Petrol prices and drive-offs

The New Zealand Herald reported yesterday:

Due to increasing costs of crude oil, the New Zealand dollar falling and increasing fuel taxes, petrol pumps are forcing a strain on Kiwis.

Some motorists are taking drastic actions to avoid the economic sting, putting in fuel and driving away from stations before paying.

Over the last few weeks, Z Energy has witnessed a small increase of motorists getting behind the wheel instead of the cash register.

"At a high level we have seen a slight increase in the number of drive-offs," a spokeswoman said.

Why the increase in drive-offs? Gary Becker (1992 Nobel Prize winner) argued that criminals are rational, and they would weigh up the benefits and costs of their actions (see the first chapter in this pdf). It is rational to execute a drive-off if the benefits of the drive-off (the savings in fuel costs because they fuel wasn't paid for) exceed the costs of the drive-off (the penalty for being caught, multiplied by the probability of being caught).

How often will people engage in drive-offs? We can think about that question in terms of the marginal benefits and marginal costs of drive-offs, as shown in the diagram below. Marginal benefit (MB) is the additional benefit of engaging in one more drive-off. In the diagram, the marginal benefit of drive-offs is downward sloping - the first drive-off provides a relatively high benefit (filling an empty tank), but subsequent drive-offs will likely provide less additional benefit, because the car's tank is already close to full. Marginal cost (MC) is the additional cost of engaging in one more drive-off. The marginal cost of drive-offs is upward sloping - the more drive-offs a person engages in, the more likely they are to get caught. The 'optimal quantity' of drive-offs (from the perspective of the person engaging in the drive-offs!) occurs where MB meets MC, at Q* drive-offs. If the person engages in more than Q* drive-offs (e.g. at Q2), then the extra benefit (MB) is less than the extra cost (MC), making them worse off. If the person engages in fewer than Q* drive-offs (e.g. at Q1), then the extra benefit (MB) is more than the extra cost (MC), so conducting one more drive-off would make them better off.

Now consider what happens in this model when the price of petrol increases. The benefits of drive-offs increase, because the value of fuel cost savings from driving off increases. As shown in the diagram below, this shifts the MB curve to the right (from MB0 to MB1), and the optimal quantity of drive-offs increases from Q0 to Q1. Drive-offs increase.

Regular readers of this blog will recognise that this situation is quite similar to the increase in honey thefts reported earlier this year. Petrol prices are expected to increase further through the rest of this year. Petrol stations should be preparing themselves for increases in drive-offs. Consumers can probably expect more petrol stations to move to having their pumps on pre-pay.

Read more:

• Why honey thefts are on the rise