Price increases are a form of rationing — a good one

“Price gouging” during a pipeline-induced gas shortage

I recently had a good conversation with some socialist-leaning persons via the internet on the subject of “price gouging” during the ongoing hurricane evacuation from Houston. They view price increases on essential goods during the evacuation as immoral, using gas and bottled water as examples. I disagree, and will argue that keeping prices low in these circumstances is in fact the greater source of moral hazard and more likely to end in harm to a larger number of individuals than raising prices.

Consider a specific situation: A gas station during Hurricane Harvey. Let’s assume the following:

  • The gas station is in an area likely to be flooded, and the station itself is likely to be flooded
  • It is on a major evacuation route
  • The owner had the same notice of evacuation as everyone else, i.e. a matter of hours
  • The normal price of gas is $4
  • The underground tanks now hold 1000 gallons of gas, which will not be resupplied before the crisis is over

Now, the owner’s goal for this thought experiment is to maximize the number of people who are able to escape the area, without creating a bottleneck that endangers the overall flow of traffic.

Three options immediately present themselves.

  1. ) Continue as normal

Continue to sell gas at normal prices and in unlimited quantities. Gas remains priced at $4 and people may purchase as much as they like.

2.) Ration the fuel

Given that typical gas tanks range between 12 and 25 gallons, with extreme outliers above and below for things like heavy duty trucks and hybrids, the ration amount must be set according to those numbers to meaningfully affect the amount that people buy. A ration set at 16 gallons would affect only truck and SUV drivers who are already low on fuel. For the purpose of this thought experiment, let’s set the ration at 10 gallons — a number which will impact the majority of vehicles and stretches the tanks to a nice even 100 divisions.

3.) Raise prices very high

The controversial option. Prices need to be high enough to be *markedly* different from usual in order to affect buying behavior significantly. $4.50 gas may dissuade a tiny number, but in an emergency it will not dissuade enough to make a difference.

I’ve seen many claims of $8 gas during Harvey, so that’s the number I’ll use for the rest of this thought experiment. Neatly double the usual price, and enough that the loaded term “price gouging” will certainly pop into many minds.

Now, I’ve excluded some exotic options here, such as coordinating distribution somehow with other stations, rationing according to need, or having dynamic pricing based on ability to pay or similar factors. These solutions may seem very nice on paper, but the situation at hand does not realistically allow for such sophisticated processes to be put in place. Perhaps they could have been put in place far in advance, but that’s a topic for another discussion.

Which of the three options gives the best result? In order to assess this, I’ll propose a sample population of 200 drivers who feel that they need gas to safely escape (who I’ll refer to individually although they may or may not have passengers) with a wide variety of vehicles, incomes, and distance needs. Let’s assume that these 200 people just happen to represent an exact slice of American wealth distribution, from poverty all the way to 1%er elite, and that their cars represent an exact slice of fuel needs, from 40mpg hybrids all the way to a heavy duty truck pulling a horse trailer and making 5mpg.

Option 1: Sell as usual

The results:

  • The very wealthy (2 people) buy as much as they can.
  • The upper class (8 people) buy as much as they can.
  • The upper middle class (26 people) buy as much as they can.
  • The lower middle class (22 people) buy as much as they can.
  • The poor (142 people) buy as much as the can. A few of them (let’s say generously 5%) can’t afford to buy enough, and they are screwed.

Assuming an average gas tank size of around 15 gallons and that tanks are on average half empty, the gas lasts for 1000/15*2 = 133 vehicles. I simulated this in Excel and got results that look like 125, 145, 138, etc.

Everyone after car #133 is screwed.

The very poor are screwed.

Net result: About 67 drivers are screwed.

Option 2: Ration the gas

The results:

  • Everyone who can afford to buy 10 gallons and can use that much buys 10 gallons.

So 33 people take 330 gallons, leaving 670. Distributing this across a range of 1–10 gallons gives us a median of 5.5 gallons for the remaining vehicles, or 121 vehicles filled to their content.

Total vehicles filled: 154. I simulated this in Excel and saw results like 150, 157, 164.

The very poor (generously ~5%) who couldn’t afford what they needed are still screwed.

Everyone after vehicle 154 is screwed.

Everyone who had an unusually high need for gas — the family in the Suburban with a 22 gallon tank, the driver hauling three horses to safety behind a heavy duty pickup, and the guy who wanted to buy 40 gallons so he could fuel his boat and his neighbors boats for rescue efforts — screwed.

Option 3: Raise prices

  • Although I will argue as an aside that 1%ers are pretty price sensitive, let’s assume that the guys in the S-Class and the Range Rover buy as much as they can.
  • The upper class have a price sensitivity of 50%, so half of them buy only what they need.
  • Upper middle class price sensitivity: 75%
  • Lower middle class price sensitivity: 100%
  • The number of poor people who have enough for the normal prices but not enough for the higher prices causes the number who cannot afford what they need to double, to let’s say 10% (14 drivers.) Again, I think this is generous, but the math still works out.

Now we get into somewhat complex math. I won’t bore you with the details, but in short, we need to take into account the combination of price sensitivity, need, maximum tank size, and ability to pay, then use this blended approximation to predict the number of vehicles which receive fuel.

I wasn’t able to derive an explicit formula for this option, so I simulated it with the equation: (Need + (Additional Empty Capacity * (1-Price Sensitivity))) * Ability to Pay (1 for able, 0 for not.)

The result was that the gas ran out around car 190. Results include 189, 200+, 182, etc.


I hope at least some of you are still with me after all that wonkiness, but the point should be clear.

To summarize:

  • Selling normally screws the most people — around 67 people will go without gas, plus those who can’t afford the normal prices are screwed as they are in every scenario.
  • Rationing screws fewer people than selling normally — around 45 drivers will be left without gas. This is an improvement over selling normally, but comes with a major drawback — people who need unusual amounts are specifically screwed. This includes people trying to evacuate in large vehicles (likely to hold more people), evacuate with with animals, or evacuating in older vehicles which need more fuel to travel the same distance (more likely to be a lower-class person.)
  • Raising prices screws the fewest people — between 0 and 20 people, most likely. It screws more poor people, which is bad, but it helps more people than it hurts in this scenario. Plus, those who need the fuel the most — animal evacuators, rescuers, etc, can buy as much as they need because they know that the fuel will be worth the additional cost.

Why is this true, though? Why do we instinctively have a bad feeling when we see “price gouging”, when it’s the optimal way to allocate a scarce resource?The issue is something called moral hazard. As you will likely read in coming weeks, flood insurance is an example of moral hazard — it’s a non-market incentive that causes people to make decisions which are harmful to the larger system. We taxpayers will be paying a lot of money to help the people of Houston who are on the flood insurance program, because it subsidized construction that should have been prohibitively expensive due to the high real cost of insuring structures in flood zones. The program is already many billions of dollars in debt, so Houston is a cost which it absolutely cannot absorb without additional injections of cash.

Keeping gas prices low when supplies are critically short creates a similar moral hazard — everyone from the guy in the S-Class to the guy in the Corolla will cheerfully fill the tank because they have no incentive not to. There is no signal that supplies are low, and there is nothing to encourage frugality with gas when it is priced normally.

High prices remove this moral hazard and force buyers to change their behaviors. This does harm the very poor, and that is bad. I hope that the very poor were able to find help. But keeping prices low for everyone hurts far more people. Rationing through pricing is a hard choice, but it’s also the right one.

(As an aside, something that occurred to me while writing this is that under a socialist or more-socialist system, rationing by high prices becomes a better option. If a highly successful socialist system were in place, the very poor would not exist and so everyone would be able to afford the gas they need, and the wealthy would be more price sensitive and less prone to overconsume, as they would be much less relatively wealthy. Plus, a socialist government would presumably be more disposed to make evacuees whole for their costs incurred while fleeing.)