Elon Musk said home prices will crater - and it prompted a sharp rebuttal from the CEO of housing giant Redfin

• Elon Musk said this week that home prices will tumble soon, following those of commercial real estate.
• Redfin's CEO responded, saying the loss of demand for commercial real estate is driving up demand for residential real estate.

Billionaire Elon Musk said Monday that house prices are set to plunge, and that they would follow the path of commercial real estate which is already "melting down fast."

However, Redfin CEO Glenn Kelman countered his take in a tweet of his own on Tuesday:

"But the loss in demand for commercial real estate is what's driving demand for residential real estate. People who work from home need more space at home. Sales volume is down because inventory is down. Today, home prices increased for a second straight month."

The remote-work boom and waning need for office space has led to many vacant commercial real estate buildings, which Musk's initially referred to.

Kelman, though, said that home prices are up as Americans search for more space to work from home.

On Tuesday, the S&P CoreLogic Case-Shiller National Home Price Index climbed 0.4% in March compared with February, marking the second straight monthly gain.

On an annual basis, home prices are down 2.2%, Case-Shiller data shows, with the West Coast seeing declines and the East Coast seeing price increases.

The outlook for home prices is hazy. Zillow has said that home prices have already bottomed, while Moody's and Fannie Mae still expect prices to drop further.

To be sure, the Tesla chief's concerns aren't unique. Other economists and commentators have raised similar alarms about the Federal Reserve's rapid interest rate hikes, and the pressure those place on the property sector.

Higher interest rates make borrowing more costly, making homes less affordable as mortgage payments go up.