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Recall that in the RCK model households choose their consumption and savings so as to maximise current and future utility (i.e. future generations). Then the objective function is given by $$ U = \int_{0}^{\infty} u[c(t)]e^{nt}e^{-\rho t}dt$$ The RCK model assumes the functional form of utility $$ u[c(t)] = \frac{c(t)^{1-\theta}-1}{1 - \theta} $$ Note that ...


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If I understand correctly you are not interested just in saving but to mathematical approach to normative questions in general. This approach is actually quite common in the whole literature that uses normative economics. For example, the question of redistribution is predominantly normative question, because as opposed to questions of social efficiency, ...


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No it is not. The benchmark Ramsey model allows for positive and negative investment. Treating the case of non-negative (or "irreversible" investment) is considered an extension. See Barro & Sala-i-Martin (2004). Economic growth (2nd ed) Appendix 2B for a short discussion and Section 5.1.2 pp 242-247 for an Endogenous growth model with ...


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