1. The use of the logarithmic utility function has been widespread in the literature to analyze public pension schemes, cf. Feldstein (1985), Verbon (1986, 1987), Veall (1986), Smith (1982). The particular form of the utility function chosen implies some restrictions on the possible results. Some of these restrictions will be relaxed in chapter 7.
2. Maximizing eq. (3.2) under the budget restriction comes down to maximizing L = logcy + plog{(w-cy)r}. Differentiating with respect to cy produces as the first-order condition, cy = w/(1+p).
3. In the present case, if the individual happens to live for two periods, his budget restriction reads, cy +co /r = ½(3-p)w. Thus the function to be maximized equals logcy + plog{½(3-p)wr-cyr}. Differentiating with respect to cy produces (1+p)cy = ½(3-p)w, which is equal to the expression produced in the text.
4. For an early discussion, see Arrow (1968) and Pauly (1968).
5. For an analysis applied to this particular case of pension schemes, see Diamond, Helms and Mirrlees (1980).