Arnold Kling  

Pricing and Marginal Cost

VA Hospitals as Quality Leader... Income Distribution and the Le...

Don Boudreaux looks at cases where prices should be above marginal cost.

Jones builds the bridge and charges tolls to pay for it. When the bridge is not congested, the marginal cost of allowing each driver access to the bridge is zero. Is the optimal toll zero? According to textbook theory: yes. According to the much-wiser Coase: no. If Jones were forced, by whatever means, to charge a price equal to his marginal cost of zero, clearly he would not recover his cost of building the bridge. Equally importantly, other investors would have no way of knowing if, and how much, additional investment is appropriate in building bridges to span the Mississippi.

If the future is going to see more of our GDP provided as bits rather than atoms, then we are going to have to develop a lot more tolerance for pricing above marginal cost. We also are going to have to develop a lot more tolerance for price discrimination--a point which was impressed on me by reading the classic Information Rules by Carl Shapiro and Hal Varian.

I do not think that there are easy answers in these cases. For example, with the bridge, you might have a toll that varies by time of day, to reflect congestion costs. 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.

Another issue cited in Boudreaux's post is predatory pricing, and Armen Alchian's apparent doubt in the existence of such. I think that from a competitor's point of view, predatory pricing may exist, although from a consumer's point of view it is much rarer. That is, if you were Netscape, then you got driven out of the browser market. But even after the competition disappeared, the Microsoft browser was not priced above marginal cost.

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

Comments and Sharing

TRACKBACKS (6 to date)
TrackBack URL:
The author at Division of Labour in a related article titled Two bridges too far? writes:
    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... [Tracked on January 25, 2005 4:38 PM]
The author at PRESTOPUNDIT -- "An intense brain-buzz, guaranteed" (2blowhards) in a related article titled THE RIDDLE OF THE BRIDGES -- writes:
    Don Boudreaux: consider a bridge spanning the Mississippi River. Jones builds the bridge and charges tolls to pay for it. When the bridge is not congested, the marginal cost... [Tracked on January 26, 2005 1:19 AM]
COMMENTS (6 to date)
Bill Stepp writes:

Regarding "predatory pricing," Netscape 7.0 is alive and well, complete with tabbed browsing.
Microsoft has fierce competititon in the browser market, such as Firefox and Opera. In fact, the Soft One has been losing browser market share for quite a while.
I can't think of a single case in which "predatory pricing" was ever bad for consumers.

Brad Hutchings writes:

Good question and great example. People who see competition as necessary for their to be a market would say at least 2 -- so that there is a choice. If you're familiar with the San Francisco Bay Area, it's easy to visualize the silliness of that position. In that case, sure, the Bay Bridge has competition -- if you want to drive clear down to the San Mateo bridge in Oakland and San Francisco traffic. Of course, there is competition from ferries and BART as well, much as cable provides competition to telephone. Again, great example.

I think the social optimum has more to do with capacity than number of bridges. If the total capacity is such that congestion can be mitigated by pricing signals, then we have the social optimum. If high congestion pricing doesn't reduce traffic to reasonable levels and high congestion is a recurring and frequent problem, then the system could use more capacity. People might even be willing to pay higher non-congestion pricing so that congestion happens less often.

Bob writes:

Doesn't the optimal investment in bridges have to be where the "reduced congestion" benefit from the next bridge no longer exceeds the cost of the bridge? Seems like a basic question of equating marginal cost/benefit or am I missing something?

Marginal price does seem to tend to marginal cost, even when it's close to zero - aren't digital products (absent itunes, and we'll see about that) pretty much all turning to fixed subscription pricing?

Lawrance George Lux writes:

Does Anyone see the fallacy of the above argument. The Costs of Bridge construction and maintenance will be the minimum Cost of the Toll, while the variance of Toll rates between Peak and Slack will reflect the Expense of conjestion. lgl

Paul writes:

Isn't this a bit of a straw man though? Those advocating marginal cost = 0 would have a two part rate. You pay a lump sum then you cross for 'free' during off peak.

Ben Dawson writes:

I guess if you look hard enough you can find a non-zero marginal cost for driving over the bridge during off-peak hours.

The capital cost for borrowing money to build the bridge is measured per unit of time (some amount of interest per year).

So if it takes some amount of minutes to drive over the bridge, assuming during non peak times you are the only car on the bridge, the capital cost for that amount of time is a start for the marginal cost.

If one person drives the only car that goes over the bridge in one day, then in some sense the marginal cost for that car is the cost of keeping the bridge open for one day, including the capital cost that keeps the enterprise from going bankrupt.

The marginal cost goes down neatly from one car a day until the point where there is more than one car on the bridge at the same time. If there are not drivers are willing to pay that, there are too many bridges.

We're leaving the region I'm comfortable trying to model when we start talking about multiple cars on the bridge. (If we haven't already left, or if were were ever there.)

At this point drivers can auction the right to be on a bridge with fewer cars.

If the bridge operators were to set a limit or cars per unit of time in advance, they could collect a scarcity rent - above the marginal cost.

What limit maximizes bridge operator profits? That depends on the demand characteristics of the drivers.

The social optimum is pretty easy. No scarcity rent. Given good enough capital markets, enough bridges are built that drivers just pay their per-time shares of the capital costs.

Without good enough capital markets, the amount of available scarcity rent (i.e. congestion) that signals that it will be profitable to make a new bridge depends on how not good enough the capital markets are.

Comments for this entry have been closed
Return to top