Customers shouldn't pay less when they use a self-checkout, they should pay more

The New Zealand Herald reported last week:

State representative Nikki Lucas has introduced a bill that would require retail businesses selling food in the state to offer a 10% discount to those who used the self-checkout lane.

“Retail businesses increasingly rely on self-checkout systems to reduce staffing and operational costs by shifting responsibilities traditionally performed by employees onto consumers,” she wrote...

Consumer NZ head of advocacy Gemma Rasmussen said her organisation thought there was validity to the argument in New Zealand, too.

Call me radical, but I think that Lucas and Rasmussen have this backwards. Customers shouldn't pay less when they use a self-checkout, they should pay more. To see why, I'm going to rely on the concept of price discrimination - where the seller sells the same good or service to different groups of consumers for different prices.

Consider two groups of consumers (impatient, and patient), and two options (self-checkout, and regular checkout). The first group of consumers is impatient, and they want to get out of the store as soon as possible, and for that reason they prefer to use self-checkout. This group can be said to have a short time horizon for their purchases. This short time horizon makes their demand for goods less elastic (less sensitive to price). The second group of consumers is more patient, and they are willing to wait. This group can be said to have a longer time horizon for their purchases, which makes their demand for goods more elastic (more sensitive to price).

If supermarkets want to price differently for each group, which group should pay the higher price? The answer to that question is shown in the two diagrams below. Both diagrams show a firm with market power (a supermarket), and each diagram corresponds to one of the sub-markets. The sub-market on the left represents the patient buyers, who have more elastic demand - notice that the demand curve D1 is relatively flat (which means that a change in price will have a big effect on the quantity that these consumers demand). The sub-market on the right represents the impatient buyers, who have less elastic demand - notice that the demand curve D2 is relatively steep (which means that the same change in price would have a smaller effect on the quantity that these consumers demand, than it would for the patient consumers). The marginal cost (MC) is the same in both sub-markets - it doesn't cost the supermarket any more to sell a product to an impatient buyer than what it costs them to sell that same product to a patient buyer. [*]

The supermarket will maximise profits by selling the quantity where marginal revenue (MR) is equal to marginal cost (MC) - this is the standard short-run profit-maximising condition (as I discussed in this post). In the impatient sub-market, the profit-maximising quantity occurs where MR2=MC, which is Q2. In order to sell that quantity in the impatient sub-market, the supermarket should set the price equal to P2. The problem with that high price P2 is that in the patient sub-market, no consumers would be willing to buy the good at all. The supermarket can increase profits if it charges a different price in the patient sub-market from the price it charges in the impatient sub-market. In the patient sub-market, the profit-maximising quantity occurs where MR1=MC, which is Q1. To sell that quantity in the patient sub-market, the supermarket should set the price equal to P1. In other words, the supermarket should charge a higher price to the impatient consumers, and a lower price to the patient consumers.

The problem here is that supermarkets don't know (for sure) which group (impatient or patient) any particular consumer belongs to. But by offering different checkout options, the customers can sort themselves into the impatient (less elastic demand) group and the patient (more elastic demand) group, because the impatient consumers use the self-checkout. In other words, the supermarket should charge a higher price to the users of the self-checkout.

This is an example of menu pricing (or second-degree price discrimination) - where the consumers are presented with a menu of options, and they select the one they prefer.  Crucially, the seller knows that some menu options appeal to consumers with more elastic demand, and other options appeal to consumers with less elastic demand. In this case, there are two menu options - self-checkout, or regular checkout, and the supermarket knows that the self-checkout appeals to the impatient consumers who should be charged a higher price.

So, customers who use a self-checkout right now shouldn't be arguing to lower prices. They should think themselves lucky that supermarkets aren't optimising, because if they were, the prices at self-checkouts would be higher than at regular checkouts.

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[*] You could argue that it doesn't cost the same to offer purchase through regular checkouts and self-checkouts. However, how big is the cost difference, really? Let's say that it takes two minutes to scan your items, but would take three minutes through the regular checkout, because the payment process tends to take a bit longer at a regular checkout. With self-checkout, the supermarket would save three minutes of labour. Say that the supermarket pays their checkout staff $30 per hour (somewhat more than the minimum wage). By using the self-checkout, you've saved the supermarket $1.50 of labour in this example (3/60 * $30). Except, that calculation doesn't take into account that the self-checkout is not a zero-labour option. There is usually a checkout person who has to watch over the consumers using the self-checkout. So, the saving is actually a bit less than that. It almost certainly isn't close to the 10 percent discount that Lucas is arguing for. Most of the cost of the items that you buy at the supermarket is the wholesale cost that the supermarkets pay, not the checkout labour cost.