Negative externalities and property rights

Overview

This application was inspired by Roy Ruffin's 1996 article "Externalities, Markets, and Government Policy" (https://www.dallasfed.org/~/media/documents/research/er/1996/er9603c.pdf). It shows two parties, one of whom harms the other in the process of producing a service. The application focuses on the game theoretic modeling of the situation, the contrast between Nash equilibria and social optima, the impact of negotiation on efficiency, the impact (or lack thereof) of the allocation of property rights, the impact of a Pigovian tax, as well as the allocation of its tax revenue.

Expected Student Learning Outcomes

- Model a strategic scenario using game theory
- Evaluate the possible efficiency and welfare implications of externalities
- Explain, compare, and evaluate market-based and government-based solutions to externalities

Information Given to Students

Before tackling this applications, students have read the chapter on externalities. Furthermore, they have solved in class another application that focused on the graphical analysis of externalities.

The purpose of this application is to go beyond the graphical analysis and show a game-theoretic interpretation of a scenario exhibiting externalities, highlighting aspects that are not immediately evident in the graphical analysis, like the importance of who receives (or rather, who should not receive) the revenue from a Pigovian tax. This application also makes evident the reasoning that led to the Coase theorem.

After a very brief description of the scenario (first paragraph), part 1 asks students to analyze this scenario with the graphical tools they have used in a prior application. Note that the textbook covers this graphical analysis, but not the game-theoretic analysis students will have to do on their own.

A couple of paragraphs describe the scenario in more detail, defining specific players, strategies, and payoffs. Occasionally teams may need a clarification or reaffirmation of what happens in certain instances (for example, what's the damage to the farmer if two trains run across two planted fields).

Part 2 asks students to construct a payoff matrix. You may want to ask students to have Liz or Union Pacific on the rows, as player 1. Once everyone agrees on the same payoff matrix after some discussion, you can move on to part 3.

Parts 3 and 4 can be done in one step, without comparing team answers in between. This is the second application in this module where students have solved for Nash equilibria, but it is the first time they are dealing with a 3x3 payoff matrix, and the first time they see a Nash equilibrium that is not in strongly dominant strategies. This may possibly lead to some confusion if a student had not previously fully understood how Nash equilibria work (how can I solve for Nash equilibrium if Liz doesn't have a dominant strategy?). Having teams exchange approaches on solving for Nash equilibria would be useful. The instructor should make sure everyone understands proper ways of finding Nash equlibria, and that not all strategies are dominant or dominated.

Part 5 focuses on negotiation as a means to reach a higher joint payoff, so that the Nash equilibrium coincides with the "socially-optimal outcome" (with emphasis at the beginning of the exercise that for now we are focusing on this very narrowly defined society of two). Teams can come up with different payoffs that are successful. In the discussion across teams, it is useful to reach a more general result, with a range of payoffs that satisfy our requirements.

Parts 6 and 7 reverse the property rights, and allow students to discover that the same issues come up in this instance, and that negotiation still can lead to the socially-optimal outcome. This result naturally leads to a discussion of the Coase theorem, and the conditions under which it applies. This discussion can first start within teams, then extend to discussion across teams.

Part 8 shows how an appropriate Pigovian tax changes the incentives in such a way that the Nash equilibrium coincides with the socially efficient outcome. Students may be confused as to what is socially efficient in this case, since they may only focus on the payoffs to the farmer and Union Pacific, whereas the tax revenue used to provide services in another part of the country is also relevant. This is a good time to highlight the similar outcomes of the game-theoretic analysis vs. the graphical analysis used in the textbook.

Part 9 shows something that was not evident in the graphical analysis: the revenue from the Pigovian tax should not go to the victims of the negative externality. If that happened, those affected by the negative externality would actually increase their activities, resulting in an inefficient outcome.

Another option would be to replace Part 9 with a discussion on the fairness of the different payoffs that come from different property rights.

I love the richness of this exercise.

Note that in my class each team has a small whiteboard (sometimes called a huddleboard) to respond to most questions, and they share their results by raising their whiteboards simultaneously (the whiteboards/huddleboards are small and light enough that they can be raised by one person, and they are big enough that everyone can observe the results of all other teams).

Observation of student answers and discussion. Capstone test at the end of the module. The final exam also tests these learning outcomes.