Lessons in demand elasticity
Posted by Daniel Hall on December 13, 2007
Update: The Maryland plan was approved, and the link to the Post article now goes to an article summarizing the vote to approve. (I can’t find the original article on the Post website.)
The DC Metro system is planning to raise fares on riders to cover a budget shortfall. I’ve argued previously this is a bad idea — the district should toll roads and implement congestion charges and use those funds to cross-subsidize mass transit instead — but what caught my eye in today’s article in the Post was a more basic economics lesson. The board is considering two primary proposals, one from the city, one from the suburbs:
The public debate that led up to that proposal pitted suburban board members, who want to keep parking fees and train fares low, against urban members, who want to keep bus fares low for low-income riders. …
Under both plans, the largest increases would affect rush-hour subway riders, who make up the biggest portion of daily users. Both proposals would increase rush-hour boarding charges by 30 cents, to $1.65 per trip, a 22 percent increase. But the Maryland plan would raise the maximum fare per trip by 60 cents, to $4.50, instead of 80 cents, to $4.70. The Maryland plan also seeks a smaller increase in Metrorail distance charges during rush hour. …
At Metro parking lots, where the daily fee is as high as $4, the public hearing proposal called for a $1.15 increase. The Maryland plan calls for a 75-cent hike for six months, with an option to increase it by 25 cents after that.
So, to summarize, the city wants to raise the price of the longest rush hour trips, and the price of parking at the lots in the outer suburbs, by a bit more than what the suburbs are proposing. Proponents of both proposals think their fare increases will cover the funding gap:
The increases are meant to raise $109 million to help close a projected shortfall in next year’s budget. Under the public hearing proposal, officials estimate the plan would generate about $111 million and that some, but not many, customers would stop riding. Nearly three-fourths of the money would come from the increase in rush-hour train fares, an additional 25 percent from increased parking charges, and 1 percent–about $1 million–from higher bus fares for riders who pay cash.
Maryland members say their alternative would raise between $104 to $109 million because they are predicting that even fewer riders will abandon the system because of higher fares.
So, now the economics: the article says that officials estimate “that some, but not many, customers would stop riding.” So, good, they do think that demand curves slope downward — higher prices mean fewer trips demanded — but they also think demand is somewhat inelastic: “not many” customers would stop riding. Proponents of the Maryland plan think their plan would raise basically the same amount of money despite having smaller fare increases. How? They estimate demand is extremely inelastic: “even fewer riders will abandon the system because of higher fares.”
So what do the numbers imply about their assumed demand elasticities? Well, I looked up the Metro budget, and, although I’m not entirely not completely sure I’ve got this right, it looks like in the year previous to this funding increase the passenger revenue for Metrorail is expected to be almost $460 million and the parking revenue about $50 million.
So, focusing on the rail revenue numbers, the article implies that the city’s proposal would raise a little over $80 million in additional rail revenue, let’s call it $83 million. (That’s about three-fourths of $111 million.) The article doesn’t specify the ratios of expected new revenues in the Maryland plan, but let’s assume they’re roughly the same. That means the Maryland plan will raise slightly less in new rail revenues; let’s call it $80 million.
Warning: completely speculative assumptions to follow!
For simplicity let’s say that half of all riders pay the short trip fare (currently $1.35 and proposed at $1.65) and half pay the long trip fares ($3.90 now and either $4.70 or $4.50 in future). Under the city proposal I calculate an average fare increase of about 21%. I estimate that the quantity of trips demanded — calculated from the total revenue figures of $460 (now) and $543 (future) divided by the average fares — falls by 2.5%. This implies a price elasticity of 0.12. That’s pretty inelastic.
For the Maryland proposal, on the other hand, the average fare increases by 17% and the quantity of trips demanded… stays exactly the same. Proponents of the Maryland plan think that higher Metro fares won’t lead to any reduction in demand? Hmm, something makes we think someone is twiddling with elasticity assumptions to get the numbers to work out the way they want…
It’s actually far worse than that, however, because not all trips are rush-hour trips. Once you start assuming that rush-hour trips are only a portion of total trips, and take into account that non-rush-hour fares aren’t increasing, it quickly begins to look like proponents of both plans are expecting fare increases to lead to more trips demanded. My head hurts.
And don’t get me started on the parking revenue figures. If current parking revenues are about $50 million, how is a roughly 20% price increase supposed to lead to about 50% more revenue? That’s what I’m assuming the article means, after all, when it says that one-quarter of the ~$110 million in new revenues would come from parking charges.
It’s enough to make me think I’ve gone horribly wrong somewhere, but I can’t find any obvious mistakes. If readers notice any errors or oversights feel free to point them out in the comments. And don’t forget what I said at the beginning — Metro fares should be lowered, not raised.