Introduction to Modern Economic Growth Warm glow preferences assume that parents derive utility from (the warm glow of) their bequest, rather than the utility or the consumption of their offspring This class of preferences turn out to constitute another very tractable alternative to the neoclassical growth and the baseline overlapping generations models It has some clear parallels to the canonical overlapping generations model of last section, since it will also lead to equilibrium dynamics very similar to that of the Solow growth model Given the importance of this class of preferences in many applied growth models, it is useful to review them briefly These preferences will also be used in the next chapter and again in Chapter 22 Suppose that the production side of the economy is given by the standard neoclassical production function, satisfying Assumptions and We write this in per capita form as f (k) The economy is populated by a continuum of individuals of measure Each individual lives for two periods, childhood and adulthood In second period of his life, each individual begets an offspring, works and then his life comes to an end For simplicity, let us assume that there is no consumption in childhood (or that this is incorporated in the parent’s consumption) There are no new households, so population is constant at Each individual supplies unit of labor inelastically during is adulthood Let us assume that preferences of individual (i, t), who reaches adulthood at time t, are as follows (9.21) log (ci (t)) + β log (bi (t)) , where ci (t) denotes the consumption of this individual and bi (t) is bequest to his offspring Log preferences are assumed to simplify the analysis (see Exercise ??) The offspring starts the following period with the bequest, rents this out as capital to firms, supplies labor, begets his own offspring, and makes consumption and bequests decisions We also assume that capital fully depreciates after use This formulation implies that the maximization problem of a typical individual can be written as (9.22) max log (ci (t)) + β log (bi (t)) , ci (t),bi (t) 437