> I'm just wondering if it is even
>possible for the supply and demand curves to be shaped shaped in such a
>way that the Laffer curve does not apply to some market.
Since you asked...
Take an income tax and the very standard constant elasticity formulations for
demand and supply (they are called constant elasticity because a one percent
increase in the wage always causes the same percentage increase in labor supply
(b) and the same percentage decrease in labor demand (a) no matter what the
wage is):
Ld=D w^(-a)
Ls=S [w(1-t)]^b
which implies
w=(Ld/D)^(-1/a)=(Ls/S)^(1/b) (1-t)^(-1)
If I did my algebra correctly with Ld=Ls=L
L^(1/b+1/a)=D^(1/a)S^(1/b) (1-t)
or
L=[D^(1/a)S^(1/b) (1-t)]^(ba/(a+b))
so
Revenue=twL=C t (1-t)^[b(a-1)/(b+a)] (C a constant function of D and S)
If a is less than 1 (a one percent increase in the wage causes less than a one
percent decline in labor demand) and you take the limit as t goes to 1 you get
revenue going to infinity - - not exactly a Laffer curve. With an elasticity of
demand less than 1 wages rise more than enough to compensate for the reduction
in labor supply caused by the tax increase.
With these demand and supply equations a little calculus yields the result
that the tax rate that maximizes revenue is
t (rev. max)=(a+b)/[a(1+b)]
which is greater than 1 (which is impossible the way the tax rate has been
defined) if a is less than 1. It asymptotes to 1/(1+b) as minus the demand
elasticity (a) goes to infinity and 1/a as supply elasticity ( b) goes to
infinity (and therefore zero as both approach infinity). From what I remember,
typical estimates of a are (a lot) less than 1, but some come in somewhat above
it. Typical estimates of b are .1 with very high estimates for aggregate labor
supply coming in around .2. Being generous (a=1.5, b=.2) that would give a
revenue maximizing tax rate of .94. Another calculation you see is that people
assume that demand is infinity elastic in the long run (which follows for small
countries in some trade models with constant returns to scale) and compute
1/(1+b) as the revenue maximizing income tax. That will give you the sort of
value that one poster mentioned (.8 ish). Note what you have to assume to get
revenue maximizing rates down where income tax rates are in thi!
s country - - extremely high elasticities of demand along with Ls elasticities
of close to 2 or more which are way out of bounds for anything anyone has
computed for long run supply (think about what it would imply for what the work
week should have done over the last century if elasticities were that high).
Another calculation you can perform with these equations is what the effect of
a tax increase will be on revenue. With a=1.5 and b=.2 and a tax rate of 33% a
one percentage point increase in the tax rate causes about a 29 percent
increase in revenues - - obviously not a whole lot of leakage due to decreasing
labor supply and demand.
The main reason why the Laffer curve takes so much abuse is calculations like
this. I don't know of any serious public finance economists who believe that we
are anywhere near the point of maximum revenue on most important taxes. Anyone
working in public finance knew full well that additional tax revenue wouldn't
equal the change in the tax rate times current wL long before Laffer drew his
curve on a napkin for Jack Kemp, but those people knew better than to suggest
that a tax cut could be self financing. The only cuts I've ever seen where
serious arguments were made that they were self financing were capital gains
cuts (for example the cut in 78). There was a fall in revenue from capital
gains taxes when they were increased in 1987, but that appears to have been due
to a huge flurry of selling of assets in December of 86 in anticipation of the
higher rates and really says nothing about what the long run revenue effects of
the higher rates would be. In my judgement reasonabl!
e estimates still suggest that even capital gains tax increases are revenue
increasing in the long run. - - Bill Dickens
William T. Dickens
The Brookings Institution
1775 Massachusetts Avenue, NW
Washington, DC 20036
Phone: (202) 797-6113
FAX: (202) 797-6181
E-MAIL: [EMAIL PROTECTED]
AOL IM: wtdickens
