(Bloomberg) -- Buying a home should be getting easier formillennials amid sustained gains in U.S. hiring. Instead,increased demand for a scarce supply of starter homes is pushingprices beyond their grasp.

Prices for the least expensive previously owned homes —properties at 75 percent or less of the median — were up 10.7percent in August from a year earlier and now represent the onlyone of four price tiers to surpass the peak reached during thehousing bubble, according to a housing index from CoreLogic Inc.The August pace was 5.9 percent above its pre-recession highin October 2006.

Related: 5 reasons millennials aren't buying insurance fromlocal agents

The gap in the the growth rate between the most expensiveand cheapest homes is now the widest since 1983, with thelatter rising at a pace that's 5.2 percentage points higher thanthat of the top tier.

"You’ve got the front end of a big wave of first-time homebuyersbut the supply of affordable housing is not there to meet thatwave," said Sam Khater, CoreLogic's deputy chief economist. "Whatyou’re seeing in the housing market is a reflection of thepolarization of income. The builders are looking at it from thatperspective: 'If I have a choice of going up- and down-market, I’vegot to go up-market.'"

The starter-home supply crunch is worsening, adding to thepressure on prices. The bottom third of the market accountedfor 24.4 percent of listings in August, according to propertywebsite Zillow. That's down from 25.6 percent a year earlier.In Denver, where the shortage is extreme, the lowest tieraccounted for just 16 percent of inventory.

Copyright 2018 Bloomberg. All rightsreserved. This material may not be published, broadcast, rewritten,or redistributed.