Transportation Economics/Positive externalities: Wikis


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< Transportation Economics

Positive Externalities


Positive and Negative Feedback: A Systems Approach


Equilibrium in a Negative Feedback System

Negative feedback loop

Supply and Demand comprise the economists view of transportation systems. They are equilibrium systems. What does that mean?

It means the system is subject to a negative feedback process:

An increase in A begets a decrease in B. An increase B begets an increase in A.

Example: A: Traffic Congestion and B: Traffic Demand ... more congestion limits demand, but more demand creates more congestion.

Supply and Demand Equilibrium

Transportation costs both time and money. These costs are represented by a supply curve, which rises with the amount of travel demanded. As described above, demand (e.g. the number of vehicles which want to use the facility) depends on the price, the lower the price, the higher the demand. These two curves intersect at an equilibrium point. In the example figure, they intersect at a toll of $0.50 per km, and flow of 3000 vehicles per hour. Time is usually converted to money (using a Value of Time), to simplify the analysis.

Illustration of equilibrium between supply and demand

Costs may be variable and include users' time, out-of-pockets costs (paid on a per trip or per distance basis) like tolls, gasolines, and fares, or fixed like insurance or buying an automobile, which are only borne once in a while and are largely independent of the cost of an individual trip.


However, many elements of the transportation system do not necessarily generate an equilibrium. Take the case where an increase in A begets an increase in B. An increase in B begets an increase in A. An example where A an increase in Traffic Demand generates more Gas Tax Revenue (B) more Gas Tax Revenue generates more Road Building, which in turn increases traffic demand. (This example assumes the gas tax generates more demand from the resultant road building than costs in sensitivity of demand to the price, i.e. the investment is worthwhile). This is dubbed a positive feedback system, and in some contexts a "Virtuous Circle", where the "virtue" is a value judgment that depends on your perspective.

Similarly, one might have a "Vicious Circle" where a decrease in A begets a decrease in B and a decrease in B begets a decrease in A. A classic example of this is where (A) is Transit Service and (B) is Transit Demand. Again "vicious" is a value judgment. Less service results in fewer transit riders, fewer transit riders cannot make as a great a claim on transportation resources, leading to more service cutbacks.

These systems of course interact: more road building may attract transit riders to cars, while those additional drivers pay gas taxes and generate more roads.

Positive feedback loop (virtuous circle)
Positive feedback loop (vicious circle)

One might ask whether positive feedback systems converge or diverge. The answer is "it depends on the system", and in particular where or when in the system you observe. There might be some point where no matter how many additional roads you built, there would be no more traffic demand, as everyone already consumes as much travel as they want to. We have yet to reach that point for roads, but on the other hand, we have for lots of goods. If you live in most parts of the United States, the price of water at your house probably does not affect how much you drink, and a lower price for tap water would not increase your rate of ingestion. You might use substitutes if their prices were lower (or tap water were costlier), e.g. bottled water. Price might affect other behaviors such as lawn watering and car washing though.

Network Externalities

The idea underlying network externalities is that a network is more valuable the more people (destinations) who are on (served by) it.

Examples from communications include:

  • telegraph,
  • telephone,
  • fax,
  • email,
  • World Wide Web,
  • automated teller machines, and
  • the English language.

In transportation, examples include:

  • railroads,
  • highways,
  • airports,
  • shipping containers.

Other examples include

  • the typewriter keyboard,
  • electrical sockets,
  • nuts and bolts,
  • weights and measures (SI or the metric system)

and anything else that has been standardized.


Identify 4 other technologies (related in some way to transportation) in which network externalities exist (that have inter-organizational standards). […]


Terms that are often used in describing network externalities:

  • Lock-in
  • Path Dependence
  • Critical Mass
  • Increasing Returns
  • Agglomeration Economies
  • Take-Off
  • "Metcalfe's Law": The value of a network increases with the square of the number of members.

How Networks Grow

To start, a network much have value to some network members at a minimal size (exceeding the cost of joining), or it must be subsidized. Success conditions for a new network suggest

  1. it must either be compatible with existing networks (i.e. not really so new), or
  2. be significantly more valuable to get people to adopt it.

For instance, the interstate highways were compatible with the existing vehicle highway system, interchanges were built, and the same cars could use both. Railroads on the other hand were very valuable compared with canals and animal led carts against which they were initially competing, enabling their success despite the incompatibility of the technologies. In short, if compatibility has costs, it can limit the market because of the extra handling costs, additional waiting time, or an additional layer of processing (such as software) required to decode things.

Mature systems suffocate nascent ones.

Construction of Revealed Demand (Fulfilled Expectation) Curve with Positive Network Externalities

(based on Economides, Nicholas (1996) The Economics of Networks. Journal of Industrial Organization, Vol. 14, no. 6, pp. 673-699 October 1996)

A demand curve for a typical good is downward sloping, the more it costs, the less that will be consumed. However, the demand for a network good rises with the number of members of the network (Economides 1996). Each user of the network creates a positive externality for other users. Thus, networks exhibit a seemingly upward sloping demand curve, self-limiting at saturation, with perfectly inelastic demand.



Figure 1 constructs the revealed demand curves for positive network externalities. Let P(n; ne ) be the willingness to pay for the nth unit of the good when ne units are expected to be sold (assume each consumer purchases only one unit of the good). The network is more valuable the more units are sold. With only one consumer, (n=1), the network is not particularly valuable, so the implicit demand at n=1 (D1) is low, lower than at D2, which is lower than D3, etc. Drawing a line between the number of consumers (n) and the implicit demand curve at that number (Dn) traces out an approximately parabolic shape, P(n, n).


P(n, n) is the equilibrium price where the demand curve for a network of size n (De) intersects the vertical projection of the network size when the number of consumers (network size) is e. P(n, n) is thus the fulfilled expectations (or revealed demand) curve, the set of prices that the nth consumer would actually pay to join the network which would sustain n-consumers. The fulfilled expectations demand is increasing for small n if any one of three conditions hold:

  1. “The utility of every consumer in a network of zero size is zero, or
  2. there are immediate and large external benefits to network expansion for very small networks, or
  3. there is a significant density of high-willingness-to-pay consumers who are just indifferent on joining a network of approximately zero size.”


While demand rises with the number of members, thereby exhibiting positive critical mass under perfect competition, there is a saturation point, such that increasing the number of members does not add value. Such a system exhibits multiple equilibria (the largest of which is stable), and under perfect competition, the amount of network may be under-supplied because the positive externalities cannot be internalized to the producing firms.

Intersection with U-shaped cost curves

We might then think about intersecting our parabolic demand curve with our U-shaped supply curve. Ignoring tangencies, four key outcomes are possible, as shown in the figures below. In the three cases (A,B,C) where the curves intersect, the intersection on the right side, denoted Q*, would be a stable equilibrium. However, to get to the intersection on the right, one might have to pass through the intersection on the left.


Analogy between Scale and Scope economies on the cost side

In the chapter on costs we noted that there exist scale and scope economies on the cost side. Scale economies indicate it is cheaper to produce a given amount if more units are being produced (as a fixed cost can be spread over more units) and scope economies indicate it is cheaper to produce multiple goods together rather than separately.

On the demand side, we noted above network externalities, which are analogous to scale economies, it is more valuable to consume the more consumers there are. Goods may also be more valued if consumed together rather than separately (e.g. complements) or because variety is preferred to monotony. These Variety or Inter-technology externalities are analogous to economies of scope.


(based on Garrison W, Souleyrette R, (1996), "Transportation, Innovation and Development: The Companion Innovation Hypothesis", Logistics and Transportation Review, vol. 32, pp. 5-38).

The economy is a series of linked markets. The "companion innovation" hypothesis suggests that improvements in transport energize other sectors of the economy.

Does the demand curve include those positive externalities?

How smart are markets?

Does willingness to pay change over time at a rate greater than the discount rate?


The reorganization and innovation lead to productivity growth, which should be captured from a macro-economic perspective (see the lecture on transportation and productivity). If positive externalities are not captured (and negative are), there is clearly underinvestment.

Learning Curves

Average variable costs decline with output and time as processes get more efficient (people get smarter). Research and Development is a function of market size, which helps explain the process.


Consumption Economies

Average fixed costs decline with market size.


In markets with large fixed costs that have cost recovery as an aim (public infrastructure as an example), this can be very important. As the market grows, the cost per user drops. This of itself should increase demand – and can be seen as a positive consumption scale externality

S-Curves and Linked S-Curves

Schematic of Logistic Growth Curve (S-Curve)


Mogridge hypothesis

(see Mogridge, M.J.H., D.J. Holden, J. Bird and G.C. Terzis, 1987, The Downs/Thomson Paradox and the Transportation Planning Process, International Journal of Transport Economics, 14(3): 283-311.)

TE-Positive-Mogridge1.png TE-Positive-Mogridge2.png

Why did the automobile take-off? Because at all values of auto-mode share, the automobile has a faster travel speed than transit, even though the city might be better off as a whole (have an overall faster speed) if the congestion from autos was avoided altogether and everyone rode the bus.

Is this correct? Or does the second figure more accurately reflect the empirical evidence?

Application of Positive Externalities

  • Do Positive Externalities Exist (or are they Internalized?) Discuss …
  • What does this say for the prospects of Intelligent Transportation Systems?
  • What are the prospects for Automated Highway Systems as opposed to Intelligent Vehicles (and relatively Dumb Roads)?

Increasing and Decreasing Returns and Equilibrium

(see Arthur, Brian (1990) Increasing Returns and Path Dependence in the Economy. The University of Michigan Press.)

Increasing Returns, Decreasing Returns, and Combination, Ref. Arthur (1990) The probability that a ball is red as the number of balls picked increases from 0 to 100.


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