I should say, first, that in going over my own practice essays I'm always a little embarassed by the know-it-all, matter-of-fact tone of voice. I apologize if you find that annoying and/or inappropriate to the format.
The question was this:
"Why and how should the welfare state provide insurance? What are the implications of changes in household composition for the provision of social insurance?" [Asked in the 2003 Exam]
Before discussing how the welfare state should supply insurance, it is worthwhile to specify the nature of social insurance more fully. The whole of society can be thought of as a risk portfolio, with individuals who earn more than they `cost' to society the positive investments and individuals who cost more to society than they earn the negative investments. One particular individual changes status over the life cycle: when he is employed he is a positive risk, when unemployed (during or after his career) he is a negative risk. Disabled people are more likely to be a net cost to society over the course of a lifetime than permanently healthy individuals, but the most important point is that there is randomness for each individual. Someone who expects to be a net benefit might nonetheless face a chance of debilitating illness, for example. Because each individual faces some risk, it can generally be thought of as an efficiency improvement to mitigate the risk by pooling it, effectively matching society's bad investments with offsetting good investments. Except in cases where individuals have a large endowment, foregoing some wealth (in the form of taxes) for the certainty that a random occurrence will not spell disaster is a welfare improvement.
The welfare state's insurance function extends to all of the situations in which individuals become a net cost to society. In practice, it is often difficult to distinguish between the state's redistributive function and its insurance function. Examples of how the welfare state provides insurance include workers' compensation when injury prevents earning, unemployment benefits, public pension programs that provide income to people beyond retirement, and more specifically, the disability insurance that is often included in the pension system. Programs that have a more obviously redistributive function (in addition to insurance) include transfers to families with little or no earnings and national health insurance and/or healthcare programs.
Like any insurance program, the welfare state suffers from asymmetric information. The most often considered case is adverse selection, when the existence of insurance itself changes society's portfolio of costs and benefits. More specifically, individuals will decrease their labor supply (and thus earnings) if they know that earnings will be replaced by state benefits. The fact that benefits are withdrawn means that there is a positive marginal income tax on earnings at the withdrawal point. Remedies to the resulting labor supply `distortion' take two general forms. First, there has been a move toward `negative' income taxes in the form of earnings subsidies like Working Families' Tax Credit in the UK and Earned Income Tax Credit in the US. Moffitt (2003) points out that such policies `convexify' individuals' budget sets since they have a phase-out period that varies the return to a marginal unit of labor supply, and thus recipients will position themselves in the middle of the benefit range so that they work as well as draw benefits. Blundell (2000) points out the possibility that employers could `harvest' the benefit by setting wages with the recipient's benefit schedule taken into account. There is also the possibility for collusion between employees and employers on documentation. The second remedy to adverse selection is to mandate a quantity limit on state benefits, as the 1996 Welfare Reform legislation did in the US. That legislation did indeed increase labor supply, though there is no evidence for the common argument that time limits in addition to work-training requirements result in increased human capital when the period of dependency is over, so that increase earnings take people out of the welfare system permanently. Additionally, the 1996 legislation moved individuals in both `directions' away from welfare; the increase in prison populations in the US is a manifestation of greater dependence (thus cost to society), not less as is the case with the move from welfare to work.
A change in household composition implies a change in society's risk portfolio. In Western Europe, the aging population means that the pool is inherently riskier since there are more net-cost individuals within it. Increased riskiness would generally mean that more insurance is justified, though current public debate in Europe centers around decreasing social insurance provision. One solution is to decrease the average benefit (if society is unwilling to undertake full replacement of pre-retirement earnings). Europe also suffers from adverse selection in that generous insurance provision provokes individuals to retire earlier and become net costs to society. Eliminating the option for early retirement would remedy that to an extent. In the other direction, increased immigration to Europe and North America improves society's risk portfolio since immigrants are generally working adults (or children whose earnings outlook taking school into account is a net positive). Immigration is the major factor that has improved the solvency of the US' social security system over the past ten years, and widespread discontent with the fact that asylum seekers in Europe receive benefits could be mitigated if they were allowed to work, transforming themselves from net costs to net benefits.
The state's insurance function is among its most important because in providing that public good it fulfills a function that individuals would not if they acted independently.
One thing I didn't say in the essay: the argument for social insurance does not rely only upon the idea that any individual might be struck by disaster during his lifetime, but also on the basic common humanity that gives each of us a responsibility for everyone else in our society. That is a little too good an idea for economists to grasp, for the most part.