9Strictly speaking, this is not true, because 
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 
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 
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 
on the level of 
before period 
while neglecting its effects on 
’s dynamics during this interval. C‘est la
vie.