Arnold Kling at EconLog poses the following riddle, adding a twist to Don Boudreaux’s
example of a for-profit bridge:

[Suppose the following:] You charge $1 at off-peak times, and $5 at peak times. You get 10,000 off-peak riders per day and 1000 peak-time riders per day, for $15,000 a day in revenue. Suppose that breakeven revenue is $6,000 a day.

Now, suppose that a competitor opens a bridge. Then my guess is that the toll will be competed to zero when there is no congestion, so that both bridge-owners become dependent on the congestion charge to recover fixed costs. At peak time, price competition is less fierce, because riders are willing to pay a little extra to be on a less congested bridge. However, there are only 1000 people willing to pay $5 a day for the privilege of a peak-time ride, so now neither bridge can recover its costs.

For Discussion. In the bridge example that I laid out, what is the socially optimum number of bridges?

First, I have a nit-picking objection to Kling’s example. With two bridges and the same 1000 drivers, congestion at peak time should be less than with one bridge. A peak-time driver therefore gets a better product (a faster trip) for his $5. So shouldn’t the number of people willing to pay $5 be greater with two bridges? In his example, it’s the same in both cases (1000 people).

Anyway, to answer the discussion question: given only Kling’s data, we can’t tell whether two bridges are better for social wealth than one. The bridge owners jointly go from $9000 in surplus to negative $7000, a loss of $16,000. But 10,000 people who used to pay $1 now cross for free, adding $10,000 in consumer surplus. We don’t know how many more, for whom $1 was too high, benefit now that the bridges are free off-peak. If the demand curve for off-peak travel is linear from (say) zero QD at $2, to 10,000 QD at $1, it hits 20,000 at $0. The area of the added consumer surplus (rectangle plus triangle) would be $15,000 (and the traffic would be no worse). Other shapes and positions for the demand curve would give other amounts, some of them greater than $16,000.

Clearly an example can be formulated in which both of two (indivisibly sized) bridges lose money, even though a single bridge would make a profit, and the loss in producer surplus is known to exceed the gain in consumer surplus. If we suppose that two bridges have been built, then we conclude that the market has failed to reach the efficient outcome. But given the data of such a case, why would the second bridge be built? If the second entrepreneur can anticipate what will happen, won’t he choose not to build?

Here’s the most important point: Kling is asking the wrong question. As F. A. Hayek argued in “The Use of Knowledge in Society,” calculating the social optimum when “we” have all the relevant information “is emphatically not the economic problem which society faces. … The reason for this is that the ‘data’ from which the economic calculus starts are never for the whole society ‘given’ to a single mind which could work out the implications, and can never be so given.”

Only under a regime of open competition, which requires free entry, do we begin to learn where the demand curves actually lie and where the breakeven point (minimum cost) actually lies. So the more fundamental question is: What is the best method for society to determine the number of bridges? And the answer is: Free entry.