# Experiment 3 Pollution, taxes, and permits

## 3.1 Introduction

### CORE projects

Concepts in the experiment are related to the material in:

What policies are effective in mitigating negative externalities like pollution? In the presence of negative externalities, markets fail to attain efficiency, and competitive trading usually leads to inefficient outcomes. Can an appropriately chosen tax improve efficiency? Could such markets be regulated efficiently using a fixed supply of tradable pollution permits?

This experiment presents a competitive market where students act either as mine owners or as demanders of coal, used for heating their homes. Burning coal emits soot particles, which amount to a total pollution cost of €20 for every unit of coal traded. The total pollution cost is equally distributed among all the participants.

The experiment consists of three scenarios that share the same distribution of suppliers and demanders:

1. a coal market with no government interference, resulting in an equilibrium with ‘too many’ trades;
2. the coal market with a ‘pollution tax’ that equals the total cost of the negative externality; and
3. the coal market with the extraction of coal regulated using the efficient number of marketable pollution permits. Scenarios 1 and 2 can be played online or in class. Scenario 3 can only be played in class and uses paper pollution permits.

Trading can be ‘online’, where students post buying and selling offers and transactions result from accepting standing offers; or ‘offline’, where negotiations are done verbally and, once an agreement is reached, students type in the agreed price on their devices. While online sessions can only use online trading, in-class sessions can use either online or offline trading.

The experiment provides students with the experience of a market in the presence of a negative externality. It gives them an insight into the functioning of Pigouvian taxes and pollution permits. Using the data of the experiment, students will be able to draw step demand and supply functions (see, for example Exercise 8.3 in The Economy), compute surplus and inefficiency, and compare the theoretical predictions with the experimental outcomes. It also helps students to understand the concept of market equilibrium and the differences between social and private marginal costs.

You may find it useful to read about the experiences of instructors before getting into the detail of setting up the experiment, especially if you are new to running classroom experiments.

This experiment is based on ‘The Coal Market Experiment’ from Experiments with Economic Principles by Ted Bergstrom, Marcus Giamattei, Humberto Llavador, and John Miller.

### Key concepts

This experiment will help students understand the following key concepts:

• Market failure
• Negative externality
• Pigouvian or corrective tax

## 3.2 Requirements

### Timing

You can conduct a two-scenario session (coal market and pollution tax) in 30 minutes or less. If things go smoothly, you should be able to run all three scenarios (including pollution permits) in a 50-minute session. Running the experiment online will speed up the transaction process, but reduces personal interactions between students since it does not allow them to shop around and experience the process of negotiating a price.

### Resources

Instructors and students need a smartphone, tablet, or laptop that has a web browser and is connected to the Internet. The Market and Tax Scenarios can be conducted online or in class. The Permits Scenario only works in class and requires printing the permits beforehand (a permit print-out PDF is available). For in-class experiments, a projector is necessary to help with instructions, results, and discussion. The experiment will be run in classEx.

### Number of participants

The experiment functions well with groups of very different sizes. In our experience, it works best with groups of between 25 and 50 students. A minimum of 12 students is needed to have at least one participant of each type. Small groups require special attention to ensure market competition. Also, because the pollution cost per transaction is constant, in very small groups students may become too aware of the pollution cost they suffer from their own transactions, partially internalizing the externality. Very large groups may slow down trading and make the convergence to equilibrium in only two rounds more difficult. As an alternative, you could split the class and run parallel markets, telling students that each one represents a different island or city.

## 3.3 Description of the experiment

In this experiment, students act either as suppliers (mine owners) or as demanders of coal that is used for heating homes. They can sell or buy at the most one unit of coal. Every trade imposes a total pollution cost of €20. The total cost of pollution is equally distributed among participants. Demanders are endowed with a Buyer Value, representing their different valuations for a warmer house, while suppliers have a Seller Cost, representing the different extraction costs. The distribution of buyer values and seller costs stays constant throughout the experiment.

You can easily substitute the concept of ‘scenario’ for ‘experimental treatment’ if it works best for your class. In Experiencing Economics, we use the term ‘scenario’ to be less technical and more flexible.

The experiment consists of three scenarios. Scenarios 1 and 2 can be played online or in class. Scenario 3 can only be played in class and requires paper permits. Each scenario has two rounds.

• Scenario 1 (market) represents a market with no government interference, resulting in an equilibrium with ‘too many’ trades. Students obtain the profits of their transaction, minus pollution costs that are calculated at the end of the round. The level of pollution depends on the number of transactions. Those who do not trade obtain negative gains equal to the pollution cost (that is, they do not gain from trading but still suffer from the level of pollution).
• In Scenario 2 (taxes), a pollution tax is subtracted from the profits of each supplier who sells. This tax is set at €20, equal to the total cost of the negative externality caused by one trade. (The revenue collected from the tax is divided equally among all participants in the experiment at the end of each round.) With the pollution tax, the only trades that should take place are those that make positive net profits, once the total amount of pollution cost they cause is subtracted from the buyer’s and seller’s profits.
• In Scenario 3 (permits), pollution control is managed by means of marketable pollution permits. The number of pollution permits issued is equal to the efficient number of trades (those consistent with maximizing total profits, net of pollution cost). Everyone who sells a unit of coal must possess a pollution permit. Those who do not initially own a pollution permit can buy one from individuals who are endowed with a permit. Students may obtain profits from the coal market, as in Scenario 1, as well as from the pollution permits market. As before, pollution costs are subtracted from the profits of each participant.

You can choose between online trading, where students send buying and selling offers through their devices, and transactions result from accepting standing offers; or offline trading, where students negotiate verbally and transactions are formalized once students input and accept the agreed price on their devices. Obviously, online sessions can only use online trading. While in-class sessions can use either online or offline trading, we recommend offline trading if your group is not too large and students can easily move in the classroom to shop around.

## 3.4 Step-by-step guide

### Detailed instructions

Go to the ‘Quick summary’ section if you have previously run the experiment and just need a brief reminder of the instructions.

The full experiment would run all three scenarios, analysing the effects of both a Pigouvian tax and tradable pollution permits to regulate the externality. But it is also possible to restrict the analysis to just the effect of a Pigouvian tax by running only Scenario 1 (‘Trading in Scenario 1’), that acts as the baseline, and Scenario 2 (‘Trading in Scenario 2’). You can run the scenarios as follows:

• in class: Scenarios 1 and 2, or Scenarios 1, 2, and 3 (with paper permits). Trading can be ‘online’ or ‘offline’.
• online: Scenarios 1 and 2 only (the Permits Scenario cannot be run online). Trading has to be set ‘online’.

In online trading, students send buying and selling offers on their devices, and transactions result from accepting standing offers. In offline trading, students negotiate and transactions are formalized once students input and accept the agreed price on their devices.

1. Enter the Pollution, Taxes, and Permits game in the CORE tab in classEx. Click ‘Play’.
2. Once all your students are logged into classEx, open the parameters window, introduce the number of players and choose ‘Trading of Coal’ = ‘Offline’ if you are running an in-class session with offline trading, or ‘Trading of Coal’ = ‘Online’ if you are running the experiment online or in class with online trading. The other parameters are only necessary if you are running the scenario with pollution permits. They are described in the instructions for Scenario 3. Throughout this section, we will use the default settings (Figure 3.1), which assumes online trading, 31 participants, and 7 permits. See the ‘Advanced settings’ section for details.

Remember to type the number of participants in the parameters to ensure the correct calculation of individual pollution costs and the right distribution of types.

Figure 3.1 Parameter values for a class of 31 students, 7 permits, and online trading. See the ‘Parameters’ section for a detailed explanation.

1. Make sure students understand the instructions. Ask if there are any questions, and then proceed to Scenario 1.

Remind students that trading is not mandatory and that zero profits are better than losses.

#### Trading in Scenario 1 (baseline): A market without government intervention

1. Click the ‘Start’ button. Before students start trading, announce that in all scenarios of this experiment, each unit of coal that is sold will cause €d worth of pollution costs to each participant. The individual pollution cost d is displayed on the instructor’s screen (Figure 3.2). Note: the individual pollution cost is calculated as d = 20/P, rounded to two decimal points, where P is the number of participants.

Figure 3.2 Instructor’s screen showing individual pollution costs equal to €0.65 per transaction, corresponding to a class of 31 students. Remember to type the number of participants in the parameters of the game to obtain the correct individual pollution costs.

1. Students will see on their devices the screen shown in Figure 3.3, depending on whether they are suppliers or demanders, respectively.

Figure 3.3 Student’s screen for an online trading session. For offline trading, the demander’s screen does not include a ‘Buy’ button because students negotiate the price verbally and only the seller needs to type in the price agreed to submit the transaction.

A coal miner (supplier) with seller cost of €18.

A demander with a buyer value of €35.

1. Give students enough time to trade. After trading stops, end the round by clicking the ‘Feedback’ button. Students will receive feedback showing the results of this round, including pollution costs (an example is shown in Figure 3.4).

If the number of trades made were T and the damage caused by each trade to each participant were €d, every person who participated in the experiment (even those who didn’t make any trades) would have pollution costs of (T × d).

Figure 3.4 Feedback in the Market Scenario for a coal miner with seller cost of €18 who sold at a price of €23. Pollution costs per person in the round amount to €8.39.

1. Repeat steps 1–3 if you wish to run a second round. It may be sufficient to run just one round, especially if students have already participated in other experiments with a similar trading mechanism.

In your last round, after sending feedback, ask students to keep a record of their profits or losses in this round. We will use this information in the discussion.

#### Trading in Scenario 2: A pollution tax

In Scenario 2, trading proceeds as in Scenario 1. But a €20 pollution tax is subtracted from the profits of each supplier who sells a unit of coal. It is a good idea to emphasize the fact that they should make a trade only if it doesn’t cause them to lose money. Repeat that zero profits are better than negative profits.

Figure 3.5 Feedback in the Tax Scenario for a coal miner with seller costs of €13 and who sold one unit of coal for €34. Pollution costs are offset by the tax transfer.

1. After trading stops, end the round by clicking the ‘Feedback’ button. Students will receive feedback showing their results for this round, including pollution costs and the tax transfer (an example is shown in Figure 3.5).

The total revenue collected from the pollution tax is distributed in equal shares to all participants in the experiment. As before, pollution costs are subtracted from the profits of each of the participants. Thus, in a round of Scenario 2 where there are T trades and P participants, when calculating a student’s profits, classEx automatically subtracts T × €20/P = T × d in pollution costs and adds €20 × T/P as a tax transfer.

The Pigouvian tax of €20 is set to match exactly the pollution cost from each transaction.

1. Repeat step 1 if you wish to run a second round.
2. In your last round, after sending feedback, ask students to write down their profits or losses on a piece of paper. We will use this information in the discussion.
3. Before starting the Permits Scenario (if you are running it) you may want to open the discussion on ‘voting on a pollution tax’.

This scenario adds a degree of complexity because it involves two simultaneous markets—the coal market and the pollution permit market, and currently can only be run in the classroom. Mine owners cannot supply coal until they have obtained a permit. The amount a mine owner is willing to pay for a permit depends on the price that they can expect to receive from selling a unit of coal.

Permits are traded offline using paper permits (see Figure F in the ‘Student instructions’ section). Suppliers need a permit code to sell their unit of coal. The instructor should keep the permit code secret and provide it to the seller in exchange for a permit. The default permit codes are 53398 for Round 1 and 12788 for Round 2, but they can be personalized in the parameters of the experiment.

To run this scenario, proceed as follows:

1. Print enough permits in advance, using the permit print-out PDF, and cut them apart. Use the formula in the box below to calculate the number of permits per round to be printed. Before each round of Session 3, distribute the pollution permits, preferably to types 5, 8, and 11. Types represent the different roles (Figure 3.8) and students can check them on their screens (for example Figure 3.3 shows the screens of types 2 and 3). Types 5, 8, and 11 are the least likely to make a transaction in the market for coal and hence have all the incentives to trade their permit. Also, the revenue from selling the permit helps to compensate for their bad luck in the allocation of roles.

### Number of Pollution Permits to Print

Let P be the number of participants. Let N and R be the quotient and the remainder of the division P/12, so that P = 12 × N + R. If R < 6, you need to print p = 3N permits for each round you plan to run. If R ≥ 6, p = 3N + 1. For example, in a class of 31 students you need 7 permits per round, since 31/12 = 2 × 12 + 7, and hence p = 3 × 2 + 1 = 7.

1. Inform students of the number of pollution permits that have been issued. To help students get an idea of what prices to expect in the coal market, you should point out that the demand curve is the same as it was in the Tax Scenario, and that the number of permits is close to (perhaps the same as) the units of coal sold in that scenario. You can then suggest, more or less subtly, that the competitive equilibrium price of a unit of coal in this scenario is likely to be similar to that in the Tax Scenario. You could even draw with your students the demand curve for coal on the board at the front of the classroom.
2. Designate one area of the room as the Permits Trading Pit and another as the Coal Trading Pit. Students should go to the appropriate trading pit when they want to buy or sell permits or units of coal. classEx does not show information on the transactions of permits. It may be a good idea to make that information publicly available by writing it on the board.
3. When a supplier wants to use a permit to sell a unit of coal, they must approach the instructor and exchange the permit for the permit code needed to submit the contract in their device. The instructor should remember to take the paper permit from the student when providing the permit code. This practice prevents students from selling the permit after having used it to produce, which is a common mistake. Recall that each round has a different code for permits and that codes can be personalized in the parameters of the experiment.

Note that classEx does not collect the cost of a pollution permit nor the profits from trading permits, and therefore does not include them when reporting total profits. This information is on the paper permits and must be added manually after the experiment if you need it.

### Find out more Advanced settings

This section is not necessary to run the experiment and the class discussion, it just provides further information on personalizing the classEx settings and parameters. You can skip it and go directly to the ‘Student instructions’ section if you just want to follow the standard settings, as we used in the ‘Step-by-step guide’ section.

#### Parameters

classEx allows you to personalize many of the settings for the experiment by changing the parameters. Figure 3.1 presents the default values for a session with 31 students and online trading. Notice that it is necessary to input the number of participants for a correct distribution of types, and that, in the ‘Trading of coal’ menu, you must choose ‘Online’ to have transactions online or ‘Offline’ to have students trading in the classroom. Also, if you plan to run the Permits Scenario, you need to include the number of permits that will be issued and keep a record of the permit codes for each round. The number of rounds per scenario is fixed at 2. You can always skip rounds, but you cannot add additional ones.

#### Allocation of types

Let P be the number of participants. Let N and R be the quotient and the remainder of the division P/12, so that P = 12 × N + R. Figures 3.6 and 3.7 provide information on the distribution of Seller Costs and Buyer Values respectively, for Scenarios 1 and 2. Figure 3.8 shows the correspondence between the type displayed by classEx in the student’s screen and the student’s role in each scenario of the experiment.

Seller cost
Remainder R 8 13 18 23 28
0 N 2N N N N
1 N 2N N + 1 N N
2 N 2N N + 2 N N
3 N 2N N + 1 N + 1 N
4 N 2N N + 2 N + 1 N
5 N 2N N + 3 N + 1 N
6 N 2N + 1 N + 1 N + 1 N
7 N 2N + 1 N + 2 N + 1 N
8 N 2N + 1 N + 3 N + 1 N
9 N 2N + 1 N + 1 N + 1 N + 1
10 N 2N + 1 N + 2 N + 1 N + 1
11 N 2N + 1 N + 3 N + 1 N + 1

Figure 3.6 Distribution of Seller Costs.

Remainder R 20 25 30 35 40
0–2 N N N N 2N
3–5 N N N N + 1 2N
6–8 N N + 1 N + 1 N + 1 2N
9–11 N N + 1 N + 1 N + 1 2N + 2

Figure 3.7 Distribution of Buyer Values.

Type Role in Scenarios 1 & 2 Role in Scenario 3
1 Supplier with Seller Cost €23 Demander with Buyer Value €35
2 Supplier with Seller Cost €18 Supplier with Seller Cost €23
3 Demander with Buyer Value €35 Supplier with Seller Cost €18
4 Demander with Buyer Value €25 Supplier with Seller Cost €13
6 Supplier with Seller Cost €13 Demander with Buyer Value €30
7 Supplier with Seller Cost €28 Demander with Buyer Value €40
8 Demander with Buyer Value €40 Supplier with Seller Cost €28
10 Demander with Buyer Value €20 Supplier with Seller Cost €13
11 Supplier with Seller Cost €8 Demander with Buyer Value €20
12 Supplier with Seller Cost €13 Supplier with Seller Cost €8
X Supplier with Seller Cost €18 Supplier with Seller Cost €18

Figure 3.8 Distribution of types in classEx.

For example, in a group of P = 31 students, 31 = 12 × 2 + 7, and hence N = 2 and R = 7. For Scenarios 1 and 2, it follows from Figure 3.6 that there are 2 suppliers with Seller Cost of €8, 5 suppliers with Seller Cost of €13, 4 with Seller Cost of €18, 3 with Seller Cost €23, and 2 with Seller Cost €28. From Figure 3.7, there are 2 demanders with Buyer Value of €20, 3 with Buyer Values of €25, €30, and €35, and 4 with Buyer Value of €40.

Each run is identified with a unique runID. Figure 3.9 describes the most relevant variables included in the Excel file.

Tab Variables
• playerID: a unique player identification code assigned by the program
• Logtime: time of first entry
• externalID: participant personal identification code (only if this option has been selected by the instructor)
decisions Information about profits obtained by participants.
Profits are identified by playerID and round. classEx numbers rounds consecutively without differentiating between scenarios.
• Market Scenario: rounds 1 and 2.
• Tax Scenario: rounds 3 and 4.
• Permits Scenario: rounds 5 and 6.

Recall that profits in the Permits Scenario do not include gains or losses from buying and selling permits.
globals Information about parameters, like endowment, currency, and maximum amount of punishment
matching Matching of playerIDs to groups
contracts List of transactions. For each transaction classEx collects:
• Round
• Quantity (always equal to 1 in this experiment, since only one unit can be bought or sold)
• Price
• Status (confirmed, open, withdrawn, or rejected). Only confirmed transactions took place.
payoffs List of real payouts, together with a winning code (only for games played with this option)
stagehistory Internal code for tracking the progress of players throughout the stages of the game

Figure 3.9 A description of the variables in the exported data.

### Quick summary

This section is intended for instructors who have already run the experiment in the past and just need a brief reminder of the instructions to get them going. It assumes that your students are already logged in to classEx and ready to start the experiment.

Recall that Scenarios 1 and 2 work both online or in class, but Scenario 3 can only be run in class. If you are planning to run the Scenario 3, print enough pollution permits beforehand. (See details in section ‘Trading in Scenario 3: Tradable pollution permits’.)

1. Check that the parameters are set according to your preferences. See the Parameters section for details. In particular, remember to introduce the number of participants and select the trading mechanism: ‘online’ or ‘offline’. If planning to run Scenario 3, type in the number of permits issued (Figure 3.1).
2. Announce that each unit of coal sold imposes a damage d on each participant. (classEx shows this cost in the transactions screen.)
3. Begin Scenario 1 (baseline market).
1. Open trading in Round 1. As transactions are submitted, the instructor screen projects price, Buyer Value, and Seller Cost to the whole classroom.
2. If you are using ‘online transactions’, the instructor’s screen will also display open buying and selling offers.
3. When trading stops, send feedback.
4. Run a second round. (You may decide to skip it if the price and quantities are close to theoretical predictions.)
4. Begin Scenario 2 (taxes). Remind students that this is Scenario 2, and that for each trade, the seller must pay a tax of €20 in addition to their Seller Cost. Proceed as in Scenario 1.
5. Begin Scenario 3 (permits).
1. Remind students that this is Scenario 3, and that in order to sell a unit of coal, each mine owner must turn in a pollution permit to receive a permit code to proceed with the transaction. Announce the number of permits issued and discuss the expected price for a unit of coal knowing that the demand is the same as in Scenario 2.
2. Distribute pollution permits to students of Types 5, 8, and 11. (Refer to the box Number of Pollution Permits to Print for the number of permits to print.)
3. Open trading in Round 1. Make sure that the seller turns in a filled-in pollution permit in exchange for the permit code.
4. Proceed to the second round.

## 3.5 Student instructions

These are also available in the students’ version.

A PDF of the student instructions and homework questions is also available.

### Introduction

Winter nights get cold on the Isle of Effluvia. With heavy blankets, one can get along without heat, but a warm fire is much appreciated, especially by those whose houses are not well insulated. The surrounding seas are turbulent, the coastal shores are treacherous, and no trading boats can bring fuel. Solar panels and green technology have not reached Effluvia. The only available fuel is locally mined coal, which Effluvians burn in old coal stoves. Heating a house for the season requires 1 unit of coal. Coal stoves pollute the air, emitting soot particles that cause health problems to all Effluvians.

The island has a coal market where residents can buy coal from the mine owners. Each unit of coal that is purchased will result in additional pollution that harms all Effluvians. Because of this pollution, trades that benefit both the buyer and seller have side effects that harm others not involved in the transaction. Such side effects are known as harmful externalities. Because of these externalities, unrestricted trade in the coal market will lead to an inefficient outcome in which ‘too much’ coal is burned. This experiment explores market interventions that are designed to reduce the amount of pollution and to benefit all Effluvians.

In this experiment, there are three possible scenarios. They all share the distribution of buyers and sellers and a similar procedure to formalize a transaction. Your instructor may decide to run all three or just some of them.

### Instructions (for all scenarios)

You will try to make profits by buying or selling one unit of coal. In each Market Scenario, you will be assigned a role, either as a mine owner who can supply one unit of coal, or as a demander who can buy one unit of coal (Figure A).

Figure A Screenshots of mine owners and coal demanders.

The supply side

Screenshot of a coal mine owner or supplier of coal.

The demand side

Screenshot of a coal demander for online trading. The ‘Buy’ button does not show in offline trading (see Figure D).

If you are a mine owner, you will be assigned a Seller Cost (the cost of extracting coal) and you can sell at the most one unit of coal per round. If you sell a unit of coal for a price P, and your Seller Cost is SC, then your profit from the transaction is the difference, P − SC. If P < SC, you are better off not selling and taking zero profits rather than doing it for a loss.

If you are a demander, you will be assigned a Buyer Value. You can buy at the most one unit of coal per round. If your Buyer Value is BV, and you buy one unit of coal for a price P, your profit from the transaction will be BV − P. If you have to pay more than your buyer value for a unit of coal, you are better off not buying any coal and taking zero profits rather than doing it for a loss.

At the beginning of the experiment, the instructor will tell you the amount of damage imposed on everyone by pollution from burning one unit of coal. If, for example, one unit of coal causes €0.50 damage to everyone, and if 20 units are sold, then every participant in the experiment, including those who make no trades, will have to suffer a pollution cost of €10, and the profits of each participant in the experiment will be reduced by €10. Everyone in Effluvia, whether they buy, sell, or do not transact at all, will suffer the pollution cost. You will learn the cost of pollution at the end of each round, once the total number of transactions is known.

Your instructor will announce whether you are using online or offline trading.

In the online market, coal miners can send a selling price that demanders will see in the contracts section of their screens (Figure B). Similarly, buyers can send a buying price that suppliers will see in the contracts section of their screens. Whether you are a supplier or a demander, your offer (if you made one) and all standing offers you can accept are shown in the contracts section of your screen. You can withdraw your offer and make a new one only if it has not been accepted yet. You can accept an offer by clicking on the ‘accept’ button. Note that once you accept an offer or your offer gets accepted, all other offers are automatically rejected as you can only trade one unit of coal.

Selling

A seller has sent a selling offer (marked as OWN) and has received one buying offer. The seller can still withdraw the offer as no buyer has accepted it yet.

A coal buyer has received three selling offers and must decide whether to accept any of them or none. The buyer has not made a buying offer yet.

When a buyer accepts a selling offer or a seller accepts a buying offer, the transaction takes place and is displayed on the instructor’s screen. Since only one unit can be traded in each round, the buyer and the seller cannot make any more transactions until the next round. Standing buying and selling offers are also displayed on the instructor’s screen (Figure C). Look at it frequently for a general picture of standing offers and to get an idea of the price at which coal is being traded.

Figure C Instructor’s screen showing one completed transaction and standing buying and selling offers.

Sellers and buyers must find each other and agree on a price. If they reach an agreement, the seller should type the price and the buyer’s ID into their screen and click the ‘SELL’ button. The buyer must accept the offer to finalize the contract (Figure D).

Figure D Offline trading. Once a buyer and a seller have reached a verbal agreement, they can formalize the transaction in their devices.

Selling

The seller types in the agreed price and the buyer’s ID on their screen and clicks the ‘SELL’ button.

The buyer must accept the offer to finalize the transaction. Before the transaction is finalized, both the buyer and the seller can withdraw.

The transaction

Once the buyer has accepted the transaction, the unit of coal moves from the seller to the buyer. They cannot do anything else until the next round, as a maximum of one unit of coal can be bought or sold in each round.

Sales contracts are publicly displayed on the instructor’s screen (Figure E). Look at this screen frequently to get an idea of the price at which coal is being traded.

Figure E Instructor’s screen showing completed transactions.

It is a good idea to think in advance what you will do the first time you are in the market and start bargaining with other students. There are many strategies you could use and there is not a single right answer. But remember to ‘shop around’ and look at the prices that have already been posted on the instructor’s screen.

### Instructions for Scenario 2 (Pollution Tax)

In the second scenario, the ‘government’ imposes a pollution tax, which is collected from mine owners. The tax revenue that the government collects will be redistributed in equal shares to all participants. In this scenario, if a mine owner with Seller Cost SC sells a unit of coal to a demander with Buyer Value BV for price P, and if the tax per unit of coal is T, then the mine owner’s after-tax profit from the transaction is (P − SC − T) and the buyer’s profit is (BV − P). In addition to any profits that you may make from buying or selling coal, you will receive an equal share of the government’s tax revenue, and will suffer a loss of income equal to the amount of pollution cost caused by the coal that is used by demanders.

If you are a mine owner, remember you only have to pay the tax if you sell your unit of coal. If your cost of selling a unit of coal (including taxes) is higher than the price you are offered, you are better off not selling any coal and taking zero profits rather than selling for a loss.

### Instructions for Scenario 3 (Pollution Permits)

In the third scenario, a mine owner is allowed to sell a unit of coal only if they have a pollution permit. At the beginning of each round, some participants will receive marketable pollution permits (Figure F). The original owner of a pollution permit can resell this permit to anyone else, but a pollution permit can be used only once to sell a unit of coal and only by a mine owner. Pollution permits are traded on paper. When someone buys a pollution permit, the buyer and the seller of the permit must write their ID numbers (found underneath the player icon on their devices) and the sales price on the permit. The seller of the pollution permit receives a profit equal to the price at which the permit was sold. Unlike coal, pollution permits can be resold in the permits’ market.

Figure F Example of tradable pollution permit.

Having a pollution permit, a mine owner is allowed to sell a unit of coal to a demander. In order to do so, a mine owner must obtain a code from the instructor in exchange for the pollution permit. The mine owner must type this code on their screen, in addition to the buyer’s ID and the price (Figure G).

Figure G Screen for a mine owner in Session 3. The mine owner must type in the code obtained in exchange for a pollution permit, the buyer’s ID, and the agreed price in order to formalize the transaction.

A mine owner’s profit is the price they receive for a unit of coal, minus their Seller Cost, minus the price they pay for a pollution permit (if they need to buy one). A buyer’s profit from the purchase of a unit of coal is their Buyer Value minus the price they pay for the unit of coal. In addition to profits (or losses) that individuals make from buying or selling coal, they can also make profits from buying and selling permits. As before, all participants will suffer a loss of profits equal to the amount of pollution cost imposed on each person by the amount of coal used.

## 3.6 Predictions

### Predicted results

Under the tab ‘prediction’, classEx provides graphs with the supply and demand curves and the competitive equilibrium predictions for the number of participants in your session. Figure 3.10 shows a particular example for a group of 31 students.

Figure 3.10 Supply (blue line) and demand (orange line) curves for a group of 31 students. The intersection between demand and supply represents price and quantity theoretical predictions for each scenario.

Scenario 1

The market without intervention.

Scenario 2

The market with a €20 sales tax.

Scenario 3

The market with 7 pollution permits.

In the absence of government intervention (Scenario 1), the equilibrium price is €23 and the equilibrium quantity is 13 units of coal. The total amount of profits on transactions is €229. Total pollution costs suffered by all participants in the experiment are 13 × €20 = €260. Therefore, total profits, net of pollution costs are €229 − €260 = −€31.

In practice, the mean price tends to be close to the equilibrium prediction, but it is common to obtain two or three fewer transactions than predicted. (See the What might go differently? section.)

With the €20 sales tax (Scenario 2), the supply shifts up, and the equilibrium price and quantity change to €33–35 and 7 units of coal, respectively. It is usually necessary to run two rounds. While quantities sold tend to be closer to the equilibrium quantities than in the Market scenario, it is also common to have one or two fewer units sold than the equilibrium quantity. Some students may be tempted to convince others not to make transactions, not realizing that taxes compensate for pollution costs. You should forbid or discourage public statements.

For Scenario 3, given that there are 31 students, you should have distributed 7 pollution permits (see the box Number of Pollution Permits to Print), and 7 units of coal should be sold. We see from Figure 3.10 that if 7 units of coal are sold, the competitive equilibrium price of coal must be in the range €30–35. Then, a supplier with a Seller Cost SC should be willing to pay around €32.50 – SC for a pollution permit.

At the end of the experiment, results are presented in two tabs on the instructor’s screen. The first tab (‘chart’) shows the timeline of transactions for the different rounds. The second tab (‘on average’) shows the quantity sold, average price, and other statistics. You may expect to obtain something similar to Figure 3.11 and Figure 3.12, which show the results from the reference example in classEx: an experiment run in class, offline trading with 33 students at Pompeu Fabra University in 2016. You can observe that transactions fall and prices increase when either a pollution tax or pollution permits are introduced, and that both instruments have similar outcomes.

Figure 3.11 Timeline of transactions of an in-class session with offline trading run at Pompeu Fabra University on 14 November 2016 with 33 first-year students.

Figure 3.12 Transaction statistics of an in-class session run at Pompeu Fabra University on 14 November 2016 with 33 first-year students.

### What might go differently?

In the Market scenario (Scenario 1), it is common to obtain two or three fewer transactions than there would be in competitive equilibrium. Observe (Figure 3.10) that the demand and supply curves are very close together for the last units sold, showing small gains from trade. It is possible that some buyers and sellers who can make a gain do not find each other. Another possibility is that some students may misunderstand the effects of externalities and think that their own sales would have a stronger effect on the pollution costs that they suffer than is actually the case. A third possibility is that some students may choose to sacrifice their own profits to reduce pollution. We suggest that near the end of each round, you make some effort to encourage students who haven’t traded to look once more for a trading partner. For instance, when trading appears to have stopped, you could check the average price in this round and ask if there is anyone else who wants to sell and anyone who wants to buy at this price. If there are buyers and sellers who answer in the affirmative, you can offer them a chance to trade.

In the Tax scenario (Scenario 2) quantities sold tend to be closer to the equilibrium quantities than in Scenario 1, but frequently one or two fewer units tend to be sold than the equilibrium quantity. Some students may be tempted to convince others not to make transactions, not realizing that taxes compensate for pollution costs. Try to avoid public announcements. It is also common to have some students selling at a loss because they forget about the tax, especially in the first round. Bring attention to these transactions before starting the next round (you can do it without having to identify the perpetrators).

In the Permits Scenario (Scenario 3), it is common for some suppliers who received a permit to use that permit, even though they could make higher profits by selling it. This usually results in the efficient number of units sold, but an inefficient allocation of production. In some instances, there might be one or two fewer transactions if mine owners endowed with a permit and a high seller cost cannot find a buyer for their unit of coal and yet fail to realize that they could make money by selling the permit. All these situations are good opportunities to discuss the sophisticated reasoning that permit owners must make in order to decide whether to use the permit or sell it.

## 3.7 Discussion

A good discussion during and after the experiment is important. Ask your students the following questions to frame the discussion.

Comments in the ‘Predictions’, ‘What might go differently’ sections, and in The Economy (Section 12.1, Section 12.3, and Section 20.5) and in Economy, Society, and Public Policy (Section 11.7) provide useful further information.

### Interpreting the graphs

• How does the number of transactions and prices compare between scenarios?
• Do the tax and the permits have similar effects?

### Voting on a pollution tax

This thought experiment is a veil of ignorance type of argument (see Section 5.3 in The Economy).

At the end of the Tax Scenario you could use a thought experiment. Recall that students are assigned the same type in both the Market and the Tax Scenarios. The discussion offers the opportunity to highlight the problems of implementing a pollution tax, even when there is a close to a unanimous preference for a low pollution society.

• First, ask the following question: ‘Suppose Scenarios 1 and 2 represented two alternative societies and you did not know the role you would be assigned in each society. That is, you do not know whether you would be a mine owner or a consumer, nor your seller cost or buyer value. Which of the two societies would you prefer to live in?’

In our experience, Scenario 2 is the (close to) unanimous choice.

• Second, ask students to look at the actual profits they made in each of those two scenarios. Announce that you are considering taking into account only profits from either Scenario 1 or Scenario 2, and that the decision will be made by a show of hands, according to majority voting. Scenario 2 should win the vote, but there are now several students who vote in favour of Scenario 1.
• Now, inform the students that both scenarios had the same distribution of suppliers and demanders, and point out that the show of hands was equivalent to a referendum over imposing a tax on pollution when ‘everybody’ preferred a society without pollution. This opens the discussion to several issues, including: private vs social preferences, social dilemmas, who pays and who suffers the externality, and concentrated vs diffuse interests.

### Relating the experiment to real life

• Which situations in real life may be similar to the game you just played?
• Why do people not fully take into account the pollution they generate with their actions?
• How is this situation (the class experiment) different to the real-life situations we have just discussed?

### Reflecting on the decisions that players made

• Did buyers and sellers take into account pollution in their decision to buy or sell in the Market Scenario? What about in the Tax Scenario?
• Why did some mine owners decide to sell their permits instead of using them to sell one unit of coal?

### A hypothetical situation

• Suppose that at the beginning of the Market Scenario a student had made a speech about pollution and had tried to convince others not to use coal. Do you think it would have been possible to attain the efficient quantity?
• Economic theory predicts that in the presence of negative externalities, competitive trading usually leads to inefficient outcomes. Although it is not, in general, efficient to eliminate negative externalities entirely, an appropriately chosen tax can improve efficiency. Alternatively, negative externalities can also be regulated in an efficient way by means of a fixed supply of tradable permits. How do the theoretical predictions compare with the experimental outcomes?

### Critical evaluation of the experiment

• Which assumptions have been used in the experiment?
• How do these assumptions compare to real-life situations?
• Do you think the behaviour would change if the game was played for real money?
• Do you think the behaviour would change if the game was played with thousands or millions of people?
• What other mechanisms could help to reduce pollution?

## 3.8 Homework questions

These are also available in the students’ version.

These questions can be set for students to work on outside the classroom or can be completed and discussed in the classroom. They may help students reflect on their experience and understand their and others’ behaviour in the experiment.

For these questions, you will need to provide your students with the following information: the distribution of seller costs and buyer values (obtained from Figure 3.6 and Figure 3.7); transactions, prices, and profits in the last round of each scenario (from a screenshot of the instructor’s screen or from the data file downloadable from classEx); pollution cost per unit and pollution tax; and, if you are analysing Scenario 3, the number of pollution permits distributed.

Data from your experiment can be downloaded as an Excel file from the ‘Data’ menu in the instructor’s screen in classEx. You can also use this data to create your own questions. A description of the data variables can be found in the ‘Downloading the data from your experiment’ section.

Your instructor shared with you the following information regarding the experiment: transactions, prices, and profits in the last round of each scenario; the distribution of buyer values and seller costs; the pollution cost and pollution tax; and, if you are analysing Scenario 3, the number of pollution permits distributed.

### Comparing Scenarios 1 and 2

Exercise 8.3 in The Economy shows how to draw supply and demand ‘curves’ when they are step functions.

1. Calculate the total costs of pollution and the total profits (net of pollution costs) for each scenario and compare them.
2. Using the distribution of types, draw a graph showing both the demand and supply curves, with and without the pollution tax, and calculate the predictions of the theory for a competitive market.
3. Compare the theoretical predictions for price, quantity, and surplus at equilibrium with the experimental results.

### Scenario 3

1. For Scenario 3, the supply curve becomes vertical at the number of permits issued. The demand function is the same in all three scenarios. Use the demand and supply curves to find the equilibrium price of a unit of coal. (If there is a range of competitive equilibrium prices, assume that the price is at the midpoint of its range.)
2. Use the equilibrium price of a unit of coal to calculate the maximum amount that each type of supplier would be willing to pay for a pollution permit.
3. Use the information in the previous question to draw the demand curve for pollution permits. On the same graph, draw a vertical supply curve at the number of permits that were issued in the experiment, and find the competitive equilibrium price for permits.
4. Compare your findings in the previous questions with the experimental results.

Also available in the students’ version.

## 3.10 Instructor experience

In this section, we hear from instructors about their experience of running the experiment with their students.

### Gianmarco Leon-Ciliotta Unversitat Pompeu Fabra, Barcelona, Spain

I usually run this experiment in the introduction to microeconomics class at UPF, but it works well for undergraduates at any level. The key concepts that this experiment helps me explain are: (i) market failures, (ii) the social vs private benefit (and corresponding equilibria), (iii) government interventions, and (iv) social choice based on positive vs normative criteria.

To motivate the experiment, I like to start with a discussion in which I ask them for policy solutions to some current environmental problems. For example, I ask their thoughts about the ban on plastic bags in supermarkets. Here, you will typically have students who advocate full bans, whereas others would prefer that we impose a price on them. This is a great segue for talking about social vs individual benefits and the role of public policy.

For cases in which students haven’t been exposed to the simple market experiment with perfect competition, I typically start by running one or two sessions. This helps get them familiar with the mechanics of the market, understand the surpluses and understand that, in the absence of any frictions or failures in the market, competitive markets maximize the social surplus.

I then move on to introduce the externality. A key concept to underscore here is that everyone pays the external cost, regardless of whether transactions have been made or not. This is key for the functioning of the experiment, and sometimes students have a hard time conceptualizing it, so it is good to present this idea with a few examples of positive and negative externalities. The point should be crystal clear after the first session, where we introduce pollution without taxes.

In the final session, we introduce corrective taxes. After this session, I present students with a discussion about social choice. I do this by telling students that, unlike in other experiments, the benefits from this class will not represent the outcomes obtained in all sessions, but rather will come from just one session, and the session we use will be decided by a simple majority vote. (In my experiments, I incentivize students by assigning part of their grades based on the benefits obtained, but this discussion should work regardless of whether you do this or not.)

The choice students have to vote on is between (i) the session with pollution and no taxes, and (ii) the session with pollution and taxes. Most students will choose (ii), but in many cases this would be motivated by individual benefits, rather than by realizing that this is a more efficient outcome. After counting the votes, I emphasize that we just made a democratic social choice. While economic theory (and the results of the experiment) shows that the outcome with taxes is more efficient (positive outcome), the choice of whether to tax or not depends on what society values most (normative outcome). Also, the setting is a good one for talking about the difficulties in taking our basic results to policymaking, for example, how do you determine the correct tax rate and what are the perils of getting this wrong.

### Theodore C. Bergstrom University of California, Santa Barbara, US

This experiment was conducted at the University of California Santa Barbara for an introductory economics class of 500 students. The experiment was conducted in 10 section meetings with attendance of about 48 students per meeting. The entire experiment was conducted before the advent of classEx and used paper contracts and blackboard posting.

For Session 1, in which production is not taxed, the competitive equilibrium price must fall in the range from $23 to$25. Five of these sections conducted two rounds of this session and five had only one round. In all sessions, the mean price at which sales took place was either in this range or very close to it. (The lowest mean price for a section was $20.80 and the highest was$24.)

The equilibrium number of trades varied from section to section with the number of persons who attended. In most sections, there were two or three fewer trades than there would be in competitive equilibrium.

In Session 2, with a pollution tax of $20, the competitive equilibrium price range was$30–$35 for some sections and it was just$35 for others. All sections ran two rounds of this session. Mean prices in the last round of each session ranged from $30.70 in the lowest session to$34 in the highest.

Quantities sold in Session 2 were very close to the competitive predictions for all sections, though frequently one or two less units were traded than would be the case in competitive equilibrium.

In Session 3, the number of permits issued was chosen so that the competitive equilibrium price for coal was $35. If the permits were all acquired by the miners with the lowest seller costs, then they would be obtained by those with seller costs of$10 or less. Since in equilibrium, the price of coal would be $35, the willingness to pay of those with seller costs of$10 would be $35 −$10 = $25. Since permits are available in fixed supply, the equilibrium price for permits would be$25.

Most of the sections had time for only one round of this experiment. The mean price of coal ranged from a low of $26.50 in one section to a high of$31.10 in another. The mean price of permits ranged from $9 to$15. Thus the price of coal was lower than the predicted competitive equilibrium price and the price of permits was substantially lower than equilibrium, even conditional on the lower-than-equilibrium price for coal. It would be very interesting to see whether prices in these two markets would move closer to equilibrium levels in repeated trials after students have observed previous outcomes.