Raising the minimum wage doesn't happen in a vacuum, according to new research on Chipotle.

When Chipotle Mexican Grill Inc. raised its minimum wage in San Francisco, it raised its prices proportionately, according to William Blair, a global investment banking and management firm, which issued a report on Tuesday to its investors.

As part of the company's weekly survey, it examined 10 Chipotle markets across the country and each location's relative price changes. In half of the markets — San Francisco, Denver, Minneapolis, Chicago and Orlando, Fla., — food prices increased by about 4 percent and were limited to beef.

In San Francisco, however, where the city has increased the minimum wage by 14 percent, all of the Chipotles in the area saw an "across-the-board" price increase. The hike included the chicken, pork, tofu and vegetarian prices, all of which increased 10 percent. The cost of steak and barbacoa rose 14 percent.

The jump comes after the minimum wage rose from $10.74 an hour to $12.25 on May 1, one wage increase on the path toward San Francisco's 2018 goal of a $15 minimum wage.

Mark Perry, a scholar at the American Enterprise Institute and economics professor at University of Michigan's Flint campus, named the parallel price increase after a popular adage, calling the reciprocity a "TANSTAAFMWH — there ain't no such thing as a free minimum wage hike."

"And the 10-14 percent price increases at Chipotles in San Francisco are just the new math problem now facing the restaurant chain's customers, who'll now be paying about $1 extra for each burrito bowl," he said.

Perry made clear that complications over minimum wage "is not really a political problem, it's a math problem."

That is because when restaurants pay their workers more, they have to make subsequent changes in other areas of their business model to compensate for the money that they are giving employees.

"There simply isn't any magic pot of money that lets employers pay higher wages just because the government says so, without making adjustments elsewhere like cutting workers' hours, reducing their non-cash fringe benefits, and/or passing the higher wages along to consumers in the form of higher prices," said David French, vice president of the National Retail Federation.

Fast-food restaurants spend roughly 30 percent of their revenue on wages, 30 percent on ingredients and 40 percent on everything else, including rent, advertising and capital costs. Profit typically is about 5 percent of a restaurant's revenue.

To adjust for higher wages, employers can choose to reduce the amount of capital they invest in their business, which translates to fewer jobs. Likewise, if employers are encouraged to distribute their labor more effectively, that leads to fewer jobs because as productivity increases, the number of workers can decrease. Or restaurants could simply raise prices. However, if customers must spend now more on one thing, they will have less to spend on another, which can cause job losses.

With a $15 minimum wage, the average fast-food restaurant would have to raise prices 38 percent from current amounts, found James Shark of the Heritage Foundation. This means that a McDonald's Big Mac meal would increase from $5.69 to $7.82, Chipotle's steak burrito bowl from $6.65 to $9.14, Burger King's Whopper from $6.15 to $8.46 and Subway's chicken breast footlong from $6.50 to $8.94.