A correspondent, Casey Mulligan, using the analytics of a simple aggregate production function, written in intensive form as y = f(k), derives
(1) dw/dx = 1/(1-t),
where dx = -kf'(k)dt is the static cost of the tax cut per worker.
The details are in Professor Mankiw's post, and under some circumstances reducing the tax rate on capital increases the wage rate.
There's more intuition at Professor Steven "Big Questions" Landburg, and Professor John "Grumpy Economist" Cochrane works through the algebra at length. Plus a disquisition on the role of the algebra.
The example is gorgeous, because all the production function parameters drop out. Usually you have to calibrate things like the parameter α and then argue about that.And Professor Mankiw's invocation of the single sector macroeconomics model suggests a way forward to answer a commenter question at Grumpy Economist. "What does the government do with the tax money?"
This is not the same as the Laffer curve, which I think causes some of the confusion. The question is not whether one dollar of static tax cut produces more than a dollar of revenue. The question is whether it raises capital enough to produce more than a dollar of wages.
This is also a lovely little example for people who decry math in economics. At a verbal level, who knows? It seems plausible that a $1 tax cut could never raise wages by more than $1. Your head swims. A few lines of algebra later, and the argument is clear. You could never do this verbally.
There might be a way to capture the essential elements of taxation and government activity modifying either the Uzawa two sector growth model or the Lewis dual sector development model.
The challenge is to set things up in a way that doesn't too explicitly force the results, and I haven't done anything formal, this is just thinking at the keyboard. Suppose that some part B (honoring John Kenneth Galbraith's "bezzle") of aggregate output Y gets embezzled. But law enforcement activities -- OK, mediating institutions generally, including the rules of contract and property -- can reduce (albeit never eliminate?) the bezzle. Governing is financed out of taxes, and there appears to be the possibility of taxing beyond the level at which the bezzle can no longer be reduced, thus we get rent seeking.
There might be some elements of this presentation of the two sector growth model that will reward careful study. Consumers pursue maximum utility, where their per capita consumption is y-b-t. As workers, they allocate their effort between the goods sector, where their compensation is the value of their marginal product, and the governing sector, where their compensation is ... to be determined without forcing the results.
There's probably some of this elsewhere in the research, but I'm not aware of it. I'd be pleased to hear of any systematic thoughts on political economy and taxation that can clarify the conditions for governance being symbiotic with commerce rather than parasitic on it (rent seeking), or with commerce becoming parasitic on governance (old style corruption.)



