Capital Gains Taxes Are Double Taxation

Last post, I mentioned this argument by Scott Sumner against capital gains taxes. I found it hard to follow, but he links to these posts by Steve Landsburg that make basically the same point more simply, IMO. And it made me realize that I've always thought about capital gains taxes incorrectly. This is another case where our intuition isn't very good at math, and we don't realize when we shouldn't trust that intuition. I'll try to sum up their basic point as simply as possible.

We (and most countries) tax income at a higher rate than we tax capital gains. Most people, including myself, will think this means that people who successfully invest a lot of their income will be taxed much less overall. This will lead to cases such as the well-known example where in most years Warren Buffett pays less taxes than his secretary. But our intuition is wrong here; a tax on income is effectively a tax on your future capital gains because it reduces the amount you can invest, and all capital gains are in proportion to how much you invested. Any additional capital gains tax means you will pay a higher tax rate overall. I had to walk myself through the math to prove to myself that this is right:

Largely stealing from Steve Landsburg's example, assume there are two people named Bob and Tom that each make $100. Bob invests that money in a stock that doubles in value, but Tom does not invest any of it. So overall, with no taxation, Bob would make a total of $200, and Tom would make a total of $100.

Now assume a 50% income tax and no capital gains tax. They still make $100, but after tax they have $50. After doubling that money with his investment, Bob increases his money to $100, and Tom just sticks with his $50. Compare that to what they would have made with no taxes: they both have 50% less, even though Bob's capital gains were not directly taxed.

So... if you add a capital gains tax of 10%, Bob now pays $5 on his $50 gain, which leaves him with $95 out of the $200 he would have had with no taxes. That is an effective tax rate of 52.5% in the long-run! And yet, when Bob pays that additional tax, people will look at that single point of taxation and incorrectly think he is paying less taxes than the rest of us. Moral of the story: this isn't a case of people not paying their "fair share".

However, I don't think this means that we must not tax capital gains as Scott Sumner says, assuming one agrees with progressive taxation (as he does). For the sake of simplicity, I'll save that for another post.