This paper introduces a theoretical framework for studying the effectiveness of aid for recipient countries, receiving aid to finance their public investment. It contributes to the debate on the nexus between aid and economic growth and in particular on the conditionality of aid effects. Focusing on autonomous technology, government effort, corruption in the use of aid, fixed cost and efficiency in public investment, we can distinguish 4 levels of circumstances following which, the same aid flows may have very different effects. Given donor's rules, we determine conditions under which the foreign aid can generate economic growth in the long run for the recipient. We also discuss the conditions leading to an economic take-off and an escape from the poverty trap. Analyses of the dynamics of capital also give conditions for a convergence towards a middle income trap or endogenous fluctuations around it