Some brief but straightforward algebra.

The part of my post yesterday that dealt with deadweight loss from taxes was a little brief. Even if you go to the original article in Defining Ideas, you won’t find the actual computation. So here it is.

DWL is is proportional to t^2, where t is the tax rate. (t^2 means t-squared)

Original tax rate for our high-income Californian is 54.1%.

New tax rate for our high-income Californian is 56.7%.

This 2.6-percentage-point increase is a 4.8% increase. (2.6/54.1 = 0.048, which is 4.8%.)

So why doesn’t the DWL increase by just 4.8%? Because of the square relationship I referred to in the article and above.

Let original DWL be DWL1. Because of the proportionality property, we can lump all the other components of DWL into C. C is the same whether we are dealing with the original tax rate or the new higher tax rate.

So DWL1 = C*t1^2, where t1 is the original tax rate.

DWL2 = C*t2^2, where t2 is the new tax rate.

To get the percent increase in DWL, first divide DWL2 by DWL1.

DWL2/DWL1 = C*t2^2/C*t1^2 = t2^2/t1^2.

t1 = 0.541; t2 = 0.567.

So DWL2/DWL1 = 0.567^2/0.541^2

= 0.321/0.293

= 1.096.

Therefore DWL increases by 9.6%.  QED.