y. For the Bentham function:
Generally the dynamic marginal is lower than the static marginal. In fact, when tax parameters are indexed in a certain way, then the tax can have the same growth rate as income, and then the dynamic marginal rate equals the average tax rate. This holds for individuals and for the macro data if all individuals are on a balanced growth path. Let the balanced growth rate be bgr:
(13.4)
The following is a small example of how a dynamic marginal rate can equal a normal average. Let exemption be $10000, and let the statutory marginal rate thereafter be 50%. Someone earning $50000 pays the tax of $20000, on average 40%. Let all incomes grow 5%, and exemption be indexed on national income. Then exemption becomes $10500, income $52500, tax $21000, again 40%. Thus on the (dynamic) “marginal dollar” this person doesn’t pay 50% but 40%.
For the Bentham tax function we can derive a simple expression for individual growth. We are most interested in expected developments. Let personal income grow by rate