Net Present Value Laffer Curve

Everyone knows the Laffer Curve; it's so simple we can explain it on the back of a napkin.  If we tax at 0%, then government revenues will be zero.  If we tax at 100%, government revenues will be zero.  And we know from last year that if we tax at ~30%, government revenues are positive.  So we have some "curve" connecting those three points.  Such a curve could be displayed graphically below (click to enlarge).  It looks like the top of the curve is 60%.  If we have a tax rate of 30%, and increase our taxes to 31%, then we might think we're on the left hand side of the demand curve.  This article shows why that's wrong thinking.

But taxes have an effect on GDP growth!  We might write down some mapping between the two (click to enlarge):

 Then, if we only look at constant-tax policies, we have a few GDP growth paths depending on our policy (click to enlarge):

 Then we can write the different revenue paths as well, the product of taxes and GDP (click to enlarge):

 Then we have the net present value laffer curve, where the peak is at 30%. Even though if we raised taxes in this period, our tax revenue would increase, it is more than harmed by the deficits to future growth (click to enlarge).

Rule of thumb: the relevant concept is not the Laffer Curve, it's the net present value Laffer Curve.  The NPV Laffer Curve has a much lower peak than the Laffer Curve.