This paper analyzes optimal paths in a one-sector growth model when the technology is not convex. In such a case, we prove that optimal paths converge to the upper steady state iff the initial wealth is above a critical level. Then, we first show that, thanks to debt and/or R&D, the poverty trap may be avoided. Second, we introduce a distortion: corruption that mostly has dramatic consequences on growth, but may have a beneficial effect if it is not high and if it improves productivity (incentive effect).