On optimal growth models when the discount factor is near 1 or equal to 1

When Is 0.999... Equal to 1?

where Hj := ∑ j i=1(1/ i) are the harmonic numbers. This question in the title is beyond the scope of a mathematics journal. There are, however, mathematical papers proving identities that were discovered because numerical computation pointed to a simple answer. The anecdotal evidence then accumulates in a misleading manner: when the conjectured identity is false we are less likely ever to know...

Some Notes On "When is 0.999... equal to 1?"

In joint work Robin Pemantle and I (2004) consider a doubly infinite sum which is not equal to 1, as first suspected, but evaluates to a sum of products of values of the zeta function. Subsequently, I report on this project.

Inputs Accumulation Or Productivity: Which Factor Is The Leading Contributor To Economic Growth In Iran?

Stochastic Optimal Growth When the Discount Rate Vanishes

It has been shown that long-run optimality of the limit of discounted optima when the discount rate vanishes is implied by a condition on the value function of the optimal program. We suggest a new method to verify this condition in the context of one-sector optimal growth. The idea should be more widely applicable.

Integer Nc 1 Is Equal to Boolean Nc 1

We show that the product of n 3 3 matrices of n-bit integers can be computed in P -uniform FNC1. Since this problem is complete [BOC92] for formul in f+; g on n-bit integers, we conclude that \algebraic NC1" on integers is equal to the usual Boolean notion of NC1 functions.