One way to explain to lawyers why income effects don't create deadweight loss

All tax law profs who read any economics know, because it says so in any Public Economics (or for that matter Price Theory) textbook, that income effects, unlike substitution effects, don't give rise to deadweight loss.  But sometimes they don't have the right intuitive handle on why this is so. I happen to have just thought of a new way of putting it (I think) crisply that I'll plan to use in the future as needed.

For a typical set-up, say I'm saving for retirement, and all of a sudden a new tax on saving is imposed.  It's a tax increase for me, not a re-jiggering of tax computation schemes, and the money is going to be spent on someone else.  So will I now save less for retirement?  (This is not yet the deadweight loss question, of course - but I'll get there momentarily.) To make things really simple and straightforward, let's assume that the pre-tax rate of return to saving stays the same, so the after-tax rate of return is reduced by the tax.

The analysis everyone knows goes as follows.  The substitution effect indicates saving less, because I am now at the margin unable to buy as much retirement consumption, per unit of reduced current period consumption, as I could have absent the tax.

However, the income effect indicates saving more.  One way to put this is that my budget line has shifted inward. The packages of current consumption plus retirement consumption that I can afford have grown smaller, since I can no longer buy as much retirement consumption per unit of forgone current consumption.  If I am optimizing by equalizing the marginal utility of the last unit of consumption in both periods, I will want to share the hit between current period consumption and retirement period consumption, rather than having the latter take the entire hit from the reduction in the after-tax rate of return.

Standard bottom line: the net effect on my current period saving is theoretically indeterminate.  But now we get to the efficiency analysis.  Let's assume here (counterfactually, I think) that there are no externalities whatsoever associated with the amount saved, so we are thinking just in terms of deadweight loss from prospective savers' decisions.

Now one gets to the point that substitution effects indicate inefficiency, whereas income effects do not.  Again, to people with legal rather than economic training this may seem like just some sort of bizarre thing they've learned that doesn't seem to make intuitive sense, even though they know it is correct based on the weight of authority.  So how can we make the intuition more salient?

Let's start with the case where net saving is exactly the same as before, since its reduction by reason of the substitution effect precisely equals its increase by reason of the income effect.  How can there be no change in total saving, yet now there is inefficiency?

To explain that, let's break apart the two sets of cases.  Forgone saving by reason of the substitution effect means there were instances where a transaction was out there, ready to be made, and the tax wedge prevented it from happening.  E.g., suppose the pretax interest rate is 5%, and that if I had saved and invested $100 in period 1, someone would have been willing to pay me up to $105 in period 2. Say I'd require at least $104 in period 2 to be willing to do this, but the tax rate on saving is 40%, so I'd have only $103 after-tax.  The deal doesn't happen, and there's lost surplus of $1 (from the excess of what they were willing to pay me over what compensation I required in order to be indifferent).  The deadweight loss from this is not affected by the fact that some other transaction might be taking place that wouldn't have otherwise, in which someone saves and invests more because the income effect induces them to want to save more.

So finally to the point, why don't income effects indicate inefficiency?  E.g., isn't there a "change" if I save more because the new tax has knocked me down a peg?  Answer, yes is there is a change relative to the counterfactual scenario where the tax hadn't been imposed, but change relative to some alternative scenario isn't the point.  Changes in behavior by reason of income effects are an example of re-optimizing.to get the best result you can under your new circumstances.

Here's another example.  My uninsured home is destroyed by a hurricane, so I decide to work more due to the income effect.  Or, I win $10 million in the lottery, so I decide to work less due to the income effect.  Each of these is a "change" in behavior, relative to the scenario where the trigger event didn't occur, but neither is "inefficient."  (Of course, I'm better off than previously if I win the lottery, and worse off than previously if the hurricane strikes, but that's a separate point.)  Rather than there being inefficiency from the "change," it means that I'm re-optimizing.  I would be failing to make the best choices for myself, as between work and leisure, if I couldn't re-jigger my choices to reflect the new information and/or my new circumstances.

Substitution, of course, also involves reoptimizing, but in light of an externality (disregarding taxes paid because at the margin they benefit others, not oneself).