Price cutting or undercutting is not the only answer.
Are there any other ways you can reduce the cost to the client without you having to take a hit on the hourly rate. e.g. less frequent cleans (charged at the same price), extras that can be stripped out of the job making it quicker (thus cheaper but at same hrly rate), maybe only doing any awkward to reach windows every other clean, be honest with the client, this is not a case of reducing quality to be cheaper, I'm sure you will be able to think of others.
Just as a thought, and this may not be applicable in your case, but is a good pricing strategy that may prove useful in the future, if your faced with a price competition scenario. Consider "packaging pricing" e.g. quote the window clean service with say upvc deep clean, or a carpet clean or gutter clean etc. so you quote the client one price for a number of services which "hides" the price of the individual elements, its much easier to maintain a decent margin when doing this. I appreciate this may not be feasible in all cases but hopefully an idea worth some thought and that might be useful some day.
anyway I'm probably giving away a bit more than I should for free...
