## Friday, October 27, 2017

### Corporate tax burden again

This post continues the question, who bears the burden of the corporate tax? The next post will have broader thoughts on the tax plan and economists' reaction to it.

I'm responding in many ways to Larry Summers, who weighed in on the corporate taxes issue in a Washington Post oped. He eloquently and concisely makes most of the arguments floating around now against the corporate tax cut, so I don't have to wade through the venom in Krugman posts to find nuggets of economic sense that one discuss on objective grounds.

This is a long post, so let me summarize the conclusions

1) Even if stockholders do bear the burden of the corporate tax, that is entirely the stockholders who are there when the tax is announced. Current stockholders bear little or no burden.

2) The novel "monopoly" argument is seriously deficient.

3) Even if stockholders bear the burden of the corporate tax, the corporate tax is an insanely inefficient way to make a more progressive tax code.

So who does bear the burden of the corporate tax?

I think every economist in this debate admits, if some reluctantly, that "corporations" pay no taxes. As an accounting matter, every cent corporations pay comes from higher prices, lower wages, or lower payments to shareholders. The only question is which one.  And indirect general equilibrium effects are central.  The question is not just, how do corporations respond immediately, but how do wages, prices, and capital in the whole economy adjust. "Make corporations pay their fair share" is just nonsense.
The sales tax is a good place to start thinking about this question. Corporations "pay" sales taxes, but It's a natural first guess if the sales tax were abolished, prices would stay about the same and we'd pay less overall. Customers "bear the burden" of sales taxes. That's the same thing as saying the sales tax comes out of the wage, as wages only matter relative to prices.

I doubt anyone's first guess would be that companies would raise prices one for one with the reduced sales tax, and stockholders would get higher dividends. We also might guess that companies would sell more, raising output, and try to hire more people increasing employment and wages.

(Let me add quickly that these effects of sales tax are not obvious when you do the economics right. This is just an example to help people see that who pays the tax isn't necessarily the same as who bears the burden of the tax. )

Now, who bears the burden of the corporate tax? The usual principle is that he or she bears the burden who can't get out of the way.  So, how much room do companies, as a whole, have to raise prices, lower wages,  lower interest payments, or lower dividends? It used to be thought that it was easy to lower payments to shareholders -- "the supply of savings is inelastic" -- so that's where the tax would come from. The newer consensus is that companies as a whole have very little power to pay less to investors, as you'll see in detail below, so the corporate tax comes from lower wages or, equivalently, higher prices. Then, indirectly, reducing the corporate tax would increase capital, which would result in higher wages.

Which stockholders bear the burden

Summers disagrees, feels that stockholders bear most of the burden of the corporate tax, so lowering the corporate tax would primarily benefit stockholders, as explained in his  Washington Post oped

The main point of my [justly famous 1981] paper ... was that because of slow adjustment costs, the impact of tax changes was felt primarily on asset prices for a long time. This meant that as my paper showed, the primary impact of a corporate tax cut would be to raise after-tax profits and the stock market. This in turn, as I noted, primarily benefits wealthy individuals.
Let's unpack that. Suppose for a moment that essentially all the corporate tax comes out of lower dividends, not higher prices or lower wages. And let's even leave new investment off the table, either because adjustment costs are large (Larry) or out of the feeling that corporate profits come from some "monopoly rent" unrelated to the capital stock.

What happens then if we lower the corporate tax rate? As Larry points out, stock prices rise. If the company grows at the rate $$g$$, then $P_t = \int_{s=0}^\infty e^{-rs} (1-\tau) D_s ds = (1-\tau) D_t \int_{s=0}^\infty e^{(g-r)s} ds$ $P_t = (1-\tau)\frac{D_t}{r-g}$ Reducing the tax rate $$\tau$$ raises the stock price, and, here, does nothing else.

But think about how this works. The day the corporate tax is announced, the stock price drops by the new tax rate. Then the price stays low, but the return is the same as before. You pay a lower price to get the lower dividend, leaving the return the same, $$r$$ here.

So the entire corporate tax is pre-paid, or borne, by the stockholders who are unfortunate enough to be around when the corporate tax is announced.  Anyone who buys shares after the corporate tax is imposed gets the shares at a lower price, so his or her return is entirely unaffected by the corporate tax.

People who buy shares after the corporate tax is imposed bear no burden of the tax. The corporate tax does not affect the rate of return received by current owners at all, because they got to buy at low prices.

So much for corporate taxes soaking the rich. This is an important fact, missing in all the distributional analysis I have seen.

Now, think about lowering or (let us hope, someday) repealing the corporate tax. In my grossly simplified example, as in Larry's claim, the only impact will be to raise stock prices, and to give a big burst of value to whoever holds stocks on the merry day that the tax cut is announced.

Larry claims that this "primarily benefits wealthy individuals." Well, maybe (more on that later). But Larry leaves out that, if so, we are only giving back some of what was taken on the day that the corporate tax was announced. Maybe right, maybe wrong, but this is not a gift, it is a partial restoration. Since Larry's point is entirely about redistribution, this is not an inconsequential point.

You may object,  most shares have changed hands, so it is a restoration to different people, and in that sense maybe a gift. But it is not a pure gift.

Alexander Hamilton faced a similar issue with revolutionary war debt. A lot of this debt had been bought by soldiers, but as the chances of the debt being repaid declined, its value declined. Many soldiers sold their debt for pennies on the dollar to "speculators." By proposing to pay back the debt at face value, restoring the previous value of the debt, Hamilton did something that primarily benefitted these "speculators." Assuming the state debts was surely a "handout to the rich," bondholders then being like stockholders now plausibly better off than the average citizen. The bonds were a sunk cost, as Larry views today's capital.  But Hamilton did it, for reasons that now seem wise. Fortunately, not every decision revolved around redistribution then.

Larry's case, that capital is fixed in the short run, amounts to the usual argument that the government can grab existing wealth without distortion, so long as it promises "just this once" and not to grab future wealth. Alas, the "just this once" promise has proven futile in the past, and wealth holders learn not to save. Hamilton, among other things, bought reputation, vital when the country needed to borrow again. Larry is mostly worried about giving a present (or returning a theft) to current owners of capital, never mind the "long run" of capital formation. But reputations matter, and the long run comes quicker than you think, a fact those of us of a certain age can tell you.

You may object to all this that we have not  seen any big stock price movements along with rather substantial changes in corporate taxes over history. I agree. Which points exactly that the first assumption is wrong -- that corporate taxes don't come out of dividends in the first place, but rather out of prices and wages. And if the price didn't go down when the corporate tax was imposed, it won't go up when the corporate tax is removed.

Is the rate of return really constant?

Larry would quickly object to my example that I held the rate of return constant as I changed the corporate tax rate.  Larry disputes that assumption:
Second, neither the Ramsey model nor the small open economy model is a reasonable approximation for the world we live in. In the Ramsey model, savings are infinitely elastic, so the real interest rate always returns to some fixed level. In fact, real interest rates vary vastly through space and time, and generations of economic research show that the savings rate rather than being infinitely sensitive to the interest rate is almost entirely insensitive to the interest rate.
The United States is not a small open economy. If it were, the effect of an effective investment incentive would be a major increase in the trade deficit as capital inflows forced an excess of imports over exports. I imagine that President Trump at least feels that a greatly augmented trade deficit is not good for American workers.
Let me unpack those arguments. You are a "small open economy." The rate you pay at the bank is the same no matter whether you borrow $100 or$1000; the price you pay at the grocery store is the same whether you buy one or 20 bananas. You're not big enough to affect market prices.

The "small open economy model" says, as I have above, that if dividends and other payments to shareholders are reduced by taxation, the price of US stocks will fall until the rate of return is the same as it is in the rest of the world. The "marginal" investors whose actions determine stock prices can buy here or abroad, and they will simply sell or try to sell, pushing prices down, until their prospective risk-adjusted after-tax return is the same here as it is abroad.

The "Ramsey model" proposition is more subtle.  Any attempt to make people suffer a lower rate of return induces them to save less. Less savings means less investment and the capital stock falls. This keeps going until the before-tax marginal product of capital rises enough to pay the tax and give investors the original rate of return.  The long-run after-tax return to investors is always the same. This argument is entirely domestic, and doesn't rely on any international investors. (Many commentaries ignore this, more important, effect and just talk about whether the US is big or how open capital markets are.)

This proposition is behind the now classic result that the optimal capital tax -- the corporate tax and personal income taxes on rates of return -- is zero.  (Chamley 1986 and Judd 1985.) It lies behind the modern move to consumption taxation and away from trying to tax wealth and rates of return, including the Obama administration's well-noted efforts to reduce corporate taxes. It's why we have 401(k)s, dividend and capital gains rates lower than ordinary income, capital gains step up at death, and so on. It's why most countries have a VAT and have already reduced their corporate rates.

Here's my best attempt to explain this result, beyond the previous two paragraphs.  The most basic equation in macroeconomics is $r = \delta + \gamma g$ where $$r$$ is the rate of return, $$g$$ is the economy's growth rate, $$\gamma$$ measures how reluctant people are to rearrange consumption to have less now and more later, and $$\delta$$ measures how impatient people are. (This, together with $$r=f'(k)$$ are the $$E=mc^2$$ of modern macroeconomics.) A higher growth rate $$g$$ means people consume less today than they expect consume tomorrow, and people must receive a higher after-tax real return $$r$$ to defer consumption.  (This equation is the continuous time version of $u'(c_t) = \beta R u'(c_{t+1})$ using the standard $$u'(c)=c^{-\gamma}$$.)

Now, none of these tax arguments are (yet) about the long-run growth rate of the economy. Reductions in marginal rates raise the level of output, and give a boost of growth along the way, but they do not raise the long run growth rate.  (Endogenous growth theory is not part of the argument. Yet.)

So, we have the "Ramsey" theorem:  If the long-run growth rate of the economy is unchanged, then the long run rate of return is unchanged.

Larry did not have the (apparently endless) space I have, but it's not clear how he disputes this simple and classic result -- and, by implication, the vast changes in tax policy that it has produced. Larry notes only that "real interest rates vary vastly through space and time,"  and "generations of economic research show that the savings rate rather than being infinitely sensitive to the interest rate is almost entirely insensitive to the interest rate." Neither point has anything to do with the question at hand. The theorem did not say that interest rates are constant, merely that rate of return will revert after an attempt to tax it, over very long spans of time -- the time needed to reduce the capital stock and raise its marginal product. Similarly, the research Larry refers to is about high frequency correlations between expected consumption growth and interest rates. He is right here -- tests of my above equations in monthly and quarterly data don't work well. That should give big pause to the use of business cycle models, including the models used to evaluate stimulus programs, in which those equations lie front and center. But this is a long run proposition.

In fact, the central proposition works quite well at the medium and longer runs we are talking about. Consumption growth and real rates of return move together across countries and at medium and longer runs in a country. Economic booms and booming economies have higher rates of return. Economic busts and declining economies have lower rates of return. And that variation is why real interest rates "vary through space and time!" The variation proves the equation, rather than deny it. And to leave it at "savings is almost entirely insensitive to the interest rate" really puts the central question of the effects of corporate taxes outside of economics -- and is a tellingly static view of the world.

The central question is this: Seeing that dividends are (this is Larry's assumption) going to be heavily reduced by corporate taxation, do people simply fail to react and pay the same price for the stocks, and thus suffer a lower rate of return? That's what Larry asserts, and when you think about it that way seems pretty dubious. (Investment lines up with stock prices, not with real interest rates.)

The argument is also inconsistent. If people pay the same price and enjoy (tax cut) or suffer (tax increase) lower rates of return, then lowering the capital gains tax will not lead to a big stock price increase! You can't have it both ways.

You also may object that as we do not see variations in stock market values (P/D or P/E) when corporate tax rates change, we also do not see variations in average rates of return lining up with corporate tax changes.  Again, I would say this proves the point. That we don't see either price or return changes suggests that dividends do not bear the burden of the tax, but wages and prices do instead.

Monopoly

The latest argument for corporate taxation is that somehow there is now more "monopoly power" in US business, and this justifies a higher corporate tax. Paul Krugman has been advancing this idea most strongly. I'm always suspicious when the questions change but the answer doesn't, but still, let's unpack this argument. It goes together with Larry's point that full expensing of investment alone would offset many of the disincentives to capital formation:
First, a cut in the corporate tax rate from 35 to 20 percent in the presence of expensing of substantial or total investment has very little impact on the incentive to invest. Imagine the case of full expensing. If a company is permitted to deduct all of its investment costs and then is taxed on all of its investment profits, the tax rate has no impact at all on the investment incentive. ...
...Mankiw’s model does not recognize the possibility of monopoly profits or returns to intellectual capital or other ways in which a corporate tax cut benefits shareholders without encouraging investment.
Let me try, with some trepidation, to put the argument in equations which will clarify it. We had started this discussion in the last post with  a firm problem
$\max (1-\tau) \left[ F(K,L) - wL \right] - rK$
Notice by the way how a corporate tax is different from a sales tax. A sales tax only applies to output, so the firm problem is
$\max (1-\tau) F(K,L) - wL - rK$
The sales tax distorts the decision to hire labor. The corporate tax does not distort that decision -- we  have $$F_L=w$$ because the tax applies to both of them.

But what if dividend payments were tax deductible? Then we'd have
$\max (1-\tau) \left[ F(K,L) - wL - rK \right]$
and the decision to invest would not be distorted by the corporate tax. Perhaps more clearly, suppose investment is financed by retained income, and investment expenditures are completely deductible. Then the firm's problem is
$\max (1-\tau) \left[ F(K,L) - wL - K_{t+1}-(1-\delta)K_t \right]$ where $$\delta$$ is depreciation.  Again if it's inside the brackets, the corporate tax does not distort the decision.

If you've taken an economics course, you quickly spy the problem. If the corporate tax lets firms deduct payments to workers, then lets firms deduct payments to capital, there isn't anything left! $$F(K,L)=F_K K + F_L L = rK + wL$$. If economic profits are zero, and we tax economic profits, we don't distort any decisions, but we don't raise any money either.

So suppose now there is a monopoly element, so $$F(K,L) > wL + rK$$, revenue exceeds payments to labor and the payments necessary to get physical capital. Now there is, apparently,  a profit, a pure rent, that can be taxed without distortion!

That is apparently the golden goose of public finance: some source of pure rent, some completely inelastically supplied factor, that can be taxed and does not distort any decision.

Then, and this is the crucial point, Larry (and Paul and company) are asserting that taxing corporate profits does not discourage investment in whatever is producing corporate profits, so it is non-distorting.

Well, is that true?

Here is where I get a little frustrated at the east coast approach to economic policy making. OK, there is a new idea floating around the right cocktail parties: "monopoly rents" are on the rise. So we must quickly "do something," or in this case offer a new reason for the same old answer, corporate taxes.

Really? If there is pervasive monopoly in the economy, why isn't the right public policy answer to do something about the monopoly? More to the point here, before we start taxing things, it is vital to understand what the source of the "monopoly" profit really is, and be really sure that taxing it will not discourage its production, just like that of physical capital. There is something to the story. Measures of entry and dynamism are indeed way down. Corporate profits and stock prices are high, but investment is not following them. High profits should lead to a desire to expand. But if you don't understand it, you can come quickly to wrong answers.

There are two natural stories for monopoly: 1) Government license. Just about every long-lasting monopoly in history is so because of government restrictions on entry and competition. Think taxicabs before Uber. We just had a huge increase in regulation of about 40% of the economy in Obamacare and Dodd-Frank, posing explicit and implicit barriers to entry. Regulation and compliance costs have increased dramatically in many other parts of the economy as well.  But if this is the case, government-created monopoly and then government taxation of its rents hardly seems like the ideal policy mix.

2) Intellectual property. Larry mentions this one. Google is, the story goes, a "monopoly" because it has intellectual property others can't match. Drug companies are "monopolies" because they have patents that allow them to charge high prices for drugs. Here I think Larry's (and, more vocally, Paul's) argument falls apart.  Intellectual property is not an exogenous fixed factor, the "land" of the land tax. Intellectual property is produced. If Google or the drug companies have rents to intellectual property, this is precisely the high rate of return that provides incentive for people to produce new intellectual property. And taxing it away kills that incentive. Go right back to Greg's math, and relabel "K" as intellectual property.

In sum, for the monopoly argument to go through, the monopoly rent must accrue to some really fixed factor, or to some economically wasteful investment such as lobbying. If the monopoly rent accrues to intellectual property, or anything else that must be produced, then we're right back where we started and corporate taxes damage economic growth, investment, and wages.

The argument is more pervasive. Corporate as well as personal income taxes affect people's decision to choose careers, to start a company rather than take a steady job as, say, an economics teacher. The subsequent profits may look like "rents," but they are returns to human capital investments, which will go away if taxed to highly.

Suppose there is, however, some permanent monopoly power, and it accrues to some fixed factor that current companies have, and will have forever.  Never mind how Google unseated the "monopoly" of AOL, Yahoo, and Netscape.  Even so, how monopoly power changes optimal taxes is not (to me, at least) obvious.

The question is not about individual firm's monopoly power. The question is monopoly power in the whole corporate sector. This is the opposite side of the usual fallacy of composition in taxation. Usually, a firm may scream, "we can't pay taxes, since if we raise our prices we'll lose all our business." The firm ignores the fact that everyone else has to pay the tax too, so everyone else has to raise their prices. The firm demand curve is irrelevant; the industry demand curve is irrelevant; what matters is the demand curve of the whole corporate sector.  Individual monopoly power is not at all obviously relevant to that question.

My first instinct was in fact the opposite. He or she bears the tax who cannot get out of the way. Hence, if firms have monopoly power over prices and wages, they have more power to raise prices and wages to pay taxes. This turns out not to be right, or at least up to the entry and exit margin which I haven't examined. (If you make companies pay so much taxes that they go out of business, you get fewer companies.)

The reason is that in the presence of monopoly power, firms have already raised prices and lowered wages, and adding a corporate tax does not change their incentive. Here is where much of Krugman's writing on monopoly goes wrong, in my opinion. The fact that there is more money there does not mean that when you raise taxes you get the money. Tax theory has to be about which decisions are changed by the tax. You can sense in the "monopoly" writing almost a feeling that "tax the corporations" might make sense, in part to address righteous indignation at monopoly. But it still just ain't so.

Perhaps blog readers are aware of a treatment of corporate taxes in the presence of monopoly and monopsony power of similar clarity to Greg Mankiw's example covered in the last post. It might start with Dixit-Stieglitz monopolistically competitive producers, also hiring in differentiated labor markets giving some monopsony power, and get all the general equilibrium parts right.

The inefficiency of the corporate tax as redistribution

So, in the last chain of "suppose I'm wrong about all that," let's suppose Larry is right -- corporate taxes do come out out of stockholders' pockets, and wage growth following a corporate tax cut would be small.

Look at the argument. It is entirely income-based redistribution. Larry, the preeminent public finance economist of his generation, does not make arguments about economic efficiency, tax efficiency, growth of the pie overall, the insane crony-capitalist rot by which the effective corporate tax rate is half its stated rate, or any of the other things economists normally think about when evaluating a tax. His bottom line is that a corporate tax cut will raise wages, but not enough, and it will raise stock prices, but too much, and the increase in the size of the pie is not worth letting the stockholders get more than he wants them to.

OK, but even so, the corporate tax is an insanely inefficient way to redistribute income.

Yes, direct stockholders are more wealthy than the average person. But do not forget that most stock is now held by institutions -- pension funds, including those of state and local government employees that are about to sink Illinois and California, nonprofit endowments, 401(k) plans, and so on.

Another interesting fact about rich people is that they don't spend stock market gains. (I'm pretty sure Larry would endorse this fact, for example, when disliking stimulus efforts that operate through higher stock prices.) So consumption inequality does not rise. "Paper" wealth rises, until the next stock market crash. Is this really so terrible?

Moreover, why must every single element of the tax code be evaluated on its own for its impact on redistribution across income categories? Why must every single change in the tax code always increase income-based redistribution, and be evaluated only on that basis?

Why is it out of consideration to eliminate the highly distorting corporate tax and make up the redistribution with a more progressive personal income tax, or with elimination of the state and local deduction, mortgage interest deduction, health care deduction, and charitable deduction, which only benefit people in the highest tax brackets. (Those deductions really are "tax cuts for the rich!")?

And does the government not spend money? And is not the vast majority of that money spent on redistribution (social security, medicare, medicaid, pensions, etc.?)

Economists have a few basic insights to contribute to public policy. 1) Don't tax wine more than beer in an attempt to redistribute income. Do redistribution efficiently through a progressive income or better consumption tax. 2) Evaluate things like redistribution comprehensively, not on a case by case basis. You can do a lot better if you are allowed to trade off a little less redistribution in a grossly inefficient tax for a little more redistribution in a less inefficient tax or in a spending program.

Yes, Democratic politicians have decided that their best talking point is to echo "tax cuts for the rich" no matter what the Administration and congressional republicans propose, and to attack elements they don't like (corporate tax cuts) on that basis, while conveniently ignoring regressive elements they do like, such as the deductions for state and local taxes. But does simply echoing that political talking point with equations really help us all to the goal of a better economy?

(To be fair, Larry also complained that the reduction in rates does not come with enough base broadening, so it increases the deficit -- -meaning future taxes, or unspecified spending cuts. This is a valid argument, which I will take up in the next post.)

News Flash:

The CEA has just issued a white paper,  "The growth effects of tax reform and implications for wages" I can't wait to hear the analysis. Let me guess.. "tax cuts for the rich?" No, surely that would be too predictable.

Update:

Pietro Peretto reminds me there is an active literature on optimal taxation in endogenous-growth economies, including his Corporate taxes, growth and welfare in a Schumpeterian economy , Schumpeterian Growth with Productive Public Spending and Distortionary TaxationThe Growth and Welfare Effects of Deficit-Financed Dividend Tax Cuts and Implications of Tax Policy for Innovation and Aggregate Productivity Growth.  Nir Javinovich and Sergio Rebelo have a nice recent "Nonlinear effects of taxation on growth,'' in the JPE, Nancy Stokey and Sergio have "Growth effects of flat-rate taxes" also in the JPE, and I have inside information that Chad Jones is working on it too. So, there is no lack of academic literature on the question just which kinds of taxes reduce growth, which of course leads to huge distortions. On the other hand, given the utter distaste of people in this policy discussion to talk about incentives and growth rather than redistribution at all, the lessons of this literature will likely have to wait for the next tax reform. Let us hope it's not another 31 years.

1. I don't think it's correct to argue that there will be a sudden change in stock prices on the day the corporate tax is passed. The market will price the probability of a future tax cut/increase at any point in time. Such probabilities will vary in a smoother way than you describe. Many equity commentators argue that the rally in stock prices since election day is a function of that. This is obviously unprovable but it is a possible interpretation.

2. So, let's consider a firm, let's call it Faceboogle, and it makes \$25 billion in profits and it's got one employee and a bunch of diversified shareholders. Who pays the tax then, after all your calculations and arguments above?

The monopoly argument re corporate taxes isn't "novel". And your argument rests partly on the idea "hey, let's regulate monopolies instead." a) why 'instead', why not both, b) antimonopoly needs to be a broad-based range of different tools which include using the tax system. And as for that particular "optimal taxation" school of thought, that is an exercise in airbrushing out a bunch of costs and 'distortions' (different ones, including damage to democracy, incentives to rent-seeking, etc) which contribute to the other side of the argument. The flat earth society has its 'classic results' too.

There are so many other things I could say in response to this post, but my time is too constrained, unfortunately. In short, though, with all those uninvested corporate cash piles out there, corporate tax cuts in the current era are pushing on a string. Worse than that: much worse, for they inflict great cruelty on large numbers of people, while providing marginal benefits to a smaller number of people who really don't need it.

3. >Google is, the story goes, a "monopoly" because it has intellectual property others can't match.

Not really. There is plenty of open source intellectual property available to do more or less the same thing the google does.

It is the first mover advantage that means that a competing company with vast resources and far superior intellectual property will not be able unseat or even dent google.

1. Is this in the same vein as Yahoo's 'first mover advantage' of the late 90's?

4. While the tax incidence is interesting, I would have thought the largest impact of a corporate tax would have been the deadweight loss from projects not undertaken because of the difference between the pre- and post-tax required rate of return. Has there been any attempt to size that?

5. I think you are a bit off on the monopoly rents analysis. "intellectual property, this is precisely the high rate of return that provides incentive." While you note the important focus on the CHANGE of incentives, by definition, rents are excess payments, so taking away an excess payment does not eliminate the incentive. A firm which perfectly price discriminates loses no customers. Sure, it's just difficult (and quite important) to figure out exactly how much is a rent, vs rents dissipated through rent seeking costs, which we even may call human capital, a very interesting point!
We ought to assume a monopolist is already charging the profit maximizing price, and a tax would not change that. But that is WHY the rents would be borne by the corporation. The whole question is really about what proportion of the price is rents!

When you say, "Individual monopoly power is not at all obviously relevant to that question." I think you make a mistake because it is relevant. You argue that the firm is NOT impacted by any demand curve change, since all firms would have to increase prices because of the corporate tax. (I think you meant no substitution effects?) This means that the individual firm demand curve IS relevant, and the above analysis is still valid.
If rents go to the rich, and most corporations take in a lot of rents, then it's possible that the corporate tax is decent at redistribution, but those are pretty big ifs. I agree there may be more effective ways to redistribute, not to mention this doesn't solve other inefficiencies in resource allocation from monopolies and rents.

So, looking at Brad DeLong's criticism of Mankiw's algebra, as I understand it, he's basically arguing that r (rate of return to capital) declines as t (tax rate) declines; even declines to the extent that post-tax rate or return is constant (this seems to be what he's assuming, no?).

So, Greg Mankiw assumes r is constant; DeLong assumes post tax rate or return is constant, and that r adjusts according to the tax rate so that the post-tax rate or return remains the same (correct me if I'm wrong). But to the extent that this is correct, DeLong is implicitly making a clear argument *in favor* of cutting (or even eliminating) the corporate tax, since if post-tax rate of return is constant (irrespective of tax rate), it implies that corporations bear none of the tax burden; and therefore, employees and consumers bear all of it.

In other words, if he is really against cutting corporate tax rates (which is what it seems; his tone suggests he's not just bothered by the CEA's numbers), this seems to be a Pyrrhic victory, as in order to get a lower wage increase out of the model, he seems to be making an assumption (or argument) regarding r (that is adjusts so as to leave the post-tax rate or return constant) that refutes the justification for corporate taxes at all (that any of the tax is actually borne by corporations, rather than consumers or employees).

Or am I missing something somewhere?

1. Mark,

"So, looking at Brad DeLong's criticism of Mankiw's algebra, as I understand it, he's basically arguing that r (rate of return to capital) declines as t (tax rate) declines; even declines to the extent that post-tax rate or return is constant (this seems to be what he's assuming, no?)."

Brad is probably arguing from a nominal perspective - the nominal rate of return on capital NR declines as tax rate TR declines. Meaning, if the central bank accommodates the lower tax tax rate with commensurately lower nominal interest rates, then nominal returns on capital can suffer.

I imagine the conservative reply is that real rates of return on capital would improve with lower tax rates irrespective of what the central bank does with nominal rates through a growth / productivity effect.

Comments are welcome. Keep it short, polite, and on topic.

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