As major localities from Chicago to California roll out new, higher minimum wages, one of the essential questions of the moves is their impact on the broader economy.

Clifford Hudson, CEO of Sonic, thinks that at the very least these wage hikes will show up on consumers' menus.

"I am not suggesting that there is not a challenge to move that kind of pricing, that kind of hourly wage pricing component, but these are proposed on a multi-year stage basis and there is no doubt that this is going to be inflationary as this relates to consumer product," Hudson said in his company's quarterly conference call Tuesday.

Hudson said that price hikes are simply a way to keep his franchises running profitably.

"It is going to be incumbent to fund us or them as that development occurs," he said. "To help them develop a pricing model et cetera that works for them in such a way that doesn't disrupt their business, their individual store or on a broader enterprise basis."

This isn't a radical assumption, economic theory has for years posited the link between wages and inflation, but the micro-level confirmation of the idea is worth noting.

Hudson goes on to compare the adjustment period for the minimum-wage hikes to the shift after the passage of the Affordable Care Act. He also addressed a major fear regarding the wage hikes. Here's Hudson (emphasis added):

We did the same thing with our operators as related to Affordable Care Act ... and we spent a long period of time showing how to utilize it, what to think about it from a pricing standpoint, how to engage their employees and certainly not to start cutting back employees time because we are concerned that it would negatively impact service and then in return their sales and profitability.

One of the biggest arguments against minimum-wage raises is the possibility that to cut costs, companies would either scale back employee hours or fire them altogether. No so much, according to Hudson.

While Sonic's moves may not be indicative of the broader impact of these moves, a food-service company with over 10,000 employees is a decent guide of what corporate America is thinking of the shift.