For me, this whole Vienna pool/gym thing has been like opening a big box of chocolates. Every day, there’s a different and unexpected treat.
Today its the “25% upcharge for non-residents”.
Sometimes, you bite into one of those fancy chocolates, and it’s not at all what you expected.
Of course non-residents must pay more. That’s a no-brainer, right?
On the one hand, it seems like a simple matter of fairness. Let’s suppose that Vienna taxpayers have to kick in (say) 20% of the operating costs of this facility year after year. So that the fees charged to Vienna users only cover (say) 80% of costs.
Well, then, if you don’t pay Vienna property taxes, then it’s only fair that you ought to make up for that by paying (20%/80% =) 25% more for a membership.
Obviously, we must ask non-residents to pay the full, un-subsidized price. Because they aren’t paying Town of Vienna taxes.
That’s the rationale for a 25% up-charge. It’s so that everybody pays the same, for using the facility.
It’s obvious, right? This homey little “fairness” story has a lot of common-sense appeal. I mean, surely you would not ask Vienna residents to subsidize the swimming of non-Vienna residents? That has to be nuts, right?
Sorry, that particular bon-bon is full of baloney.
First point: What does the average Vienna pool member actually pay, in total, including tax subsidy? What’s the true “ticket price” that you charge them?
Assume for a moment that the following is true:
- A family membership to this pool costs $1000 to a Vienna resident.
- 10% of Vienna families buy memberships.
- The cost of running the pool works out to be $1250 per member.
- Vienna taxpayers are making up the $250 operating loss out of property tax revenues.
Under these assumptions, how much does the average Vienna resident who purchases a membership actually pay, including both the purchase price, and the tax subsidy?
- $1000
- $1250
- $1025
The answer is c, $1025.
If everybody in Vienna pays for the pool, but only one-in-ten uses the pool, then the average pool user’s share of the tax subsidy is one-tenth of the total.
If you focus narrowly on the ticket price — that the total price of a membership, to a non-Vienna resident, must match the total amount paid by the average Vienna pool member, including what that member paid in tax subsidy — then the fair price for non-residents is $1025.
That’s because Vienna-resident pool users themselves are subsidized by all Vienna taxpayers.
There is a counter argument that, somehow, taxes are all a wash. So that even if you don’t join the pool, maybe your pool joiners don’t have their leaves vacuumed up, or use the ball fields, or something. So there is some sort of a fuzzy, we’re-all-in-this-together, it-all-averages-out argument for including the total value of all taxpayer contributions, when figuring the “fair” non-resident upcharge.
If the goal is merely one of pricing — that everybody who uses it pays the same total price — then the right non-resident price in this case is a 2.5% up-charge. Not a 25% up-charge.
Point 2: financial leverage. What’s your “fair non-resident upcharge” if operating losses are, say, 50%.
Well, it’s 100%. Based on the same naive reasoning that gives you the plausible-sounding 25% upcharge. If the taxpayer subsidy covers half the costs, then the un-subsidized membership price would be doubled. The “fair” membership fee, for those outside the Town of Vienna, would be $2000/year for a family.
So, $1000/year for a Vienna family. And $2000 a year for a non-resident family membership.
Does anything strike you as impractical about that?
As in, how many non-resident memberships would you expect to sell, given that there are three Fairfax REC Centers nearby, and those only cost $1000/year for a family membership?
Point 3: Marginal cost is probably close to zero.
If you have (say) 30 people swimming in your municipal pool, and you add one more, how much does that increase your costs?
If you said, probably close to zero, then I’d say you’re all-the-way right.
And so, until such time as the facility gets “congested” (in economics-speak) — so crowded that it’s hard to find a parking place, or there’s no room to swim laps, or you have to wait to use your favored weight or cardio machines — having more people use the facility literally costs nothing. Or very close to it.
Translation: Additional users are pure profit. Until such time as the facility gets congested from over-use.
Now how do you feel about that hefty up-charge? In particular, how smart does it look to charge so much that you totally discourage membership purchases from outside the Town of Vienna?
Point 4: Keep your eye on the doughnut, not on the hole.
The taxpayer subsidy is literally the hole in this facility’s revenues. And by focusing on that hole, you are missing the doughnut entirely.
The doughnut here is the total revenues for the pool. (Less costs, which by assumption are more or less independent of the volume of users.)
The question you need to ask is: “What non-resident upcharge policy results in the least expenditure by Vienna taxpayers”.
Which, if total costs really don’t vary significant with the number of users, amounts to, what non-resident upcharge policy results in the highest facility revenue? Again, consistent with the facility not being congested, that is, so crowded that it becomes unpleasant to use.
In short, the “fair upcharge” viewpoint is a poor way to look at this because it only focuses on costs. It ignores revenue (the doughnut). A high upcharge may, in fact, shrink the doughnut, and leave you with an even bigger hole to fill.
Point 5: The break-even “price elasticity of demand” is something like 1.0.
Formally, price elasticity of demand in this case is defined as the percentage reduction in non-Vienna memberships sold, divided by the percentage upcharge.
If a 10% upcharge results in a loss of 10% of your out-of-town membership (relative to the number you’d get with no non-resident upcharge), you’d take in roughly the same revenues with or without the upcharge. That is, price x quantity = revenue, so 110% x 90% = 99%.
Doing the math, if a 25% upcharge loses you more than 20% of your out-of-Town memberships, then imposing that upcharge is a case of shooting yourself in the foot. Because 125% x 80% = 100%. Any loss greater than 20% results in less total revenue, and so results in a bigger required taxpayer subsidy for the facility. (Assuming that marginal cost is zero, and that the facility does not get congested.)
For example, suppose that imposing a 25% upcharge chases away half of your potential out-of-town memberships. In that case, your revenues from out-of-Town members fall by more than a third. (That is, 125% x 50% = 62.5%.) If costs don’t change, then Vienna taxpayers have to make up for those lost revenues.
Conclusion
First, if you insist on charging a “fair’ price to non-residents — that is, the price absent any Vienna taxpayer subsidy — you’re going to get some sticker shock if operating losses are as high as I have projected them to be. You’ll end up trying to charge $2000/family for non-residents. And I’m guessing you’ll end up collecting next-to-nothing.
In that extreme case, it’s fairly easy to see that charging the “fair” price could easily mean shooting yourself (the Vienna taxpayer) in the foot. All the revenues that you don’t collect, from those outside of Vienna, translate into higher annual operating losses that must be covered by the TOV taxpayers.
But more generally, simple pricing rules-of-thumb may not result in the lowest Vienna taxpayer subsidy. That’s true for the upcharge decision. That’s also true for the decision on what to charge Vienna residents in the first place. I’ve been working under the assumption that we’ll charge what Fairfax charges. I’m pretty sure we can’t charge a lot more than that, and still have much business. But there’s no guarantee that charging at the Fairfax County rate is going to minimize operating losses for the facility. That would depend on Vienna residents’ price elasticity of demand for this facility.
Finally, we should face up to the possibility that, politically, we may have no choice but to shoot ourselves in the foot. Even if we knew that a “fair” upcharge would end up costing the taxpayers money, I would not want to be the person to explain why we’re letting non-Vienna residents join the pool for the same membership fee as residents.
Worse, if you had some sort of value-based price discrimination in mind (i.e. pick what pockets you can), if travel time is the big dis-utility for regular gym use, you’d charge TOV residents more than you’d charge those from further away. Try explaining that one, to a grumbling crowd of taxpayers.
Best guess, the upcharge is going to be some plausible-sounding round number. And nobody’s going to give a second thought to guessing what the impact of that will be, on Vienna taxpayers.
