How does Jpeg encoding affect the final file size of 24BPP RGB and 8BPP grayscale image? The reason I'd like to know this is because of a file size problem. I am trying to reduce an image's file size from converting it from TIFF to JPEG. A user challenge me that he notice a RGB TIFF image is three times the size of the same image but in grayscale TIFF version, but the post-convert grayscale version of the JPEG image is almost the same size as the RGB JPEG version. 

He insist that a 8BPP grayscale jpeg should have ~1/3 of the size of the 24BPP RGB jpeg. 

Then I have been told by some technical adviser afterward that JPEG will ever only exist in the form of 24BPP file, and that the grayscale jpg images I found online are all lying in their image meta data saying bit depth is 8. But so far I haven't found any proof online that confirm nor deny that claim.

At this point I have no idea if my conversion method is flawed and inflated the file size, or the fact that the so call "8BPP JPEG that takes only 1/3 of the file size" doesn't exist from the beginning. 

Is there any documentation regarding this issues online?
Take a standard R-G-B coded 24-bit image. First, suppose that all channels are coded independently. If by chance, R, G, and B are equal, each one will be converted to the same JPEG file with size $s$. 

But such an image would be visually grayscale. The corresponding JPEG compression of the grayscale would be about 3 times smaller (taking headers, etc. into account).

But in JPEG (and most image compression formats), color channels are not treated independently. They are first decorrelated into one luminance (L) and two chrominance images (U, V). If all channels were equal, ie if the image were grayscale as above, Y is the natural grayscale, U and V are zero. The latter two are compressed with almost zero-size, while the luminance is just JPEG compressed. 

So, an all gray 24-bit image and the corresponding 8-bit grayscale are JPEG compressed almost the same. In natural images, RGB channels slightly differ:



So if you convert them to YUV (luminance-chrominance), you get: 



Typically, the luminance one remains almost 8-bit in dynamics, while the two chrominance ones  are flatter, on 4-5 bits. The two latter can be compressed more heavily, as they can be downsampled (they look more low-pass) and amplitude-quantized.

Hence, to the first order, the most of the information is concentrated on the luminance part. So, if the channels do not differ too much, compressing the RGB or the grayscale with JPEG, for sufficiently high rations, is about the same.