However, Keynes (1936) explained that proper dynamic analysis inherently means that we have to consider expectations.
In this case the agent will be aware that parameters are indexed in some manner. Due to indexation, the term dq / dy can take significant values. Let q be indexed on national income growth Y. For many tax functions the indexation of parameters may take the form dLog[q] = dLog[Y] - as can be done for exemption and curvature of Tax[y]. If dLog[q] = dLog[Y] then
This again may reduce to the q / Y above. However, if we take expectations of the growth of national income, which means that the agent assumes that the other incomes do not remain constant, then:
Thus, next to knowledge about indexation, the agent will have expectations about the national income growth dLog[Y], and compare his own growth of income dLog[y] to this expectation. In terms of expectations, dq /dy does not vanish to zero. This is especially relevant when the parameter q gives exemption x that is a sizeable part of income.