Live from the Right-Wing Economists' Self-Made Fresh Incidence Hell: One more time, morons: will you at least try to understand it if presented this way?
With a fixed required after-tax rate of return r...
A proportional tax t can either be administered as a fraction of factor cost or a fraction of market price...
When a proportional tax t is administered as a fraction of factor cost, so that the after-tax rate of return plus the tax rate times the after-tax rate of return equals market price, then:
(1) $ TR_{initial} = krt $
(2) $ ΔTR_{static} = krΔt = TR_{initial}\left(\frac{Δt}{t}\right) $
When a proportional tax t is administered as a fraction of market price, so that market price minus the tax rate times the pretax rate of return equals factor cost, then:
(3) $ TR_{initial} = \frac{krt}{1-t} $
(4) $ ΔTR_{static} = \left(\frac{kr}{1-t} + \frac{krt}{(1-t)^2}\right)Δt $
(5) $ ΔTR_{static} = \frac{krΔt}{(1-t)^2} $
(6) $ ΔTR_{static} = \left(\frac{1}{1-t}\right)TR_{initial}\left(\frac{Δt}{t}\right) $
$ ΔTR_{static} $ is transferred from taxes to wages. Mankiw calculates the change in tax revenue via (1)-(2) and the change in wages via (3)-(6). That is where his factor (1-t) comes from: that is how the static gain to wages can be bigger than the loss to tax revenue even though both are the exact same area in the static calculation: they are both (capital stock) x (change in tax wedge between pretax and after-tax returns).
Draw the diagram:
Calculate the area.
One does not simply find that production and preference parameters just drop out of incidence calculations:
