Interest rate cuts, now expected to happen this summer, won't solve the housing affordability crisis — in fact, prices may rise when rates come down.

Why it matters: High mortgage rates have pushed up the cost of financing a home, and constrained the supply — some lawmakers are even urging Federal Reserve chair Jerome Powell to lower rates to improve housing affordability.

• But, but, but: It's not as simple as that. For one thing, many regions of the U.S. still have a housing shortage. That was amplified during the pandemic.

The big picture: This is the least affordable housing market for first-time buyers in more than four decades.

• The monthly cost of a typical mortgage for a house rose to 40% of a buyer's household income last year, the highest rate since the 1980s, per Capital Economics. That crashed demand from first-time buyers.

Zoom in: Mortgage rates have come down from their big highs last year, but the 30-year briefly touched 7% last week and is now 6.64% on average. It's still pretty high!

• At that rate, the typical monthly payment on a median home is about $2,600, per Redfin. Back in 2021, it hovered below $1,700.
• One result: homeownership rates for young adults — those under 35 — dropped a smidge in the fourth quarter, per a note from Thomas Ryan, U.S. property economist at Capital Economics.

But rates are only part of the story. There are also home prices. Even with rates at historically high levels, prices are still rising.

• The median home sale price is around $361,000, up 5% from the year-earlier, per Redfin's latest housing market update.

The big question: What exactly happens to prices as mortgage rates head down? Will they stay around where they are — or shoot up even more in the face of increased demand?

• Recall the housing market of 2021. Rates were at rock-bottom levels, and multiple bidders for homes pushed prices up by double-digit percentages.

Supply is the driving factor in the first-time home buyer space, writes Ryan, of Capital Economics.

• There aren't a lot of houses out there to buy — a lot of people just recently moved, after all. (Many homeowners aren't selling because they don't want to lose their low mortgage rates.)
• And, yes, if rates come down, then supply would come up. "Any drop in mortgage rates would help loosen up the housing market. It would encourage people who are homeowners to sell and buy again," says Daryl Fairweather, Redfin's chief economist.
• But with supply and demand both shooting up in equal amounts, "prices would remain high," Fairweather says.

Worth noting: In markets that are less supply constrained — think areas where new construction is happening — homebuyers will benefit from falling rates because prices are more likely to fall, Fairweather says.

• Still, sellers who don't need to sell won't be eager to make big price cuts. And as long as the jobless rate stays low, there won't be a ton of desperate sellers.

The bottom line: Mortgage rates are just one of many issues keeping homes out of reach for first-time buyers. Lowering rates could help first-time buyers — but maybe not as much as you'd think.