Transportation Economics/Positive externalities

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Remember, an externality is a cost or benefit incurred by a party due to the decision or purchase of another, who neither obtains the consent of the said party, nor effectively considers the costs and/or benefits to the said party in the decision.

Positive and Negative Feedback: A Systems Approach[edit | edit source]

Equilibrium in a Negative Feedback System[edit | edit source]

Negative feedback loop
Illustration of equilibrium between supply and demand

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

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.

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.

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.

Disequilibrium[edit | edit source]

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

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.

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.

Examples of Feedback Systems[edit | edit source]

We explore a few examples related to urban growth, accessibility, electric vehicle adoption, and urban transit.

Traffic congestion and Travel Demand (-) An example of a negative feedback system is Traffic Congestion and Traffic Demand. More congestion limits demand, but more demand creates more congestion.

Bus Bunching (+) An example of a positive feedback system is Bus bunching. Buses operating with high frequency tend to bunch. A lead bus picks up passengers, each passenger makes the bus slower. As the bus approaches the next stop, there are more passengers waiting. The following bus in contrast gets faster as there are fewer and fewer passengers waiting at each stop, since the previous bus is later and gets more boardings. Eventually the buses bunch together. This simulation illustrates and explains the phenomenon.

Agglomeration Economies and City Growth (+) Economists have sought to understand why cities grow and why large cities seem to be at an advantage relative to others. One explanation that has received much attention emphasizes the role of agglomeration economies in facilitating and sustaining city growth. The clustering of firms and workers in cities generates positive externalities by allowing for labor market pooling, input sharing, and knowledge spillovers. (Rosenthal & Strange 2004)

Accessibility and Land Value (+)

Accessibility and land value comprise a positive feedback system. Where land is expensive, it is developed more intensively. Where it is more intensively developed, there are more activities and destinations that can be reached in a given time. Where there are more activities, accessibility is higher. Where accessibility is higher, land is more expensive.

Gas tax and electric vehicle usage

Gas Tax and Electric Vehicle Usage (+) Imagine all gasoline vehicle users pay for all transportation costs. Imagine total expenses are $100,000,000 and the total number of users are 1,000,000, traveling 10,000 miles per year (for a total travel of 10,000,000,000 miles per year, at a cost of $0.01/mile), and all gasoline powered cars get 30 MPG. In that case, if all vehicles are gasoline powered, the gas tax will be $0.30/gallon (or $0.01/mile), in line with current costs. Now imagine, only half of all cars pay the gas tax, the tax jumps to $0.60 to cover costs, still quite tolerable, but as the gas tax rises, the number of gasoline powered cars should be expected to fall. The following image shows the expected gas tax based on the above assumptions with a varying number of gasoline powered cars on the road. Note especially this is a log-log scale. At 50,000 cars with gasoline engines (95% non-gasoline powered), the tax jumps to $6.00 per gallon (above European levels), but the last car has to pay $300,000 per gallon. The move away from the gas tax is a positive feedback system that will accelerate. A replacement may be required.

Urban Transit (The "Mohring Effect") (+) Fixed-route urban transit networks also have the potential to exhibit characteristics of a positive feedback system through a process known as the "Mohring effect". Since the costs facing users of public transit services include elements such as the user's time, which has a fixed component to account for time spent waiting for a bus or train, it can be shown that at higher levels of demand waiting times decrease due to more frequent service. This, in turn, makes public transit more attractive. Thus, the setting of marginal cost fares should take into account relevant user time costs in order to achieve optimality. The Mohring effect may provide an efficiency rationale for the subsidization of some urban transit services.

The Mohring effect may arise through the provision of more frequent service on a single route, as described above, and also in a network setting. For example, if the density of routes in a network are increased, the time costs faced by users in accessing the nearest stop will decrease, again reducing the total cost of a trip.

Mode Choice and the 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.)

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. Mogridge[1] and others have hypothesized that this is indeed how congested transportation systems work in the absence of charges for road access. [1]

Is the left figure correct? Or does the second figure (right) more accurately reflect the empirical evidence? The best collection of evidence to date has been compiled in a review by Mogridge[2].

Network Externalities[edit | edit source]

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

Examples of networks[edit | edit source]

Examples of networks from communications include:

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

In transportation, networks examples include:

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

Examples of network externalities[edit | edit source]

Non-transportation examples of network externalities include

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

and anything else that has been standardized.

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

Terms[edit | edit source]

Terms that are often used in describing network externalities:

Agglomeration Economies[edit | edit source]

The idea of agglomeration economies has been long considered in urban economics. Transportation of one form or another drives these agglomeration economies.

The spatial economics literature observes: Specialized and diversified cities co-exist. Larger cities tend to be more diversified. The distribution of city-sizes and specializations tend to be stable over time. City growth is related to specialization and diversity. Relocations are from diversified to specialized cities. Assumptions include: crowding, agents, labour mobility, (endogenous) self-organisation, path-dependency, systems of cities (policentricity).

The following are some quotes about agglomeration:

  • “My purpose is to show that cities are primary economic organs” (Jacobs 1969, p.6).
  • “Development is a process of continuously improving in a context that makes injecting improvisations feasible. Cities create that context. Nothing else does” (Jacobs 1984, p.155).
  • “The city is not only the place where growth occurs, but also the engine of growth itself” (Duranton 2000, p.291-292).
  • “Large cities have been and will continue to be an important source of economic growth” (Quigly 1998, p.137).
  • “Agglomeration can be considered the territorial counterpart of economic growth” (Fujita and Thisse 2002, p.389).

Agglomeration, productivity and (urban) scale in a knowledge driven economy

  • "City-regions are locomotives of the national economies within which they are situated, in that they are the sites of dense masses of interrelated economic activities that also typically have high levels of productivity by reason of their jointly-generated agglomeration economies and their innovative potentials " Scott and Storper, 2003
  • "Metropolitan spaces are becoming, more and more, the adequate ecosystems of advanced technology and economy…. [T]he decrease of communication costs does not by itself lead to a spreading and diffusion of wealth and power; on the contrary, it entails their polarization." Veltz, 2005

The following table enumerates different types of scale (intra-firm) and agglomeration (inter-firm) scale economies.

Type of scale economy Example
Internal 1. Pecuniary Being able to purchase intermediate inputs at volume discounts
Technological 2. Static technological Falling average costs because of fixed costs of operating a plant
3. Dynamic technological Learning to operate a plant more efficiently over time
External or Agglomeration Localization Static 4. Shopping Shoppers are attracted to places where there are many sellers
5. Adam Smith Specialization Outsourcing allows both the upstream input suppliers and downstream firms to profit from productivity gains because of specialization
6. Marshall labor pooling Workers with industry-specific skills are attracted to a location where there is a greater concentration.a
Dynamic 7. Marshall-Arrow-Romer Learning-by-doing Reductions in costs that arise from repeated and continuous production activity over time and which spill over between firms in the same place
Urbanization Static 8. Jane Jacobs innovation The more that different things are done locally, the more opportunity there is for observing and adapting ideas from others
9. Marshall labor pooling Workers in an industry bring innovations to firms in other industries; similar to no. 6 above, but the benefit arises from the diversity of industries in one location.
10. Adam Smith division of labor Similar to no. 5 above, the main difference being that the division of labor is made possible by the existence of many different buying industries in the same place
Dynamic 11. Romer endogenous growth. The larger the market, the higher the profit; the more attractive the location to firms, the more jobs there are; the more labor pools there, the larger the market—and so on
12. Pure agglomeration Spreading fixed costs of infrastructure over more taxpayers; diseconomies arise from congestion and pollution

Source: World development report 2009: reshaping economic geography By World Bank [3], Adapted from Kilkenny 1998[4]

Standardization and Coordination Externalities[edit | edit source]

Image of Calculator Keypad: 0, 1, 2, 3 increasing from bottom to top.
Image of Telephone Keypad: 1, 2, 3 increasing from top to bottom, with 0 at bottom.

A typical remote control for Cable TV in the first part of the 21st century has up and down arrows to adjust channels. Pushing the up (plus) button will move you away from channel 0, while the down button will move you toward channel 0 (although if you reach the final channel, you will return to home). But remote controls also have a navigation for the onscreen guide - these have an up, down, left, and right arrow. The up arrow moves you through the onscreen guide, but here up move you toward channel 0, while down moves you away from 0. The left and right arrows move you forward or backward through time.

These remote controls have a further set of controls to operate an auxiliary device like a DVD or an inbuilt device like a personal video recorder. The left arrow, following the convention from tape recorders, plays (forward in time), while the double left arrow (on the right-most side) is fast forward and the double right-pointing arrow (on the left side) moves you in reverse (rewind). Other buttons do other things.

Complaints about the complexity of modern remote controls are hardly unique[5] . Each remote is custom for a particular box, so as people accumulate boxes attached to TVs, the number of remotes increases accordingly. The utopia of the universal remote remains unreached; one hopes the situation will not sustain for another few decades before standardization moves in, or some other interface becomes widespread.

Like remote controls, keypads are another area where conventions may confuse.

Keypads on telephones and calculators represent the same ten digits, however they have different layouts. The telephone keypad, introduced with the advent of Touch Tone dialing by the Bell System in the 1960s places 0 (or O for operator, it is not always clear on telephones) at the bottom, and then numbers digits 1 - 9 in three rows of three columns each from the top. A calculator keypad (also used on computer keyboards) on the other hand, while it places 0 at the bottom, numbers 1 to 9 also in three rows of three columns, but in this case beginning at the bottom, as shown in Figure. These conventions have carried over to computers, which could array numbers in any random way, but use the different conventions to represent the different devices. Newer devices, such as television remote controls, could use either, but typically follow the telephone layout (though some have original layouts themselves, e.g. going from 1 to 4 on the first row, 5 to 8 on the second row, and 9 and 0 on the third row).

For operating a television, rarely an urgent activity, the additional cognitive load of a poorly-designed or non-standard interface is annoying, but not dangerous. With the case of election ballots, such confusion and resulting error may change the outcomes (such as the odd butterfly ballot used in West Palm Beach, Florida in the 2000 Presidential election, resulting in a disproportionate (compared to other jurisdictions) number of votes for Pat Buchanan, and likely giving the state of Florida, and thus the United States electoral college and the presidency to George W. Bush).

American travelers trying to write emails in some European countries may note that the standard QWERTY keyboard found in the English speaking world (so-named for the keys on the top-row of letters) has been replaced by a keyboard, which mainly swaps the Y and Z, but has some minor changes, dubbed the QWERTZ kezboard. This is just enough to throw off touch-tzpists (er, typists). I am sure the confusion is two-way.

For driving cars in the United States, many functions have been fortunately standardized. The brake foot pedal is on the left, the accelerator on the right. The steering wheel itself usually performs as expected. Less critical functions remain confusing, especially when switching cars, or driving an unfamiliar vehicle, such as a rental car, the difficulty compounds as this is usually done in an unfamiliar place. Where is the windshield wiper? The light switch? The brights? The transmission control? The radio? The environmental controls? The locks? The window controls? The rear-view window control? The unlock for the trunk? The unlock for the gas tank? Where is the gas tank - driver or passenger side? All vary with make, model, and year of vehicle.

Driving on the left of the right is standardized locally, but not globally. As any traveler from continental Europe, North America, or South America knows, things differ on the islands of Great Britain, New Zealand, Japan, the Caribbean, and even the island-continent of Australia and the Indian subcontinent.

Traffic signals usually report red on top and green on bottom. What does it mean when the light is simultaneously red and green? Or red and yellow (amber), or green and yellow? Or the green light flashes? All of these patterns are local, but not global standards.

Construction of Revealed Demand (Fulfilled Expectation) Curve with Positive Network Externalities[edit | edit source]

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.

Rationale[edit | edit source]

Figure 1 constructs the revealed demand curves for positive network externalities. Let 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, (), the network is not particularly valuable, so the implicit demand at () is low, lower than at , which is lower than , etc. Drawing a line between the number of consumers () and the implicit demand curve at that number () traces out an approximately parabolic shape, .

Conditions[edit | edit source]

is the equilibrium price where the demand curve for a network of size () intersects the vertical projection of the network size when the number of consumers (network size) is . 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 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.”

Saturation[edit | edit source]

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[edit | edit source]

A - supply intersects demand twice: when cost is decreasing and demand is increasing, and when cost is increasing and demand is decreasing
B - supply intersects demand twice: when cost is decreasing and demand is decreasing, and when cost is increasing and demand is decreasing
C - supply intersects demand twice: when cost is decreasing and demand is increasing, and when cost is increasing and demand is increasing
D - supply does not intersect demand

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[edit | edit source]

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.

Other Concepts Related to Positive Feedback Systems[edit | edit source]

Companion-Innovation[edit | edit source]

(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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

Schematic of Logistic Growth Curve (S-Curve)


Increasing and Decreasing Returns and Equilibrium[edit | edit source]

(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.

How Networks Grow[edit | edit source]

To start, a network must 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.

Thomas Hughes said "Mature systems suffocate nascent ones".[6] This means that well-developed technologies occupying a particular niche make it very hard for a new technology to move into that niche, since it does not have all of the compatible infrastructure and correlated compatible technologies.

Where Does Intelligence Lie[edit | edit source]

  • Smart Networks, Dumb Packets/Vehicles (Railroads, Telephone)
  • Smart Packets/Vehicles, Dumb Networks (Roads, Internet)

Important to resolve this in network design

Network Design vs. Network Growth[edit | edit source]

Network Design Problem (NDP) tries to determine “optimal” network according to some criteria (Z). - Normative

E.g. Maximize Z, subject to some constraints.

Network Growth Problem tries to predict actual network according to observed or hypothesized behaviors. - Positive

Questions[edit | edit source]

  • Why do networks expand and contract?
  • Do networks self-organize into hierarchies?
  • Are roads an emergent property?
  • Can investment rules predict location of network expansions and contractions?
  • How can this improved knowledge help in planning transportation networks?
  • To what extent do changes in travel demand, population, income and demographic drive changes in supply?
  • Can we model and predict the spatially specific decisions on infrastructure improvements?

Network Growth[edit | edit source]

  • Depends on existing and forecast transportation demand
  • Depends on existing transportation supply
  • Network can be viewed as output of a production function: N = f( D, S)

Over the long term, we expect networks to grow in the fashion of an S-Curve as discussed in the Lesson on Positive Externalities

How networks change with time[edit | edit source]

  • Nodes: Added, Deleted, Expanded, Contracted
  • Links: Added, Deleted, Expanded, Contracted
  • Flows: Increase, Decrease

The Node Formation Problem[edit | edit source]

  • Christaller’s Central Place Theory (CPT) sought to answer: How are urban settlements spaced, more specifically, what rules determine the size, number and distribution of towns? Christaller’s model made a number of idealizing assumptions, especially regarding the ubiquity of transport services, in essence, assuming the network problem away. His world was a largely undifferentiated plain (purchasing power was spread equally in all directions), with central places (market towns) that served local needs. The plain was demarcated with a series of hexagons (which approximated circles without gaps or overlaps), the center of which would be a central place. However some central places were more important than others because those central places had more activities. Some activities (goods and services) would be located nearer consumers, and have small market areas (for example a convenience store) others would have larger market areas to achieve economies of scale (such as warehouses).

Central Place & Network Hierarchy[edit | edit source]

Network Hierarchy is much like Central Places (Downtown Minneapolis, Suburban Activity Centers (e.g. Bloomington, Edina, Eden Prarie), Local Activity Centers (e.g. Dinkytown, Stadium Village, Midway), Neighborhood Centers (4th Avenue & 8th Street SE).

Central Places occur both within and between cities. Hierarchy: Minneapolis-St. Paul; Duluth, St. Cloud, Rochester; Morris, Brainerd, Marshall, etc.; International Falls, etc.

Exercise[edit | edit source]

Further reading[edit | edit source]

Thought Question: Applications of Positive Externalities[edit | edit source]

  • 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)?

References[edit | edit source]

  1. a b Mogridge, Martin J.H.; Holden, D.J.; Bird, J.; Terzis, G.C. (1987). "The Downs/Thomson paradox and the transportation planning process". International Journal of Transport Economics. 14 (3): 283–311. {{cite journal}}: Unknown parameter |month= ignored (help)
  2. Mogridge, Martin J.H. (1997). "The self-defeating nature of urban road capacity policy: a review of theories, disputes and available evidence". Transport Policy. 4 (1): 5–23. doi:10.1016/S0967-070X(96)00030-3. {{cite journal}}: |access-date= requires |url= (help); Check date values in: |accessdate= (help); Unknown parameter |month= ignored (help)
  4. Kilkenny, Maureen (1998) "Economies of Scale" Lecture for Economics 376, Rural, Urban, and Regional Economics, Iowa State University, Ames Iowa
  5. Nielson, J. (2004), ‘Remote Control Anarchy’.
  6. Hughes, Thomas Parke (2004) American genesis: a century of invention and technological enthusiasm 1870-1970 p. 461
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