Pigou Tax, Yes or No?

A small community sits on the outlet of a small river and uses the river water exclusively for unheated, unbuffered showers. The community has 50 homes, each with a single shower. The river flow is always sufficient to supply up to 60 showers in use simultaneously, so showers are not scarce goods, in terms of demand with respect to supply, and have no economic value.

After ten years of growth, the community now has 100 homes and showers, and it is no longer true that the unchanged river flow can supply all of the showers in use simultaneously.

Question :

In principle, would a supporter of a Pigou tax on road use to reduce traffic congestion support a tax on water use to reduce shower congestion? If not, why not?

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Yes, alas

A pure Pigouist would probably support such a tax, but that tax performs the same function as a private company -- with the inefficiency and perverse incentives of government. The obvious answer would be to create a water trust equally owned by each of the 100 original households, and to have it set prices somewhere near the monopolistic level, paying dividends such that people who conserved water would be compensated for it.

At worst, this solution is as good as a Pigouvian tax is at best, since it's less competitive (if the government saw water abuse as a revenue source, would they let Evian import anything without paying a tariff?).

It is not really about water

It is not really about water conservation but simultaneous use. A price system would adapt to reflect lower prices when no one is showering and high prices when everyone is, much like the energy market. It may also create the incentive to create a water reservoir if needed.

A pigovian tax would not solve the showering issue by itself. It would need to be adjusted to every hour of the day as to spread use of the showers. This would require central planning which is not efficient. Creating a water reservoir may or may not be a good idea and there would be no way to know that.

Every week, you could emit certificates giving right to a shower at a certain hour on a certain day (as much as the showers can handle) and auction them, dividing the proceeds equaly. By providing a water reservoir, you could turn cheap certificates (night time) into expensive one and sell them at a profit.

Probably not

The justification for congestion taxes is that (1) congestion increases with each marginal car, and (2) driving is fairly elastic. Under those circumstances, a tax that deters the marginal driver can improve the lot of the rest, and if this improvement is greater than the amount of the tax (or the deadweight loss of the tax, take your pick) then a congestion tax can help.

I'm not sure 2 is the case with showers, and 1 definitely isn't. As the question is stated, the congestion problem consists entirely of the sixty-first showerer, and is entirely fixed by making potential 61st-showerers wait ten minutes. It's hard to see how any sort of tax on showering generally is likely to help -- a tax on showering at particular times, perhaps, but even that would probably just shift the congestion to the untaxed edges (a frequent concern with road congestion pricing which has so far not been hugely problematic, but which might well with showers as it's easier to change your shower time than to meticulously skirt the edges of London).

I would think that the

I would think that the preferred solution would be to modify the characteristics of the good so that it is non-economic, free, again.

Number all the homes in the community from 1 to 100. Number all the 10 minute segments in every hour from 1 to 6.

Homes with odd numbers are only allowed to use 10 minute segments with odd numbers, and the same for even numbers.

Road congestion is reduced by limiting access to capacity. Prices and taxes only affect the distribution of access. It is hardly surprising that well-paid academics and politicians prefer to be able to buy access to having to submit to a chance or other distribution process.

Regards, Don

Reservoir

So what I need to live in your neighborhood under your rules is to build myself a little reservoir of water, that gets filled three times an hour for ten minutes each, all day long until my little reservoir fills up. At the end I'm using just as much water as before.

Meanwhile all my neighbors hear about my reservoir and build or buy themselves a reservoir.

So in the end we're all using just as much water as before.

Everybody's happy. As long as the system can handle it. If it can't, then it's time for another solution.

Storage

A reservoir is a far better solution, one that was mastered long ago, like in the bronze age.

There is plenty of water, just as there is plenty of road in the congestion scenario, but not enough to all use at the same time. Water, however, can be stored. It should be anyway since flows are variable in the real world.

This may seem like just neeping about the hypothetical, but it's useful to make the distinctions. Water can be easily stored. Electricity, not so easily. Road room, not easily at all. In each case there may be taxes involved to solve the problem - or not, private solutions are usually as good or better - but the goal is not always conservation or otherwise limiting consumption.

Choose the right tool for the task.

Yep. And while the free

Yep. And while the free market solution provides an incentive to building a reservoir (if efficient) by arbitraging shower claims, the tax solution creates an incentive for the tax collector (who gets a cut of the tax) NOT to create a reservoir.

Choice of Institutions

Assuming that privatization of the water flow is off the table for some reason, then yes, I think a Pigou tax would be in order. But it might better be referred to as a use fee or a toll. The function, as with almost any price, is to assure that the water gets allocated to those who value it most highly. Without pricing, you probably get people who don't get that much out of showers taking them anyway, while people who really love a good shower go without. Or the showers might get rationed by waiting, which is an inefficient waste of people's time.

So create a tax/toll/use fee, and then take the proceeds and rebate them lump-sum to the public.

Glen, I cannot see how any

Glen,

I cannot see how any form of rationing makes sense here. There is no shortage of water and it flows by whether it is used or not. All that exists is a co-ordination problem. As given, half of the population can take up to three 10 minute showers every hour of the day and the only sacrifice that the other half may suffer is that they may need to take their shower or showers either 10 minutes earlier or 10 minutes later than desired. If this is not good enough, all that is needed is to find a single alternate phase home to ensure that a given desired time slot is not used, and available.

The public road congestion problem is much tougher, but once the technical means are available to distribute limited access, there is nothing that says that the distribution must be by means of prices or taxes. It is silly to obstruct the possibilities of local co-ordination to effectively reduce demand. Money and trade may still be useful at local levels, but high global prices or taxes are unnecessary costs.

Regards, Don

I confess...

... that I didn't read your example closely enough to note the aspect of timing. However, I don't think it really changes that much. There is still scarcity for particular times of day that are most desirable for showers. If 100 people want to shower from 8:00 to 8:10 a.m. each morning, but only 60 of them can, then we need a means of deciding who gets to do so. Pricing for that period of time is one natural means of doing so. The people who value an 8:00-8:10 shower will be most willing to pay the price, and that price will reflect their having deprived other people of the ability to shower at that time. If an 8:10-8:20 or 7:50-8:00 shower is a close substitute for an 8:00-8:10 [ed] shower, then the price necessary to clear the market (by reducing quantity demanded to 60 showers) will be relatively low. If different times of day are *perfect* substitutes, at least for a large enough number of people, then the optimal price will in fact be zero. But the more desirable 8:00-8:10 is relative to other times of day, the higher the price will need to be. If your complaint is that there's no need to charge a positive price for times of day during which shower water is not scarce (like the middle of the afternoon), that's fine -- the price should be zero for those times of day. (This is what is meant by peak-load pricing, and it's what many have advocated for roads.) If your complaint is that other approaches -- such as a town meeting where a showering schedule is set up -- could also allocate the water during scarce time periods, that's fine, but I'd like to know what method you advocate. During peak hours, some people will get to shower and others will not. How should this be determined -- by willingness to pay, or by lot, or by political favoritism? I favor willingness to pay. If it's by lot, then some people who place a relatively low value on showering during the favored time will shower then anyway, and that's inefficient. You could reduce the inefficiency by letting people trade their showering permits, of course. A price would presumably emerge from the trading process. That's a good thing, since I'm primarily arguing for the usefulness of rationing by price. If it's by political favoritism, expect lots of wasteful rent-seeking. Again, some of the allocative inefficiency could be reduced by allowing a market in showering permits. If your point is that establishing a monopoly on river water could lead to inefficiency from monopoly pricing (such as prices above zero being charged for time periods without scarcity), I concede the point.

Glen,  My point is that

Glen,

 My point is that the variation in subjective valuation for a given individual between at least some time segments is so small that there is no significant return to rationing by prices.

Every individual likely has a valuation curve for time segments that looks like an inverted parabola centered on the preferred time segment. For there to be any fundamental conflict due to scarcity virtually all the individuals' curves would have to have the same center and the same very narrow width encompassing just a single time segment. Theoretically possible, but extremely unlikely.

One other possible distribution method besides the odd/even one :

 Preferential voting -

 For every 10 minute segment in the day, there are 60 available access coupons.

Each individual is asked to rank his three most preferred time segments.

All individuals are given their highest ranked choice unless and until the total for one time segment exceeds 60.

Volunteers are asked to take their second choice if they are almost indifferent to their top two choices.

If there are still more than 60 claims on one time segment, they can be distributed by chance, with all the losers getting their second ranked choice.

The lottery can be repeated every day, with no losers repeating until everyone has been a loser.

Even if individuals don't eventually find that they become almost perfectly happy with their second choice, The loss of subjective value in the distribution of time segments will be extremely small, in all likelihood.

Regards, Don