Stopping times in economic development planning: some modelling issues

Abstract

The process of capital accumulation per available worker can be shown to solve a stochastic differential equation of the diffusion type on which the process of economic development depends. Interpreting development as a learning process we are able to reformulate the conflict between the flow of social benefits and costs attached to it as a race between the average time rate of increase at time t of a process to be sought and the flow rate of social costs f expected to hold at time t, both as viewed at time s. Associated with this race there exists an optimal payoff u that solves the generalized Stefan problem

A, a = -/, in G, Px ® dt—a.s. u = < j >, on SG, Pz < S) dt—a.s. where G = (y\4 > U,y) < u(t,y) < co) and 8G = (y\4 > = "). Here we are interested in characterizing / and < j >, so that u can be represented in a meaningful way as u(s, x) = sup Ej , ∗w

with respect to all admissible stoping times if corresponding to the process satisfying the condition that at time s assumes the state x based on the microeconomic considerations, we derive a subjective rate of discount which takes into account various kinds of uncertainty and maturity establishing thereby clear links between the development and the learning process.