Growth in the Robinson-Solow-Srinivasan model: Undiscounted optimal policy with a strictly concave welfare function

In a special case of a model due to Robinson, Solow and Srinivasan, we characterize the optimal policy function (OPF) for undiscounted optimal growth with a strictly concave felicity function. This characterization is based on an equivalence of optimal and minimum value-loss programs that allows an extension of the principal results of dynamic programming. We establish monotonicity properties of the OPF, and obtain sharper characterizations when restrictions on the marginal rate of transformation are supplemented by sufficient conditions on the “degree of concavity” of the felicity function. We show that important similarities and intriguing differences emerge between the linear and strictly concave cases as the marginal rate of transformation moves through its range of possible values.