A model of social insurance with variable retirement

Models are studied, in which ability to supply labour is affected by a random variable (health) not observable by government. When ill-health strikes, the consumer must retire, but he may choose to retire in any case. Optimal social insurance policies are found for one-period, two- period, and continuous-time models. It is found that, under plausible conditions, at the optimums consumers are indifferent whether to work or not, but do work when able. Insurance contributions decrease with age, and insurance benefits increase with age of retirement. It is desirable to prevent private saving. Some comments on the U.S. Social Security system are added.