Equilibrium price dynamics in an overlapping-generations exchange economy

Abstract

We present a continuous time overlapping generations model for an endowment Arrow-Debreu economy with an age-structured population. For an economy with a balanced growth path, we prove that Arrow-Debreu equilibrium prices exist, and their dynamic properties are age-dependent. Our model allows for an explicit dependence of prices on critical age-specific endowment parameters. We show that, if endowments are distributed earlier than some critical age, then speculative bubbles for prices do exist.

Demographic-economic equilibria when the age at motherhood is endogenous

“…The properties of this solution in frameworks with a realistic demography were initially studied by Arthur and McNicoll (1978) and Lee (1980), while recent advances have been proposed by Bommier and Lee (2003) and Brito and Dilão (2010). The main difference here hinges on the fact that the demographic growth rate is endogenous.…”

“…Assumption lim →0  0 () = +∞ excludes this corner solution. Finally, the concavity of human wealth with respect to the age at motherhood is sufficient for excluding multiple local optima to problem (P) as it implies a unique solution to equation (10).…”

Continuous-Time Overlapping Generations Models

“…Due to the fair pricing of annuities, the increase in the discount rate implied by the uncertain longevity is canceled out by the increase in the annuities return (Davis, 1981). Consequently, the optimal consumption profile, given by (22), is proportional to the sum of the initial wealth and the human wealth in nominal terms.…”

“…Second, past prices, and more precisely those defined over the interval utility and endowments distributed at birth only: e (s, t) = e (t) if s = t, and zero otherwise. Then, using (22), the initial consumption of individuals born at time t does not depend on expectations and can be written as:…”

“…Moreover, if the endowment grows at a constant rate over the life span, using (22), the initial consumption of individual born at time t is given by:…”