Question

What were Rothschild & Stiglitz(1976) research problem, data, results, and their conclusions or lessons.

Answer 1

• the research problem of rothschild&stiglitz(1976) was on the topic "Eqiulibrium in competitive insurance markets:an essay on the economics of imperfect information"
• in this research they shown that in competitive insurance market,under asymmetric information,poolin contracts cannot exist in equilibrium,firms make zero profit,and under some circumstances equilibrium doesn't exist.
• the basic model; 1) demand for insurance contract : An individual purchases an insurance contract so as to alter his pattern of income across states of nature. Let W1 denote his income if there is no accident and W2 his income if an accident occurs; the expected utility theorem states that under relatively mild assumptions his preferences for income in these two states of nature are described by a function of the form, (1) fV(p, W1, W2) = (1 - p)U(WI) + pU(W2), where U( ) represents the utility of money income2 and p the probability of an accident. Individual demands may be derived from (1). A contract a is worth V(p, a) = V(p, W - aI, W - d + a2).
• Supply of Insurance Contracts: assume that companies are risk-neutral, that they are concerned only with expected profits, so that contract a when sold to an individual who has a probability of incurring an accident of p, is worth (2) 7r(p, a) = (1 -p)ai -pa2 = al -p(ai + a2)- Even if firms are not expected profit maximizers, on a well-organized competitive market they are likely to behave as if they maximized
• they discussed Information about Accident Probabilities,Equilibrium with Identical Customers,Welfare Economics of Equilibrium,robustness
• Rothschild and Stiglitz introduced the important decision theory concept of the mean-preserving spread, which leads to a partial ordering of probability distributions according to degree of risk.
• 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 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.