Chapter 5: Pensions: Extended Model
5. Pensions: extended model All the assumptions made in Chapter 4 about the situation for lower middleaged individuals are retained in the following analysis. However, our assumption of a ﬁxed retirement age is now relaxed. In the present model the last two phases of the life cycle are collapsed into one, and the share of these periods to be used for retirement/leisure (␣) and work (1 Ϫ ␣) is left for each individual to decide. L2 is now the potential rather than the actual labour supply from individuals in the group of upper middle-aged and old. The actual labour supply from this group is (1 Ϫ ␣)L2. Whether individuals work full time or part time until retirement is not important for the analysis, but to simplify the discussion we assume that they work full time. To begin with, we assume that all individuals have the same life expectancy and are oﬀered the same pension scheme. We later extend the analysis to situations where individuals have a diﬀerent life expectancy and are oﬀered a choice of diﬀerent pension schemes. INDIVIDUAL OPTIMIZATION Apart from the changes mentioned above, the model from the previous chapter is retained. With variable retirement age, the budget constraint for an individual living during the periods t and t ϩ1 is C1,t ϩRt C2,t ϩ 1 ϩRt (wtϩ1 L2,tϩ1)␣2,tϩ1 ՅY1,t ϩRt Y2,tϩ1 (5.1) Here, Y2,tϩ1 represents the individual’s potential labour income during the second period. The...
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