Their highest earner is Hazard at 200k a week and other key first team members like Cesc earn 150k a week. I doubt he'll be paid similar or more to that which is why the word substantial pay cut has been mentioned in the article.
http://www.theguardian.com/football/2014/sep/16/eden-hazard-new-record-chelsea-contract
http://www.thetimes.co.uk/tto/sport/football/clubs/chelsea/article4208321.ece
So if they pay Falcao above or around 100k a week and we pay Welbeck that much then your's is not a valid argument.
There is a reason why they didn't go for Shaw because they weren't willing to pay his wages. Chelsea have become effective in salaries and transfers now.
Here's some quotes from Mourinho himself:
“They would have been saying, ‘How is it possible I play 200 games for this club, won this and that, yet a 19-year-old comes here and gets more money than I get?’
“It would’ve killed immediately our balance and we couldn’t allow that. I don’t criticise another club for paying it. They can pay what they want. I don’t have any comment about it. But for my club we can say it would be very negative for us, especially when we can say Felipe is much less expensive. Sometimes you have to make decisions.”