Chapter 5. Public Goods as “Missing Markets”

Chapter 5. Public Goods as "Missing Markets"

The previous chapter considered positive and negative externalities as one type of situation in which "missing markets" result in non-optimal levels of private goods production and consumption. In this chapter, we consider a case in which missing markets result in nonoptimal levels of a public good?it turns out that the two cases are frequently related.

First, we must know what is meant by a "public good." A good is not defined as a public good just because it is provided publicly. A school lunch, for example, is a private good regardless of whether the parents send their students to school with their lunches or whether the lunches are provided publicly (funded with higher tax payments) by the school. It is the case, however, that public goods must generally be provided publicly because, as we shall see, their nature makes them unprofitable to provide privately.

A pure public good is defined by two traits, both critical to its definition. For a good to be a pure public good it must be both non-rivalrous in consumption and non-excludable in consumption. A private good, say a hamburger or t-shirt, is rivalrous in the sense that if you eat the hamburger or wear the t-shirt, nobody else can. A good is non-rivalrous in consumption if any individual's consumption of the good does not affect the ability of others to consume the good.

For example, the light from a lighthouse has the property that if you look at it to avoid the dangerous rocks, it does not diminish the ability of anyone else to receive the same benefit. National defense, a court system, the radio and television airwaves, global positioning signals, and other goods share this property. Examples for environmentalists would be species preservation (if the species is saved the benefits you receive do not reduce the benefits I receive) or CO2 abatement (your consumption of a less-warm earth does not diminish my ability to enjoy

the benefits from a less-warm earth).1 But the second trait defining pure public goods is equally critical to understanding their

nature. A pure public good must be non-excludable in consumption. For ordinary private goods, the customer must pay for the good or they are unable to acquire it, for example the hamburger or t-shirt already mentioned. Consider again, however, the light from the lighthouse. If the lighthouse gets built and operating, it is not possible to exclude anybody from benefitting from the light. If the species gets saved you cannot be prevented from receiving the benefits you associate with saving that species.

The non-excludability of pure public goods is the trait that is critical to why such goods are not profitable to supply privately. Suppose, for example, that you were considering building a large air filtration system that would clean up your air, but also many hundreds or thousands of peoples' air downwind from you. So, you approach them asking for donations to help pay for the expensive contraption that will benefit everyone. Each household you approach will realize two things: 1) it is too small to make a difference on whether the contraption actually gets built or not, and 2) if the contraption does get built it cannot be excluded from receiving the benefits whether it pays or not.

Another example: Someone knocks on your door and asks you to contribute toward saving the blue whale from extinction. You might say "Sorry, but you caught me at a really bad time...I have tuition to pay and school books to buy and my rent has gone up." But, you also know that the whale is either going to get saved or it isn't and the amount that you would truly be

1It should perhaps be noted at this point that, depending on provision level, a public good for one person can be a public bad for another. For example, some people feel that we have too much national defense while others think we have too little. In the global warming case, a person in Siberia might benefit from global warming while a person in Bangladesh might be harmed. In most of the contexts we will be focusing on, this distinction will not be critical to understanding.

willing to pay to save it (say $10) will have a negligible impact on the outcome. Whether the whale gets saved depends on what the other 120 million households do?if they each give $10, that adds up to $1.2 billion dollars and the whale just might get saved. But the odds of your $10 being decisive are vanishingly small. So, if you keep your $10, you can go buy two pitchers of beer to toast to the saving of the whale (if it gets saved), or you can go buy two pitchers of beer, sadly toasting to the demise of the whale (if it doesn't get saved). You have an incentive to be a "free rider," and you are just like everybody else. Since everyone has an incentive to free ride,

the ride doesn't exist?the whale goes extinct. So we have another case of a "missing market," depicted for the case of public goods in

Figure 5.1 above. But, unlike the case of externalities discussed in the previous chapter, in this case the market for saving whales or cleaning up the air doesn't exist at all. No suppliers enter the market because they cannot get demanders to pay them for something they cannot be excluded from receiving for free. Hence, in Figure 5.1 zero is produced, instead of Q* (the level

of the public good that equates marginal benefits and marginal costs). The private sector will not produce public goods, so the public sector will have to, if we

are to consume the mix of private and public goods that we desire...the mix that gives us maximum welfare given our preferences. Note, however, that Figure 5.1 is drawn "as if" we really knew where the marginal benefit and marginal cost curves are located. If we actually did have that information, it would be a trivial matter for the government to produce the optimal, Q*, level of the public good. But, of course, we do not know the position or slope of either curve is in Figure 5.1 (though the marginal cost curve is viewed as being much easier to pin down). Much of the rest of this book is about how economists attempt to ascertain where the MB curve is in Figure 5.1. If we think it is further to the left than it really is, we will under-produce the public good; if we think it is further to the right than really is, we will over-produce the public good. For reasons presented throughout the remainder of this book, the former situation?underprovision of public goods?is far more likely to occur in practice.

It should be emphasized that aggregating from individual preferences for the public good to the "market demand curve" (the MB curve in Figure 5.1) works differently from how individual preferences were aggregated for ordinary private goods when aggregating from individual to market demand. The appropriate question in the case of ordinary private goods is "How many hamburgers will be demanded at $3.00?" "How many at $2.00?" These hypothetical questions are asked for all possible prices, and market demands are the sum of individual demands. That is, we add up individual demands horizontally to find out how many hamburgers will be demanded at various prices and compare that to the number of hamburgers that will be supplied at those prices. If the aggregate quantities demanded equal the aggregate quantities supplied, the price is in equilibrium...otherwise it will either rise (if quantity demand

exceeds quantity supplied) or fall (if quantity supplied exceeds quantity demanded) as discussed in Chapter 2.

For public goods we add individual demands vertically not horizontally. That is, the appropriate question now becomes "How much will people collectively value a one-unit increase in the public good?" That this is the appropriate question stems from the fact that if a one-unit increase in the good takes place, we all get to consume that increase. If we clean up the air, the benefits of the sick and rich (which might be high) will be added to the benefits of the poor and healthy (which would be lower) to get an aggregate benefit. If that aggregate benefit exceeds the marginal cost of providing the one-unit increase, society will be better off collectively, on efficiency grounds, if the unit is produced. As long as the vertically aggregated marginal benefits exceed the marginal provision cost, we are collectively better off continuing to increase the public good (to the level Q* in Figure 5.1). If we really knew where the MB and MC curves were in Figure 5.1, the quantity of the public good that we would choose to produce would be exactly analogous to a perfectly functioning private market. We would, in this case, have the right amounts of all goods private and public.

So far, we have talked only about pure public goods, goods having both of the properties of non-rivalry and non-excludability. But it is possible to have any combination of rivalrous/non-rivalrous and excludability/non-excludability. While private goods, that are both rivalrous and excludable, and pure public goods, that are both non-rivalrous and non-excludable, are extreme cases, some intermediate cases are of great importance to environmentalists.

For a case of non-rivalry but excludability consider, up to the point of congestion, rides at an amusement park. The rides are non-rivalrous?Andrew's consuming a ride does not diminish the ability of Barbara to take a ride. But, access to the park is controlled by the owner with

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