One of the New Mexico companies is Molina Healthcare. Here's what they have to say about themselves...
"Currently, Molina Healthcare arranges for the delivery of healthcare services or offers health information management solutions for nearly 4.3 million individuals and families who receive their care through Medicaid, Medicare and other government funded programs in 15 states."
Source: About Molina | Molina Healthcare
If a New Mexico consumer's income is low enough, they'll probably see Molina at the top of the list of available carriers after applying on the exchange? I suspect that every state will have at least one or two Medicaid companies included in the handful of Exchange insurers.
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I think Allen may have hit on an important point. Here in Arizona, we have private carriers participating in Medicaid and CHIP. They are mostly small HMO's, and many of them were started by hospitals. The only big name carrier is United Healthcare. They run one called Arizona Physicians IPA, which comes under United Healthcare Community Plan, a separate entity under the United Healthcare Group umbrella. To consumers, there is name recognition there, but it is still a small HMO-type plan, with a narrow network. Perhaps this is what the big name carriers may do in the Exchange?