It's Infrastructure Week!

Is price theory infrastructure?

It’s been infrastructure week for the past 4 years now. The federal government might actually be serious this time — although that might depend on your definition of infrastructure. In today’s post, I would like to discuss things like roads, bridges, and tunnels and how we determine what they’re worth and when to replace them.

When thinking about infrastructure, it is important to remember that infrastructure fits into the category of a durable good. These types of goods last for a long time and provide a flow of services over time. This characteristic is important for determining the good’s value.

My car is a durable good. I get a flow of services from my car over time. Of course, the value of the flow of services I get from my car today is worth more to me today than the flow of services I get from my car a year from now. As a result, I discount these future benefits. My car will also require periodic maintenance. Again, these maintenance costs will be paid for over time. Even with the maintenance, my car will depreciate over time as well. When thinking about how much I should pay for my car, I should be willing to pay an amount equal to the present value of the flow of net benefits that I will receive from my car over the life of the car.

Is the price I pay for the car really the cost of buying the car? Suppose that the net present value of the flow of benefits I expect to receive from the car is $40,000 (let’s pause to let the urbanites on Twitter recoil). I should therefore be willing to pay up to $40,000 for the car. Suppose that after I buy the car, I could re-sell it at any time for $30,000. How much did the car cost?

This framing can help us to think about infrastructure.

Periodically, we are told that the infrastructure in the U.S. is crumbling and that we need to replace some of our roads and bridges and tunnels. Yet, many are skeptical of these claims. How can we evaluate the claim that we need to replace some of our existing infrastructure?

I have actually thought a lot about this and I even wrote down a model. We can start by thinking about things in the way that Alchian did, in terms of present value. The existing infrastructure that we have provides us with a flow a services over time. Replacing this existing infrastructure new infrastructure provides us with a new flow of benefits, but requires a large, upfront cost. One might be tempted to say that the cost of replacing the infrastructure is the large, upfront cost. However, that is the accounting cost. It is not the economic cost. The economic cost would not only include the accounting cost, but also the remaining value of the existing infrastructure that would be given up by replacing it. In other words, if we tear down a bridge and build a new one. We get a flow of benefits from the new bridge, but we have to pay for that new bridge and, at the same time, we lose the flow of benefits that we would have received from the old bridge.

How do we determine when to replace the bridge?

The simplest answer is to replace the bridge when the net present value of the new bridge exceeds the sum of the remaining net present value of the old bridge and the cost of building the new bridge. However, this is not correct.

To understand why, consider the trade-off that a decision-maker would face in this scenario. The net present value of the old bridge is declining as time goes by due to things like wear and tear. The longer the decision-maker waits, the lower the cost of replacement and therefore the bigger the net benefit of replacement. However, the longer that the decision-maker waits, the lower the present-value of replacement. Thus, if we know how much the value of the existing bridge will decline each year, we can determine how many years to wait before replacing it by optimally balancing this trade-off. Sometimes the optimal thing to do is wait.

This seems like a pretty useful result since it tells us exactly when the existing bridge should be replaced given the economic costs of doing so. This allows us to evaluate claims about whether or not the bridge needs to be replaced and it gives us a way to plan for the future since we know exactly how long it will last.

Unfortunately, however, life isn’t that simple.

There is often uncertainty about how the value of the existing infrastructure evolves over time. Since the value of the existing bridge is measured in terms of net present value, the value of this bridge might be unexpectedly higher next year because of a mild winter or lower input costs associated with maintenance. On the other hand, the value of the bridge might be unexpectedly lower year because of a harsh winter or higher input costs associated with maintenance.

Even though this uncertainty makes it impossible to determine the precise amount of time that the bridge will last, the problem faced by decision-makers remains the same. In fact, the decision-maker can still determine a threshold for replacement. However, instead of choosing a threshold based on the amount of time that the existing bridge should be used, the decision-maker can determine a threshold for the remaining value of the bridge. In other words, the decision-maker can specify a threshold for the value of the existing bridge such that whenever the value of the bridge falls below that threshold, it should be replaced.

What I show in the paper is that this threshold value for the existing infrastructure will be a fraction of the net present value of the new infrastructure (less the construction cost). How small this fraction is will be determined by the characteristics of the existing infrastructure.

What is interesting about this is that uncertainty actually encourages decision-makers to have a lower threshold for the value of existing infrastructure. The reason is that uncertainty always leaves open the possibility that you can get one more year out of the road or the bridge before having to replace it. The presence of uncertainty therefore suggests that we might want to allow existing infrastructure to live a little longer at the margin.

Overall, this sort of framework for thinking about infrastructure gives us a way to evaluate claims that our infrastructure desperately needs replaced because it allows us to derive specific thresholds for replacement. In doing so, it might be possible to be more transparent about what needs to be done now, what might need to be done in the future, and what doesn’t need to be replaced any time soon.