In the comments Waldman wrote:
It is not surprising to me that some theories suggest the optimal rate on capital is zero, but that’s not what you expressed in this post (and those theories are wrong). You said “captal income is taxed more heavily than wage income”. That is false. It is an assertion of fact that cannot be redeemed without abusing common language.
Your second claim is more interesting. You argue on the basis of present value that taxation renders the present value of future consumption endowed by saving less than consumption that could be enjoyed today. But taxation has very little to do with that. To compare the present value of current consumption and of future consumption, we need a rate of return and a discount factor. If the rate of return is higher than our discount factor, we will find that the PV of future consumption is higher than that of present consumption. If our rate of return is lower than the discount factor, we will find the opposite. Capital effect the rate of return actually available for future consumption, so if we choose a discount factor a priori, we might find that under some circumstances your assertion is true: taxes cause future consumption to be less valuable than present consumption. But under some circumstances, the rates of return even after capital taxes is higher than the discount rate, and your argument is false, or the average rate of return is is lower than the discount rate even before taxes, so taxes aren’t the issue and your argument is false.
To distinguish these circumstances we need to determine the discount rate we intend to use to compute present value. At a certain level, that is arbitrary. I might claim to require $120 next year to be as satisfied as I would be with $100 in consumption today, so my discount rate is 20% and saving is not worthwhile with or without taxes. Or, I might be flush today and worried about a very uncertain future, and so be satisfied if I can have $80 a year from now for deferred $100 in consumption, in which case my discount rate is -20%, and taxes I might pay against a 5% opportunity don’t much discourage me.
Rather than rely upon subjective time preferences, the usual approach to this issue is to assume that people discount future income at the best rate they can achieve at the level of risk they are willing to bear. Even if I’d be minimally content with $80 next year, I won’t except less than $105 if I can easily earn $105 by putting my money in the bank. So we use current market rates of return as our discount rate.
But, and crucially, this logic requires that we use after tax market rates of return as our discount rate. If bank interest rates are 5% but interest is taxable at 5%, then the opportunity I will be satisfied with is 4%, and that is the rate by which future income would conventionally be discounted. Of course, that 4% may be much more or much less than the discount rate of my time preference, but market rates, after tax market rates, determine the rate by which I will actually judge alternative consumption paths. I’ll eat today if that 4% is too little, I’ll save if it’s too much. In either case I’ll value $104 in the future at no more than $100 today, because I’d only need $100 today to turn that into $104.
So, tautologically, you are mistaken. Under the scenario you describe, the PV of $86.58 14 years from now is precisely $50 today.