Tutorial Notes: Public Goods Jeff Hicks November 12, 2017 Vancouver School of Economics, University of British Columbia, jeffrey.hicks@ubc.ca 1
In this note, I ll cover some basic examples of public goods, why they are often underprovisioned, and some policy approaches to correct under provision. Definitions of Public Goods Let s define two important characteristics of goods: 1. Excludability: A good is non-excludable if people cannot be stopped from using it. 2. Rivalry: A good is non-rivalrous if one person s consumption does not crowd-out other people s use of it. Definitions of public goods: 1. Pure Public Good: Both perfectly non-excludable and perfectly non-rivalrous. These are rare. Lighthouses. Military Defense. Pollution Abatement: We can t restrict the benefits of clean air (non-excludable) and my consumption of clean air does not reduce yours (non-rivalrous). 2. Impure Public Goods: These have some degree of non-rivalness and non-excludability. Highways are often cited as public goods. But highways can get congested (rivalrous), and highways can have tolls (excludability). Fish stocks are often non-excludable, despite regulators efforts, but are certainly rivalrous. Efficient Provision of Public Goods Think about two scenarios. In the first, the public good is a discrete project. For instance, build a bridge or don t. In the second, the public good is not discrete. For example, there are varying levels of public defense a country can choose, or a varying amount of pollution abatement. In the discrete case, the socially optimal choice is to build the bridge if the sum of everyone s private benefits is greater than the cost. Or in Kevin s slides, the socially optimal choice is to purchase the Netflix subscription if the sum of all three room mates valuations is greater than the subscription fee. 1
In the non-discrete case, the optimal amount of the public good (G ) is where marginal social cost is equal marginal social benefit. The marginal social cost is the marginal cost of production. The marginal social benefit is the sum of every individual s marginal private benefit. In Kevin s slides, he demonstrates this graphically: sum everyone s private individual marginal benefit curves vertically, and the optimal amount is where the social marginal benefit intersects the social marginal cost. Example: Climate Change Coordination Let s do a simple example. Assume there are only two countries on Earth, China and the U.S. Scientists have warned both countries that without reductions in carbon emissions, harmful consequences will ensue. Both countries recognize this, but abatement efforts are a public good: China cannot exclude the U.S. from the benefits of China s abatement efforts, nor vice versa. Let s represent this dynamic as follows: U.S. China Abate Ignore Abate (75, 75) ( 50, 100) Ignore (100, 50) ( 25, 25) Each country can take action or ignore. I m making this a discrete game: abate or ignore. But in reality, there are various levels of abatement countries could undertake. The boxes describe the net payoff (benefit- cost) to each country in each of the four outcomes. Here is how to read the box: Both countries abate: both countries get 75. China abates and U.S. ignores, China gets -50 and U.S. gets 100. abatement is costly. This is because U.S. abates, China ignores, U.S. gets -50, China gets 100. Both ignore, both get -25. The socially optimal decision is for both countries to abate. It is socially optimal because it generates the highest total benefit (75 + 75). 2
The problem is free riding. If the U.S. knows China will abate, then the best decision for the U.S. is to ignore. And likewise for China. Consequently, both countries ignore. As always, this is a very simplified version of reality. But the logic is clear. The incentive for countries to free ride makes it difficult for coordination. Now imagine there are over 100 countries to coordinate amongst, with constantly rotating elected officials in each one. Coordinating on international treaties becomes even harder. In general, the free rider problem will become worse as the number of potential agents rises. Example: Radio Broadcasts Radio broadcasts are available to everyone (non-excludable) and non-rivalrous. They fit the definition of a public good. Radio companies have circumvented the public-goods problem by earning advertising revenue. But there may still be under-provision. Canada runs a public radio company partially for this reason. Let s use it as an example. The public good is the number of radio shows. The marginal benefit curve for each individual is MB = 300 10Q - all individuals are identical for simplicity. There are 100 individuals. The marginal cost is MC = 5000Q. Let s add the marginal benefit curves vertically, as illustrated in Kevin s slides: MB social = MB 1 + MB 2 +...MB 100 = 100 (300 10Q) = 30000 1000Q. (1) Now, to find the optimal amount of public provision, set MB social = MC. 30000 1000Q = 5000Q (2) Q = 5 (3) So the optimal number of radio shows is 5. Implementing the Socially Optimal Choice The challenge then is twofold: a) how to truthfully elicit people s valuations, and b) how to fund the project. 3
Ideally, the government charges everyone according to their marginal benefit (Lindahl pricing). In the radio example from above, what would be the Lindahl price for each individual? It is the marginal benefit: MB = 300 10 5 = 250. But this is obviously challenging for two reasons. First, the government does not know each individual s marginal benefit. Eliciting truthful information from would-be consumers is challenging. If the government said: Jeff, tell me your marginal benefit, so I can charge you that amount, I will understate my true valuation. Mechanism design is one area of research that examines how the government properly incentivize consumers to provide truthful valuations. We won t cover that here, but interested readers should pursue further. Tyler Cowen s article, referenced on Kevin s website, is a good overview of other typical solutions to the public goods problem. 4