The number of homes for sale in Phoenix and around the U.S. is shrinking, putting a squeeze on prices that is costing buyers more, according to Zillow.

In Phoenix, inventory for all three home levels Zillow tracks are below last year’s level, and there were a total of 18,062 homes for sale in the region, according to the March statistics.

The cheapest tier of homes, those entry-level buyers would find themselves in, have seen inventory levels fall close to 24 percent over last year.

This situation…