Some temporary however simple algebra.
The a part of my publish yesterday that handled deadweight loss from taxes was somewhat temporary. Even in the event you go to the unique article in Defining Concepts, you received’t discover the precise computation. So right here it’s.
DWL is is proportional to t^2, the place t is the tax charge. (t^2 means t-squared)
Authentic tax charge for our high-income Californian is 54.1%.
New tax charge for our high-income Californian is 56.7%.
This 2.6-percentage-point enhance is a 4.8% enhance. (2.6/54.1 = 0.048, which is 4.8%.)
So why doesn’t the DWL enhance by simply 4.8%? Due to the sq. relationship I referred to within the article and above.
Let unique DWL be DWL1. Due to the proportionality property, we will lump all the opposite parts of DWL into C. C is similar whether or not we’re coping with the unique tax charge or the brand new greater tax charge.
So DWL1 = C*t1^2, the place t1 is the unique tax charge.
DWL2 = C*t2^2, the place t2 is the brand new tax charge.
To get the p.c enhance 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
Due to this fact DWL will increase by 9.6%. QED.