficult to use a magnetic pickup due to the arch of the strings over the fingerboard. Guitar strings being on a flat plane are more amenable to a magnetic coil, where you can get an even volume in the magnetic field. Magnetic coil pickups are inexpensive to make compared to other options.

Because of the arched configuration, Piezoelectric pickups and micro-phonic pickups are better suited. To get a better tone and other electronic considerations, the violin will often have active (battery powered) circuitry, increasing the cost.

Tone is also another issue. While electric guitars may get some tone variation with different wood and construction, the majority of sound is coming from the strings and magnetic coils. Electric guitars over the years have developed an accepted sound, where people are not expecting them to sound like louder acoustic guitars.

Violins do not have that history, so consumers are looking for the electric version of a violin to resemble the acoustic version, which again adds the expense of adding tone filtering circuitry or using specifically designed pickup systems.

Market rarity is also a driving factor for the price. The electric violins have a very small number of units sold each year compared to the electric guitar. Recouping the cost of development, manufacturing, distributing, and marketing requires a higher percentage return per unit sold.

Companies like Ned Steinberger and Yamaha have spent much research and development to design systems that create or emulate the tonal qualities of the violin. Other companies like Wood Violins focus more on the specialty of the product, and market specifically to the higher end consumer.

I have seen the low end instruments turn over quite rapidly. A manufacturer will produce an inexpensive version for a brief time, then disappear from the market. Usually the sound quality of the inexpensive Piezo pickup is quite harsh and brittle sounding and lacks the resonance and warmth of the acoustic instrument.

EDIT: Thinking about it, I should also add that in the electric violin market besides making instruments for performance and amplified playing, manufacturers are making instruments for "silent" playing, which includes a headphone amplifier in the instrument itself, also increasing production costs.

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In additin to Alphonso's quality answer, take a look: top-end acoustic guitars run at most a few thousand, other than some specialty customs which still end at maybe 000 to 000 USD. That same 000 will get you a decent pro-quality violin, but excellent instruments run into many hundreds of thousands of dollars. There's a lot more work involved in making a playable violin- bridge height and shape, fingerboard is not flat or fretted, etc.

The better "electric" stringed instruments, as AB wrote, are designed to produce a tone vaguely similar to the acoustics, whereas electric guitars (solidbodies at least) are little more than pitch generators. The tone is controlled with a slew of footpedals/switches/followers. I'm not trying to start a flame war here, so those of you who love your particular Fender or Ibanez solidbody just stay calm :-)