Prices have cooled in the once red-hot housing market, but competition is heating up between two generations in seemingly perpetual conflict. Millennials entering their prime homebuying years and baby boomers — many of whom are nearing retirement age — are vying for the same homes. Not all baby boomers are looking for smaller properties to spend their retirement years, and some millennials are encroaching on space in the suburbs, where their older peers would typically downsize. But most boomers have a key advantage: substantial equity from previous home purchases and higher incomes, which help them avoid the growing costs of a long-term mortgage. “Boomers are not downsizing and Millennials — first-time buyers in particular — are buying later in life. This puts both generations of buyers in head-to-head competition for similarly sized properties,” Jessica Lautz, at the National Association of Realtors.