No, its his problem as the main contractor - the contract rates will have already been priced through the Bill of quants.
But its tricky - you as the plumber do not want to earn any less, but he seems to want a better deal. The fact he has asked for this, implies that he may have another estimate, in which case he thinks there are savings to be made.
Hence, if your profit margin is too high, then you will lose the job. The motive of the main contractor may also be associated with cash flow - priced jobs are paid in stages, so he can make you wait for money. Day rate is paid weekly or monthly at most.
Its too dodgy these days to wait for any money, and I would be inclined to communicate this - say your happy with the way things are. If this is not good enough, then ask about the payments and when they will be made - if this is in stages, and you need the work - then put in a price based on your labour + 10% + retention%, and leave an apprentice on the job. The gov will pay you for the apprentice as well.
You may also be subject to retentions, so allow for this in your margin.