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5

It is basically a restatement of the first order condition - at an extrema (maxima or minima) of a well-behaved function its first derivative is equal to zero. If you are at the point of maximization, any deviation should either be of no benefit to you or violate some constraints. By continuity, it means that, unless you are constrained, at the optimal point ...


2

This first function is the ‘original’ CRRA function. $$u(c_t) = \frac{c_t^{1-\theta}-1}{1 - \theta}$$ The second function is monotonic transformation of the first function. Monotonic transformation of any utility function will still represent the same preferences (monotonic transformation preserves the ordering of preferences). $$u(c_t) = \frac{c_t^{1-\theta}...


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