New research has found that U.S. retailers charge nearly identical prices across stores, despite wide variation in customer income and local demographics.

And by holding prices steady across locations, retailers significantly increase the prices paid by poorer households relative to the rich as a percentage of total income.

The uniform pricing also ends up costing firms nearly 7 percent of profits on average because they lose out on higher prices they could charge the wealthy and lower volume for lower-income consumers.

In a working paper filed with the National Bureau of Economic Research, economists Stefano DellaVigna of UC Berkeley and Matthew Gentzkow of Stanford University reported their findings.

For the food stores studied, customers of stores in the lowest income decile pay about 0.7 percent higher prices than they would under flexible prices, while customers of stores in the top income decile pay roughly 9 percent lower prices, according to the research.

Gentzkow, who's been a professor at Stanford for two years, underscored that classical economics predicts that companies adjust prices in response to surges or contractions in demand or income. That is, firms take advantage of people who want a particular good more than others and exploit populations with higher income levels.

The researchers studied data from tens of thousands of stores in the Nielsen Retailer Scanner to extract information on weekly prices from firms while using Consumer Panel data from the University of Chicago to study customer income trends. The team focused on three store types: 9,415 food stores, 9,977 drugstores and 3,288 mass merchandise stores.

"We view this sharp contrast between within- and between-chain results as one of our key findings. It suggests that chains are either varying their prices for too little across stores in response to income, or varying their prices far too much at the overall chain level," wrote the economists in their paper.

Their research found an increase in per capita income of $10,000 for localities — equivalent to a move from the 30th to the 75th percentile — is associated with an increase in price of just 0.72 percent.

"The thing that makes it surprising to us is that those stores typically have very different consumers," Gentzkow told CNBC in an interview. "Econ 101 would tell you that inequality in incomes is going to be offset because poor people are going to end up paying lower prices."

The paper doesn't go into much on the reasons why retailers are charging the same everywhere, but it's likely that access to Amazon and Google pricing comparison tools on a consumer's smartphone is playing a role.

DellaVigna and Gentzkow suggest it may have more to do with managers at chain stores being reluctant to adjust prices for their location. "Change may impose additional costs, as managers may not be well incentivized to make the change, while fearing the cost if a change backfires," wrote the team.

But stores may be reluctant to give that power to individual locations with Amazon available to ship anywhere easily at a lower price.

"I think it's plausible that if one of these stores said now were going to start varying the prices in their stores it would come at managerial costs," Gentzkow told CNBC. Plus "people might be upset if they realize you were change the price in one store in not another."

Another important effect is that floating prices help mitigate the negative impact of local economic shocks; even when the population experiences a hit to income, reductions in local retail prices would naturally offset the damage. However, fixed prices as observed by the researchers diminish this helpful response.