For the income distribution:
First of all, even if the pie would be smaller, the system still would be efficient. Mankiw uses the word ‘efficiency’ incorrectly, mixing up growth with efficiency, and stirring up adverse feelings against income redistribution by using a wrong accusation.
Secondly, indeed, if all incomes were equalised - as even the communist parties of Russia or China didn’t and don’t succeed in doing - the pie could get noticeably smaller. However, for the practical measures we are talking about - in the 40% - 60% range for the marginal rate - the change might not be that relevant. There are not only disincentives for the rich, but also incentives for the poor to participate in society. There are so many other effects. Alleviating poverty, by getting people into jobs, could reduce the crime problem. Or, a rich person may decide to work less and spend more time on a hobby or with the kids - and might find out that he or she is actually better off. The prime comment, and the prime economic observation, is that the pie itself is relevant, but the social utility derived from it is even more relevant. If a democratic, Madisonian, society decides to redistribute income, that itself is evidence and proof that it moves to a superior welfare position.
It is true that a rich person may earn $100,000 per annum and can be outraged by a 40% or 50% tax on it, claiming that society steals it. Strangely, while governments spend so much energy in monitoring the poor, they are quite reluctant to calculate the benefits going to the wealthy. The value of industries depends upon government regulations. The value of city property is also caused by public investments. What we earn now, depends so much on what our ancestors have been doing. It is truly difficult to determine what our own personal contribution is. The $100,000 earned are only the proceeds from a market situation - but the market is an amoral beast, and not a god of justice that allocates what people ‘deserve’. And thus, having such a marginal tax rate could well be one of the necessary ‘rules of the game’ to create a both prosperous and civilised society.
Mankiw shows an awareness of this on some pages, but not integrally so.
On the subject of designing an incentive compatible tax system, he states: “Thus, policy makers face a tradeoff between burdening the poor with high effective marginal tax rates and burdening the taxpayers with costly programs to reduce poverty.” (p440).
Well, indeed, this is the current view among economists - that this current book shows to be wrong.
Mankiw’s discussion on GDP seems rather balanced. Yet, for all his caution, he still seems to favour GDP as the “the single best measure for welfare”, or “a good measure of welfare for most - but not all - purposes” (p490). I think that the latter still is unwarranted, and I’d rather would favour the conclusion: GDP is a crude measure for income - and I would keep some distance from welfare implications.