Can tax cuts pay for themselves?

I think it's interesting the notion that people have that tax cuts either pay for themselves (via increased economic growth), or that they simply drive the country deeper into deficit.

It seems to me that neither is always the case; it all depends on the tax being cut, from what level, and to what level.  I'm not an economist, so forgive my naivete on this, but a simple thought experiment and math suggests that some tax cuts sometimes can more than pay for themselves, while others would not.  In particular, is there any reason that tax cuts wouldn't work like any other price-elasticity supply-demand curve?

As a thought experiment, let's think about how pricing would affect sales of, say, a Ford F150 truck.  Let's suppose that Ford prices the truck at $1M.  It's pretty safe to assume that this is such a high price that it will choke off all demand for the vehicle.  Now, suppose Ford lowers the price by 10% to $900K.  You're still so far out on the curve that this will not nudge demand - there will still be no sales.  Suppose, instead, that they lower the price to, say, $40,000.  I don't know if that's a good price or a bad price for an F150, but you can imagine that the demand will be a large multiple more than the demand was at near a million.  If that multiple is more than 25x, then Ford will make more revenue selling F150s at $40,000 than they made at $1,000,000. 

Now lets lower the price (we're ignoring cost and profit here!) from $40,000 to $30,000, then $20,000, then $10,000, and finally to just $1,000.  The first few price reductions will likely increase sales further as the truck becomes more affordable to more and more people.  But at some point, everyone who wants an F150 can afford one and the later price reductions have negligible (if any effect) on demand.  A price cut from $1,000 to $500 is unlikely to result in double the demand because $1,000 for a new truck was hardly any barrier at all.

What does this have to do with taxes?  Everything, really.  From 1944-1963, the highest marginal personal income tax rate was in the 91% range.  That is a hugely burdensome tax rate, and puts a huge damper on the resources people have to invest in economic activity.  That rate fell to about 70% in the 1960s.  Taxes on this income bracket dropped by about 23% (91% to 70%), so if economic activity caused taxable income in this bracket to increase by 30% (= 1 / 0.77), the tax cut would have paid for itself.  The economy did noticeably pick up in this time period, though proving a causal relationship to the tax cuts is obviously difficult to do.  But it certainly passes the sniff test that a 23% cut from 90% could yield 30% more growth.


Fast forward to now with a 35% top marginal tax rate.  Imagine the same amount of rate reduction - 21percentage points.  (This represents the same portion of income that the government in the 1960's stopped laying claim to.)  The top rate would go from 35% to a mere 14%.  The same 21 points that represented 23% of the 90+% tax rate now represents a 60% reduction, and that means that taxable income in that bracket would need to grow 250% (= 1 / 0.40) to pay for itself.  35% may be a "high" tax rate, but it isn't so high one can reasonably imagine that it is restraining a more than doubling of economic activity.  Even if one proposed a proportional tax cut - 23% off of 35% (to 27%), that 8-percentage-point reduction is unlikely to yield the required 30% growth to be self-funding.

Now, nobody is proposing cuts like this on our current tax rates.  My point here is that, in the same way that each dollar of price reduction on the truck affected demand for the truck differently depending on what the overall price of the truck was, each percentage point of tax reduction also has a different impact on both the tax burden and the threshold to be "self-funding" depending on what the overall tax burden is.  A 21-point reduction from 91% behaves very differently than a similar reduction from 35%.

My analysis above is greatly simplified, and I'm not responding to any particular proposal.  My only point is to say that "self funding tax cuts" bear the burden of proof: one must not assume that a proposed tax change is or is not self-funding.