Shape-preserving computation in economic growth models

We point out the shape characteristics — monotonicity and concavity — of the value functions of optimal economic growth problems. We introduce the concept of shape preservation in approximating the value functions. We also present a shape-preserving algorithm to compute the solutions of continuous-state optimal economic growth problems. Numerical results show that shape-preserving interpolation methods are superior to others with less-sophisticated interpolation in the sense of smaller approximation errors.