Are Sports Arena Subsidies the Membership Fee in a Two-Part Tariff?

My brother Joseph points me to this piece on the perennial issue of whether sports arenas are bad deal for cities that chip in for them: “Is a sports arena an investment or a subsidy?” by Gigi Douban on Marketplace. This article is sparked by presidential candidate Scott Walker’s signing off on $250 million in public money for a new Milwaukee Bucks arena.

The thing I am wondering about is whether calculations of the benefits of subsidizing sports arenas takes into account the full measure of sheer consumer surplus of people who attend and would be willing to pay much more than the ticket price.

Plausibly, the taxes might come from primarily from the relatively rich to benefit the relatively rich, so think of this as distributionally neutral, to a first approximation. Because the average dollar benefit goes up with income, the labor supply distortion may also not be a major issue. See Louis Kaplow’s “On the (Ir)Relevance of Distribution and Labor Supply Distortion to Government Policy.” To look at it another way, the fact that people might want to make enough money to be able to afford to live in an area with the amenity of having a sports team helps avoid labor supply distortion.

The total consumer surplus from having a sports team in an area could be quite high because the benefit could be extremely high for the ultra-rich. Indeed, I would expect the benefit to go up more than proportionately with income, since sports attendance should be a luxury good. Functional forms not reflecting the extent to which sports attendance is a luxury good would underestimate the consumer surplus.

In other words, sports arenas don’t necessarily need to bring jobs and economic development for subsidies to be worthwhile–they can be worthwhile simply because people like having sports teams in their local area so they can attend in person–beyond what they pay in the ticket price.

To put it another way, arena subsidies are part of a two-part tariff pricing: because having the sports arena in the local area is a public good, the “membership fee” of being in the class of cities with a sports team in a given league is paid for by the government. Then the per-use fee is paid by those who actually attend.

Am I missing something?