Buying a home should be getting easier for millennials amid sustained gains in U.S. hiring. Instead, increased demand for a scarce supply of starter homes is pushing prices beyond their grasp. 

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

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

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

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