This study revisits the overtaking criterion in economics, in a framework without the usual convex

structures that are often used to prove existence and convergence of optimal paths. We show that the

supermodular structure plays a decisive role in shaping the behavior of the economy. We further prove

that, as the discount factor approaches 1, optimal paths under standard discounting criteria converge

in the product topology to an optimal path under the overtaking criterion. This supports the view

that the overtaking criterion can be interpreted as a limiting case of discounting criteria with discount

factor equal to 1. Our arguments rely on turnpike properties, one for the overtaking problem and one

for the discounted problems.

Keywords: Overtaking criteria; Multiple discounting; Turnpike theory; Time preference; Dynamic

Programming

JEL Classification: C61, D15, D90, O41