By Jilian Mincer and Lisa Baertlein (Reuters) - Like millions of Americans, Darnel Ware needs to save money, even if it's 40 cents on a bag of flour. He searches for those savings during his daily visits to the Family Dollar Store near his home in Fraser, Michigan, sometimes stopping by as many as 10 times a week "if there are things I need," said the 51-year-old home care provider. "I buy a lot of everything; merchandise and food products." He said he typically spends about $30 a trip on items like the soft drinks, paper cups and cookies he bought on a recent afternoon at the small store in a strip mall alongside other discount retailers and small factories five miles from Detroit. The small but frequent purchases of low-income customers such as Ware add up: Family Dollar Stores,, which operates about 8,200 stores in mainly urban sections of the U.S., is the target of an $9 billion cash takeover offer from rival Dollar General and an $8.5 billion cash and stock offer from Dollar Tree. Both competitors are betting not only on the health of the deep discount retail sector but also on the intractability of poverty in America. Mid-market retailers like Wal-Mart Stores Inc, Macy's Inc and J.C. Penney Company Inc have been struggling in recent years as consumers have been slow to return to their pre-recession, freer spending ways. On Wednesday, Target said it was cutting its full-year earnings and slashing prices. But the popularity of so-called dollar stores is growing. Shopping by the 46.5 million Americans living below the poverty line poor helped boost the annual U.S. market for deep discount stores by 45.7 percent to $48.2 billion between 2008 and 2013, according to London-based market researcher Euromonitor International. The firm projects the sector to grow to $57 billion in 2018. The U.S. Census sets the poverty line at $24,000 a year or less for a family of four. Such forecasts help explain the battle over Family Dollar, the number-two deep discount chain. Market leader Dollar General Corp on Monday made its $78.50 a share bid, which Family Dollar rejected on Thursday, citing antitrust concerns. In July, the third-ranked chain, Dollar Tree Inc, bid $74.50 a share. Family Dollar has said it prefers Dollar Tree's lower offer. The deep discounters' reliance on poor Americans, who made up 15 percent of the U.S. population in 2012, compared with 12.5 percent in 2007, has been validated by investors. From 2000 to now, as the poverty rate rose 11.3 percent to 15 percent, Family Dollar's stock price rose by about 300 percent. Against that backdrop, the bidding over Family Dollar, said Kurt Jetta, CEO of retail analyst Tabs Group, reflects an "acceptance that there will be a sizable and perhaps growing low-income population that makes dollar stores an ongoing opportunity." Not all analysts agree that dollar stores are poised for continued growth. Roger Davidson, a former grocery executive at Wal-Mart, Whole Foods Market Inc and Supervalu, said dollar stores face increasing competition from other discounters, including Walmart itself, which is opening smaller neighborhood stores. "Consolidation is now the only path to growth in sales and earnings," he said. LIMITED SIZE, LIMITED SAVINGS Deep discount dollar stores have been around for decades, but have grown by about 10,000 to about 24,500 stores in the last decade. Combined sales of the big three - Family Dollar, Dollar Tree and Dollar General - have grown to $35 billion. Dollar stores offer their customers low prices, but not necessarily the best value. For example, Huggies diapers this week were selling in a Family Dollar store for 27 cents a diaper in an 80-diaper pack. But at Walmart, shoppers could pay 17 cents a diaper if they purchased the larger 120-diaper pack. The poor often don't have the funds needed to buy in bulk, experts said. Nor do they necessarily have the wherewithal to travel to often remote big-box stores like Target and Walmart. The dollar stores play the role of "fill in" retailers, said Joan Storms, a retail analyst at Wedbush Securities. Their customers try to do most of their shopping at places like Walmart when they get paid or receive benefits, she said, but they pick up necessities and other items at the deep discount stores. The expiration of unemployment benefits for millions of jobless Americans and a reduction in food stamp payments last year also helped the deep discounters, analysts said. With less cash on hand to make regular "big shops" at places like Walmart, these consumers are more likely to turn to the dollar stores to buy a few items at a time to feed their families. With wages stagnant, even middle-class consumers follow this shopping pattern, giving dollar stores a source of revenue not wholly dependent on the lowest-income Americans. In real dollars, the median U.S. wage has declined since 1999, when it was $56,080 compared with $51,017 in 2012. Joseph Garrett, 58, a welfare-fraud investigator for New York City, was among the shoppers at a Dollar Tree Deals location in Manhattan's Harlem neighborhood recently. He said he does most of his grocery shopping elsewhere but uses the dollar store when he's looking for a bargain. The store was crowded with families shopping for groceries and school supplies. Backpacks were prominently displayed but absent the brand names of merchandise typically found at Target or Walmart. Most of the canned food also was private label rather than well-known national brands. "Everything is going up," said Garrett. "So you've got to save what you can." (Additional reporting by Anjali Athavaley in New York and Peter Suciu in Detroit; Editing by Eric Effron and John Pickering)