A quote by Henry Ford:
“Competition is the keen cutting edge of business, always shaving away at costs.”
I think the general meaning is as follows: competition makes companies reduce their costs of/for running a business.
But what is the exact meaning of “shaving away at costs”?
shaving costs = reducing them in small increments.
Where competition exists within a business market, businesses undercut their rivals (cut costs so they are charging slightly less than their rival does) to try to draw the customer towards their product or service rather than to the opposition’s product. The opposition responds by cutting their costs too - so that now their prices are slightly lower than the first business. The first business would respond again by dropping prices… thus the businesses ‘shave their costs’.