The deadweight loss of free beer

My excellent (and sports-mad) colleague Shaen Corbet shared with me a story about the Nebraska-Northwestern college football game played in Ireland last year. As reported in the Irish Mirror:

But what couldn't be predicted was the events in the Aviva Stadium on Saturday night as technical glitches saw thousands upon thousands take advantage of free food, drink and alcohol.

There was always going to be a party atmosphere for the first Aer Lingus College Football Classic since 2019, a momentous occasion to remind us just how lucky we are to have these events back.

But the Aviva Stadium was rocking like a Harry Styles gig from just a few weeks prior as queues went a dozen deep as match attendees fleeced the concession stand and bar in a one time only offer of everything being free.

A Twitter (ok, X, but it was Twitter then) user posted this video of the queues for beer, where you can see that the entire foyer area in front of the bar is jam-packed with spectators looking for free beer. Usually, if the price is reduced to zero, we would expect to see a shortage. That's because the sellers would want to sell less (because it is less profitable) at the same time that the buyers are wanting to buy more.

However, in this case, the government chose to subsidise the beer (Shaen tells me it was to reduce the chance of unruly fans getting out of control). We can see the effect of this subsidy, reducing the price to zero, using a supply and demand model as shown below. If the beer market was operating in equilibrium, the price would have been P0, and the quantity of beer traded Q0. Instead, the government paid a subsidy to the beer sellers. We demonstrate this on the diagram with a new curve, S-subsidy, which is below the supply curve S by the amount of the subsidy (which was exactly enough to lower the price from P0 to zero). The effective price for the beer sellers increases to PP, which is the zero price they receive from the spectators, plus the per-unit amount of the subsidy. The quantity of beer demanded increases to Q1, and so does the quantity of beer supplied. There is no shortage of beer.

It is worth considering the impacts on economic welfare of this subsidy though. Consumer surplus is the difference between the amount that consumers are willing to pay (shown by the demand curve), and the amount they actually pay (the price). In the diagram, at the equilibrium price and quantity, consumer surplus is the triangle AEP0. Producer surplus is the difference between the amount the sellers receive (the price), and their costs (shown by the supply curve). In the diagram, at the equilibrium price and quantity, producer surplus is the triangle P0EB. Total welfare is the sum of the two areas (consumer surplus and producer surplus), and is equal to the triangle AEB.

Once the subsidy is introduced, the consumer surplus increases to AQ1O, while the producer surplus increases to the area BCQ1O. The government loses the area of subsidy, which is the rectangle PPCQ1O (this rectangle is the per-unit amount of the subsidy, multiplied by the quantity of subsidised beer). Total welfare is the sum of consumer surplus and producer surplus, minus the subsidy (the subsidy is subtracted because it has an opportunity cost of lower government spending in other areas), and is equal to the area AEB-ECQ1 [*]. In other words, total welfare is lower by ECQ1 as a result of the subsidy. This is the deadweight loss of the subsidy.

To add insult to injury, even though the price of beer may have been zero, the cost of beer was not free. That's because you have to factor in the cost of the time spent waiting to be served (which will be much higher when the queues are longer), as well as the loss of enjoyment of missing part of the game while waiting for beer. Plus, there are external costs of over-drinking imposed on other fans. Shaen, who was at the game, tells me that there were spectators who vomited all over other spectators after over-indulging in 'free' beer. So, free beer wasn't necessarily a good deal for everyone, least of all for Irish taxpayers and for those who needed a dry-cleaner (and possibly a counselling session) after the game.

[HT: Shaen Corbet]

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[*] The overlapping areas of consumer surplus, producer surplus, and subsidy make this tricky to see. However, there is a shortcut. The area of total welfare is the area that is in-between marginal social benefit (MSB) and marginal social cost (MSC) out to the quantity that is traded (in this case, Q1). When MSB is greater than MSC, this represents positive welfare (the area AEB). But when MSB is less than MSC, this represents negative welfare (the area BCQ1).