When it comes to straight razors I’ve seen everything from a $10 “Made in China” straight razor to ones that cost well over $500. Quality is of great concern. However, an increase in price doesn’t necessarily mean an increase in shaving quality, although this can often be the case.
With straight razors the quality of the steel that goes into making the blade is of great importance. Typically, you don’t want to buy anything made in China or Pakistan as these use a very low-quality steel. If you(or someone else) is able to put an edge on it, the edge is not going to last long. Why go through all the trouble of honing a razor only to be able to use it once before it needs to be re-honed?
On the other extreme, super expensive razors often are more expensive due to the added “bells and whistles” such as scales made out of mammoth ivory or other exotic materials. Other straight razors might be more expensive due to their rarity and age. With these razors you are paying more for it because of something other than it’s ability to shave well.
The short answer is that a cheap razor will work, but you don’t want to go too cheap. Often times you can find people who pick up old straight razors at antique stores and refurbish them. Depending on the person who restores them and hones them these razors can be really good to shave with. If you opt to buy a used razor that’s been restored then this will probably run you around $50 at the low end.
The other option you have is to buy a new straight razor. A lot of places you can find new straight razors that have been professionally honed for around $100. These might not look as fancy, but they’ll give you a great shave. In my books $100 is still pretty cheap for a straight razor.
In conclusion, yes a cheap straight razor will work as long as it’s made out of quality steel and is been honed by a professional. However, don’t waste your money on super cheap straight razors that are made in China or Pakistan.