Pigouvian Tax

Pigouvian Tax Graph

The pigouvian tax graph helps us understand how this tax can solve the problem caused by negative externalities.

Fig. 1 - An industry will over-produce in the presence of a negative externality.

The graph above (Fig. 1) shows a situation facing an industry with a negative externality. Without any regulations in place, the firms will produce a quantity of Q₁, the point where their supply curve intersects with the demand curve. The marginal social cost (MSC) curve is higher than the supply (MC) curve, and the difference between them is given by the marginal external cost (MEC) curve. The MEC curve is upward-sloping because the harmful effects of pollution become substantially larger as the quantity increases.

We know that imposing a tax on pollution can help solve the negative externality problem, but how high should we set the Pigouvian tax?

Figure 2 shows a firm's perspective. Assume that the profit-maximizing level of production will produce E₁ level of emissions. Without any regulations, the firm will emit this amount of pollution. When a Pigouvian tax is implemented, the firm has the option to take certain actions and purchase some equipment to reduce emissions.

Fig. 2 - The efficient level of emissions.

The firm faces a downward-sloping marginal cost of abatement (MCA) curve, but it's helpful to read it from right to left. As the firm chooses to abate a larger amount of emissions, the marginal cost of doing so is higher because it has to take more costly actions to change its production procedures or buy more sophisticated emissions-control equipment.

The efficient level of emissions is E* because that's where the MCA and the MEC curves intersect. The government should set the Pigouvian tax at the amount of P* which targets the level of emissions at point E*.

Pigouvian Tax Examples

The most common examples of Pigouvian tax are carbon emissions, sugary drinks, or plastic bag taxes. Let's take a closer look at some real-world examples of the Pigouvian taxes together:

• Carbon tax in Canada: In 2008, British Columbia implemented a carbon tax to reduce greenhouse gas emissions. The tax per tonne of carbon dioxide emissions increased annually until it reached $50 per tonne in 2022. The tax has effectively reduced emissions while also generating revenue for the province.³
• Congestion charge in London: In 2003, London introduced a congestion charge to reduce traffic congestion and improve air quality in the city center. Drivers are charged £15 per day to enter the congestion zone during certain weekday hours.⁴
• Sugary drink tax in Mexico: In 2014, Mexico introduced a tax on sugary drinks in an effort to combat obesity and related health problems. The tax is levied on sugary drinks with a sugar content of more than 5 grams per 100 millilitres at a rate of 1 peso (about 5 cents) per liter.⁵
• Plastic bag tax in Ireland: In 2001, Ireland introduced a tax on plastic bags to reduce litter. The tax started at 15 euro cents per bag and increased to 22 euro cents by 2007. The tax has effectively reduced plastic bag use by over 90% and generated revenue for environmental projects.⁶

Carbon Tax Example

A tax on carbon emissions is an example of a Pigouvian tax. Carbon dioxide (CO2) is one of the main greenhouse gases contributing to climate change. Because of the negative consequences of climate change, societies worldwide are increasingly demanding policy actions to curb carbon emissions.

Compared to traditional command-and-control regulations that dictate who can pollute and what amount of pollution is allowed, carbon taxes are a more market-based and efficient way to address the problems of carbon emissions. Therefore, carbon taxes are used in many countries as part of their governments' climate policies.

Fig. 3 - Jurisdictions (in red) that have implemented or scheduled carbon taxes, as of 2021. Source: World Bank.

Pigouvian Tax and Subsidies

While a Pigouvian tax solves the problem of negative externalities, Pigouvian subsidies solve the problem of positive externalities.

The existence of a positive externality leads to the under-consumption of a good or service. The demand curve only reflects the marginal private benefit (MPB) of consumption while the marginal social benefit (MSB) curve is higher. The difference between them is the marginal external benefit (MEB).

In Figure 4 below, people will consume up to the quantity of Q₁ if there are no interventions. This is the point where their marginal private benefit from consumption is equal to the marginal cost. The socially optimum consumption quantity is Q* where the marginal social benefit is equal to the marginal cost. To achieve this level of consumption, the government can provide a Pigouvian subsidy that is equal to the marginal external benefit at this quantity. The Pigouvian subsidy will decrease the price for consumers from P₁ to P*. The shaded area is the deadweight loss incurred by society in the absence of a subsidy.

Fig. 4 - A positive externality leads to under-consumption.

Pigouvian Tax Pros and Cons

What are the pros and cons of a Pigouvian tax compared to the traditional command-and-control type of regulations?

The main advantages and disadvantages of Pigouvian taxes can be summarised in the table below:

Pigouvian Tax: Pros

Lower cost in achieving the same amount of emission reduction.

Let's say there are two firms, each with a different marginal cost of abatement (MCA) curve. This is shown in Figure 5. Firm 1 faces a lower marginal cost of abatement (MCA₁) than Firm 2 (MCA₂). If the regulatory authorities ask both firms to reduce their emissions to the level of 10, Firm 1 will incur an MCA of $3.5, while Firm 2 will face an MCA of $4.5 at that level.

Fig. 5 - A Pigouvian tax can achieve the same amount of emission reduction with a lower cost.

In contrast, if the government sets a Pigouvian tax at the amount of $4, Firm 1 will reduce its emissions to the level of 9 while Firm 2 will emit at the level of 11. This will achieve the same amount of emission reduction as in the case of an emission standard, but the total abatement cost is smaller. This is shown in Figure 5 as the increase in abatement cost for Firm 1 (area in red) is smaller than the decrease in abatement cost for Firm 2 (area in green) when a Pigouvian tax is imposed.

A Pigouvian tax provides an incentive for further reduction.

Compared to a traditional emission standard, a Pigouvian tax also provides an incentive for firms to reduce their emissions further. Looking at Figure 5 again, if Firm 2 acquires some new equipment that shifts its MCA curve to MCA₁, it will reduce its emissions to level 9. In the case of an emission standard, it will still have the incentive to acquire the equipment to lower its abatement cost, but it will only reduce its emissions to level 10 and has no incentive to reduce them further.

Pigouvian Tax: Cons

In the real world, we don't always know what the marginal external cost (MEC) curve or the marginal cost of abatement (MCA) curve looks like. Sometimes, this information is not available to the government because the MCA for a firm is a business secret. In other cases, there is actual scientific uncertainty regarding what the MEC of emissions is. In these scenarios, it is tricky to say which kind of regulation is better. It depends on the shapes of the two curves.

Fig. 6 - The MEC curve is steep, and the MCA curve is relatively flat.

Figure 6 shows that when the MEC curve is steep and the MCA curve is relatively flat, a traditional emission standard is better. If the government makes a small error in setting the emission standard (at the level of E_S), this will lead to a net increase in social costs the size of the yellow area. On the other hand, if the government makes an error of the same proportion in setting the Pigouvian tax (at P_T), this will lead to a net increase in social costs the size of the red and yellow area combined, which is a lot larger.

In the opposite situation, when the MCA curve is steep and the MEC curve is relatively flat, then a Pigouvian tax is preferable to a traditional emission standard given the uncertainty and potential error.

In the case of setting a price for carbon, the uncertainty in the marginal damage of each additional ton of carbon emissions can explain in part the significant variation in the prices of carbon emissions under different settings. Figure 7 below shows the implied carbon prices under different carbon taxes and emissions trading systems (ETS) in different places.

Fig. 7 - The significant variation in carbon prices under different carbon taxes and emissions trading systems. Source: World Bank.

Pigouvian Tax - Key takeaways