⁷Strictly speaking, this is not true, because j_t^k will now differ from the value associated with the initial problem. For purposes of analyzing problems of this kind (announced future changes in parameters) we will neglect the effects of the path of j_t^k on the equations of motion. Except under extreme circumstances, this should not change the qualitative results of the analysis, and doing anything else would require a very intricate analysis. This treatment is admittedly a bit inconsistent, since in the case under consideration it is precisely the change in j_t^k that motivates the firm to start adjusting its capital stock before the productivity change comes into effect; effectively, we are taking into account the effect of j_t^k on the level of λ before period t + n while neglecting its effects on λ’s dynamics during this interval. C‘est la vie.