What is the basis for progressive taxation? One principle of taxation (there are others) is "equal marginal sacrifice," i.e. that the last dollar in taxes paid by the rich and the poor should cause the same amount of pain. This is from Miles Corak:
... Alfred Marshall in his Principles of Economics, the most used economics textbook from the 1890s to the 1920s, not just in Cambridge England where he taught, but in the whole English-speaking world, wrote that:
A rich man in doubt whether to spend a shilling on a single cigar, is weighing against one another smaller pleasures than a poor man, who is doubting whether to spend a shilling on a supply of tobacco that will last him for a month. The clerk with £100 a-year will walk to business in a much heavier rain than the clerk with £300 a-year; for the cost of a ride by tram or omnibus measures a greater benefit to the poorer man than to the richer. If the poorer man spends the money, he will suffer more from the want of it afterwards than the richer would. The benefit that is measured in the poorer man’s mind by the cost is greater than that measured by it in the richer man’s mind.
In other words, losing a dollar when you already have many causes less pain than when you have only a few. Marshall’s argument is the basis for both the substance and the method of a good deal of basic micro-economics: it explains the “law of demand”—why lower prices induce people to buy more—but also why tax rates should rise with income.
Economists judge the functioning of the tax system in a number of ways: certainly the system should not be administratively cumbersome, and it should, to the greatest degree possible, not cause individuals in a well-functioning market to change their behavior. It should also treat equals equally. Finally, the tax system should raise more revenue where it will cause the least pain. And this last concern, when coupled with Marshall’s reasoning, suggests that tax rates should be progressive: as income increases, the greater the fraction that should be paid in taxes. ...