Chapter 4: Pensions: Basic Model
In Chapter 1 we mentioned three principal devices for resource pooling: the family, the market and the state. How these devices work with respect to the problem of providing consumption opportunities during old age is discussed in this chapter. We focus, in particular, on the ways and means by which the state may improve the solutions provided by private arrangements. A simple model is used to clarify the basic mechanisms of old age protection. We assume that there are just four phases of life – childhood, lower middle-age, upper middle-age, and old age – each covering some 20 years. We now disregard problems related to uncertainty and assume that everyone lives through all phases of life. We assume, moreover, that earnings are given exogenously. These assumptions are relaxed in later chapters. THE ATOMISTIC MARKET To keep the analysis simple we now disregard childhood and assume that an individual’s life cycle consists of just three periods. Since everyone is assumed to live exactly three periods, population growth is determined by the increase in new entrants at the age of 20. Let this growth rate in period t be denoted gt. As before, Ni,t, iϭ1, 2, 3, denotes the number of individuals of age i during period t. From now on we set N1,t ϭ1. By assumption, individuals work during the two ﬁrst periods of the life cycle – as lower middle-aged with earnings Y1 and upper middle-aged with earnings Y2. Exogenous Rate of Interest For the moment we assume that consumption...
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