Gunners manager Arsene Wenger has often been criticised for his reluctance to spend money during transfer periods, although this time he has recruited Santi Cazorla, Lukas Podolski and Olivier Giroud.
Hill-Wood backs the Frenchman in his stance not to overspend on players but concedes that Arsenal have limited funds.
"Arsene has money to spend but there's a limit," he is quoted as saying by The Sun. "We can't spend £50m on one player. At a certain level, we can't compete.
"I don't think Stan Kroenke is going to put the sort of dollars that Roman Abramovich or Sheikh Mansour are putting into Chelsea or Manchester City.
"That's not the way he thinks clubs should be run. Luckily, Arsene understands that. He got an economics degree from Strasbourg University so he's certainly no fool. He knows how a club should be run."
Wenger, 62, was appointed the Arsenal manager in 1996.