> 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