There are two forms of "reduced size": file size, which can - sometimes - be reduced without losing quality; and resolution, which can't.
Files size can be reduced, if you load a file and save it as a different format - but the target format has to be a lossless compression method, which JPG most certainly isn't: every time you write a JPG file you throw away information and degrade quality significantly. Having said that, because JPG is a lossy compressed format anyway, it is quite possible that a lossless compression format file may actually be bigger than the JPG input.
Resolution can't be reduced without sacrificing quality because you have to throw away information to reduce the resolution. Think about it: to reduce an image from 4x4 to 2x2 means that each pixel in the target image is an amalgam of four pixels from the original:
1122 --->> 12
1122 34
3344
3344
And the information in the source cannot be regenerated from the single pixel in the result, regardless of what you see in NCIS, CSI, and Blade Runner! It can be approximated by reference to the surrounding pixels when you "enlarge" it, but once that info is gone, it's gone for good.