Surely this is a paper that everyone has seen at some point, so I’ll keep this post brief, but I did want to point out the great opening line which somehow I’d missed before. Rothschild and Stiglitz show that in a competitive insurance market where only buyers know the probability of their house burning down, the existence of people with different risks can lead to the nonexistence of insurance in equilibrium. The problem is that high-risk people impose an externality on low-risk people. The low-risk people should have cheap insurance, if only we could separate the two. But if an insurance company offers a contract which perfectly insures low-risks, then the zero-profit condition of competitive equilibrium means that these contracts make no profit when houses burn down with the low probability p. If such a contract exists, and you are high-risk (probability p’>p), then you’ll also want to buy the low-risk contract. Under some distributions of types, there can be separating equilibria, but these equilibria only partially insure the low-risk types. Expanding the number of types (“smoothing” to a continuum of agents) only makes equilibria less likely to occur, and simple modifications of the model do not save us. Even worse, under the same informational restrictions, a social planner not bound by the zero-profit condition can sometimes offer a set of contracts that is a strict Pareto improvement.
Since many books and a number of Nobel prizes have followed this paper, I suppose it’s no surprise to the modern economist that adverse selection can limit the market’s ability to reach first best. Check out the first line of this paper, however: “Economic theorists traditionally banish discussion of information to footnotes. Serious consideration of costs of communication, imperfect knowledge, and the like would, it is believed, complicate without informing.” And this in 1976! Since essentially the opposite is true of micro theory today, let it not be said that modern economics has been stagnant.
http://homes.chass.utoronto.ca/~mturner/ec2030/readings/Rothschild_Stiglitz_QJE1976.pdf
A Fine Theorem 
[…] K. Bryan, who is a PhD student in the MEDS program at Northwestern Kellogg, has written a nice summary of the Rothschild-Stiglitz “separating equilibrium model at his blog, which is called “A Fine Theorem”; see https://afinetheorem.wordpress.com/2010/12/03/equilibrium-in-competitive-insurance-markets-m-rothschi…. […]