This is a very good post by Jared Bernstein on the issue of the low responsiveness of output to corporate tax increases.
I think there are two important things to remember on these questions: (1.) make sure you're thinking in terms of the response of the right variable, and (2.) Ask yourself how the margins change - because decisions are made on the margin.
On (1.): A lot of people are shocked when they hear things like "output is not substantially reduced by a higher corporate tax". I don't think they'd be as surprised if they thought in terms of the right variable. After tax corporate income, of course, may be reduced by a lot. That's why people expect a big output effect. If you keep your variables straight, the answer to the question "what is the effect on output?" is actually pretty ambiguous. It basically relies on two issues: (a.) what does the tax do to capacity to produce output (let's assume in the short term that is negligible), and (b.) what does the tax do to decisions that producers make? That brings us to...
(2.) How do the margins change? Lets ignore brackets and marginal tax rate issues and just keep this simple for thinking about a straight up tax rate increase. Let's say y = f(k) and pi = f(k) - rk. What is output with a tax rate on pi of zero? Solve f'(k) = r for k* and output is y = f(k*), right? Now lets say a tax rate of 90% is imposed on pi. What is output with that tax rate?
Solve 0.1(f'(k)) = 0.1r for k**, and output is y = f(k**). Hopefully you all see where I'm going with this. As it's set up here, k* = k**. As a first cut, there's no reason to expect any change in output. Of course there's a big change in after tax corporate income! But if they're profit maximizing it shouldn't change any behavior on the margin.
Now, of course the real world isn't that simple. I only gave the firm one margin to operate on. If there are other margins, of course we may have different behavior that may lower output. The most obvious example is that firms may move their activities overseas. That probably only affects certain sectors (although the corporate tax is probably a big deal for those sectors). There's also the issue of the decision to start a business in the first place.
So there are wrinkles, to be sure.
But the basic issues facing a firm thinking about profits - the basic margin they're working off of - is revenue and cost. And if we just restrict it to a simple revenue and cost model, there's not a real obvious reason to expect a big change in behavior.
This is a good example of how thinking like an economist rather than thinking with your gut reaction is critical to approaching policy.
It also explains some things politicians do that sometimes we yell and scream about, such as:
1. Tax breaks to repatriate jobs back to the U.S., and
2. Lower burdens on small businesses.
Naive economic logic says that that sort of special treatment is bad policy. And maybe it is bad policy if we clutter up the tax code with too much special treatments. But when you think about the exceptions to the simple model which I mentioned above, you start to realize there may be good reasons for politicians to do this. Optimal tax theory says that you should tax things with inelastic responses the highest and things with elastic responses the lowest, because this is least distortionary.
That's exactly what politicians are proposing when they propose tax breaks for bringing jobs back to America and for small businesses.
UPDATE: Oh and one more thing. This is one teeny tiny example of why taking math out of economics is not a good idea at all. I probably could have said that with words too (well, I mean exclusively with words), but the point isn't illustrated nearly as well if you take out the math - and that was just a dinky little optimization problem.