Fierce competition for lower-end homes, thanks to a combination of low mortgage rates and record low supply, is driving prices higher.

• That can make it difficult to figure out whether it's cheaper, on a monthly basis, to own or rent.

• The answer is: It depends where you are.

  The nation's top 50 metropolitan areas are almost evenly split on the rent versus own calculation. It is cheaper to own in 24 markets and cheaper to rent in 26, according to new research from CJ Patrick Co., based on data from First American Data Tree.

  It looked at median rent prices, median home sale prices, and taxes and insurance. For the buy calculation, it only considered homes in the lowest quarter of the price scale, which would typically be purchased by first-time buyers. It assumed a 30-year fixed-rate mortgage at 5% interest with a 5% down payment.

  Of the top 50 markets, 14 showed very little difference between the monthly costs of renting and owning a home. Cities in the Midwest and South favored buying.

  Memphis, Tennessee, for example, had a monthly rental cost of $914, which was nearly twice as much as the $462 cost of owning a home (again, a home in the 25th percentile of price ranges).

  Birmingham, Alabama; Pittsburgh; Jacksonville, Florida; Oklahoma City; St. Louis; Tampa, Florida; Atlanta; Miami; and New Orleans all showed monthly home payments that were significantly cheaper than the median monthly rent.

  On the other end of the spectrum, cities in the West dominated the list of markets where it is cheaper to rent than own a home. That is because home prices in the West are some of the highest in the nation.

  California claimed the top four spots, with San Jose, Los Angeles, San Francisco and San Diego favoring renting costs over owning.

  Rounding out the top 10 were Salt Lake City; Portland, Oregon; Providence, Rhode Island; Seattle; Sacramento, California; and Denver (New York City was almost the same as Denver).

  "In the most expensive cities, it's hard to find anywhere to live," said Rick Sharga, CEO of CJ Patrick. "This is especially true in California, where San Jose, Los Angeles and San Francisco have three of the lowest homeownership rates among the top 50 metros and also have three of the lowest apartment vacancy rates. That housing scarcity can't help but continue to drive prices up for both buyers and renters."

  Not surprisingly, in the areas where it is cheaper to own a home than rent, the homeownership rate is higher than the national average.

  The national homeownership rate in the third quarter of last year was 64.8%, according to the U.S. Census. In the areas favoring buyers, it was 65.6%. Apartment vacancies in those areas were also higher than the national average. Los Angeles has a homeownership rate below 50%, while Nashville, Tennessee's rate is around 72%.

  Home prices, especially on the lower end, are unlikely to weaken, given the critical shortage of those homes that are for sale. If more inventory does come on the market, rental vacancies will rise and rent prices will go down.

  "I'm inclined to think that the gap may actually increase over time, as many local governments are under pressure to change zoning laws to accommodate multifamily housing. If that happens, it's logical to assume that homeownership rates could fall even further in many of these cities," said Sharga.

  UPDATED FRI, FEB 7 2020 4:43 PM EST   Diana Olick @DIANAOLICK@DIANAOLICKCNBC@IN/DIANAOLICK