Maggie,
Have you managed to trace Michael in the 1871 census yet? I had a quick look but the only Michael Murphy I found in 1871 in Roxburghshire was a three year old. Lead me to wonder if your Michael was Irish and living in Ireland.

(but I just as easily may have missed him

)
The curiosity would get the better of me and I would probably purchase the child's birth or death certificate to see what it says about Michael's occupation, or perhaps even better still, the marriage certificate of a sibling - if one married around the similar time, Michael is more likely to have the same occupation.
Curious about this one as there are quite a lot of differing ideas.