Unit 10 Market successes and failures: The societal effects of private decisions

10.4 Solving the problem: Regulation, taxation, and compensation

According to the 1992 Rio Declaration of the United Nations: ‘National authorities should endeavour to promote the internalization of environmental costs and the use of economic instruments, taking into account the approach that the polluter should, in principle, bear the cost of pollution, with due regard to the public interest and without distorting international trade and investment.’

If Coasean bargaining could resolve the problem of Weevokil, the polluter-pays principle could be established by giving an initial right to clean water to the fishermen. But which ‘economic instruments’ can be used if bargaining is impractical and a private agreement cannot be reached?

We will continue to assume that it is not possible to grow bananas without using Weevokil. There are three ways in which the government might achieve a reduction in the output of bananas to the level that accounts for the social costs, namely through:

  • regulation of the quantity of bananas produced
  • taxation of the production or sale of bananas
  • enforcing compensation of the fishermen for the costs imposed on them.

Each of these policies could achieve a Pareto-efficient outcome (provided that the government had access to the required information and had the means and inclination to pursue an efficiency-promoting policy). But unlike private bargaining, they do not implement a Pareto improvement over the initial allocation in which the plantations benefited from a strong reservation position (the right to pollute) and produced 80,000 tons of bananas. Compared with that allocation, all three policies make the fishermen (and in some cases, the government) better off, while reducing the profits of the plantations. Under each policy, the polluter pays.

Regulation

The government could cap total banana output at the Pareto-efficient level of 38,000 tons. This is not quite as straightforward as it seems, because if the plantations differ in size and output, it may be difficult to determine and enforce the right quota for each one.

Compared with the initial allocation, this policy would reduce the costs of pollution for the fishermen, but it would lower the plantations’ profits. They would lose the surplus on each ton of bananas between 38,000 and 80,000.

Taxation

Figure 10.4 shows the MPC and MSC curves again. At the Pareto-efficient quantity (point B):

\[\text{marginal external cost} = \text{MSC − MPC} = $400 - $295 = $105\]

The price of bananas is $400 per ton. If the government puts a tax of $105 on each ton of bananas produced, the after-tax price for producers will be $295. Now, to maximize their profit, they will choose the output level where the after-tax price equals the marginal private cost. Use the analysis in Figure 10.4 to understand how this policy works.

In this diagram, the horizontal axis shows the quantity of bananas Q in tons per year, and ranges from 0 to 100000. The vertical axis shows the costs in dollars, and ranges from 0 to 900. Coordinates are (quantity, costs). An upward-sloping straight line passes through points (0, 200), P1 (38000, 295), and A (80000, 400) and is labelled marginal private cost. Another convex, upward-sloping curve passes through points (0, 250) and (80000, 675), is labelled marginal social cost and is above the marginal private cost line at all points. A vertical line passes through point (70000, 0). A horizontal line passes through points A and B (38000, 400) and is labelled price. Another horizontal line passes through point (0, 295) and is labelled after-tax price for plantations. The vertical distance between points B and P1 is the tax. A vertical line passes through point A and a vertical line passes through point B.
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Figure 10.4 Using a tax to achieve Pareto efficiency.

The marginal external cost: In this diagram, the horizontal axis shows the quantity of bananas Q in tons per year, and ranges from 0 to 100000. The vertical axis shows the costs in dollars, and ranges from 0 to 900. Coordinates are (quantity, costs). An upward-sloping straight line passes through points (0, 200), (38000, 295), and A (80000, 400) and is labelled marginal private cost. Another convex, upward-sloping curve passes through points (0, 250) and (80000, 675), is labelled marginal social cost and is above the marginal private cost line at all points. A vertical line passes through point (70000, 0). A horizontal line passes through points A and B (38000, 400) and is labelled price. A vertical line passes through point A and a vertical line passes through point B. At point B, the marginal social cost is 105 dollars more than the marginal private cost.
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The marginal external cost

At the Pareto-efficient quantity, 38,000 tons, the MPC is $295. The MSC is $400. So the marginal external cost is MSC – MPC = $105.

Tax = MSC – MPC: In this diagram, the horizontal axis shows the quantity of bananas Q in tons per year, and ranges from 0 to 100000. The vertical axis shows the costs in dollars, and ranges from 0 to 900. Coordinates are (quantity, costs). An upward-sloping straight line passes through points (0, 200), (38000, 295), and A (80000, 400) and is labelled marginal private cost. Another convex, upward-sloping curve passes through points (0, 250) and (80000, 675), is labelled marginal social cost and is above the marginal private cost line at all points. A vertical line passes through point (70000, 0). A horizontal line passes through points A and B (38000, 400) and is labelled price. Another horizontal line passes through point (0, 295) and is labelled after-tax price for plantations. The vertical distance between the horizontal lines is the tax. A vertical line passes through point A and a vertical line passes through point B.
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Tax = MSC – MPC

If the government puts a tax on each ton of bananas produced equal to $105, the marginal external cost, then the after-tax price received by plantations will be $295.

At the after-tax price of $295: In this diagram, the horizontal axis shows the quantity of bananas Q in tons per year, and ranges from 0 to 100000. The vertical axis shows the costs in dollars, and ranges from 0 to 900. Coordinates are (quantity, costs). An upward-sloping straight line passes through points (0, 200), P1 (38000, 295), and A (80000, 400) and is labelled marginal private cost. Another convex, upward-sloping curve passes through points (0, 250) and (80000, 675), is labelled marginal social cost and is above the marginal private cost line at all points. A vertical line passes through point (70000, 0). A horizontal line passes through points A and B (38000, 400) and is labelled price. Another horizontal line passes through point (0, 295) and is labelled after-tax price for plantations. The vertical distance between points B and P1 is the tax. A vertical line passes through point A and a vertical line passes through point B.
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At the after-tax price of $295

To maximize profit, the plantations will choose their output so that the MPC is equal to the after-tax price. They will choose point P1 and produce 38,000 tons.

Consult an online dictionary to hear how to pronounce ‘Pigouvian’.

Pigouvian tax
A tax levied on activities that generate negative external effects so as to correct an inefficient market outcome. See also: external effect, Pigouvian subsidy.

The tax corrects the price message, so that the plantations face the full marginal social cost of their decisions and make a Pareto-efficient choice. They produce 38,000 bananas, where the tax is exactly equal to the marginal cost imposed on the fishermen. This approach is known as a Pigouvian tax, after the economist Arthur Pigou, who advocated it.

The distributional effects of taxation are different from those of regulation. The costs of pollution for fishermen are reduced by the same amount, but the reduction in banana profits is greater, since the plantations pay taxes as well as reducing output, and the government receives tax revenue.

Enforcing compensation

The government could require the plantation owners to pay compensation for the costs imposed on the fishermen. The compensation required for each ton of bananas will be equal to the difference between the MSC and the MPC, which is the distance between the two curves in Figure 10.5. Once compensation is included, the marginal cost of each ton of bananas for the plantations will be the MPC plus the compensation, which is equal to the MSC. So now the plantations will maximize profit by choosing point B in Figure 10.5 and producing 38,000 tons. The shaded area shows the total compensation paid. The fishermen are fully compensated for pollution, and the plantations’ profits are equal to the true social surplus of banana production.

In this diagram, the horizontal axis shows the quantity of bananas Q in tons per year, and ranges from 0 to 100000. The vertical axis shows the costs in dollars, and ranges from 0 to 900. Coordinates are (quantity, costs). An upward-sloping straight line passes through points (0, 200), (38000, 295), and A (80000, 400) and is labelled marginal private cost. Another convex, upward-sloping curve passes through points (0, 250) and (80000, 675), is labelled marginal social cost and is above the marginal private cost line at all points. A vertical line passes through point (70000, 0). A horizontal line passes through points A and P2 (38000, 400) and is labelled price. A vertical line passes through point A and a vertical line passes through point P2. The area between the vertical line through P2, the marginal private cost line, the vertical axis and the marginal social cost curve is the total compensation paid.
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Figure 10.5 The plantations compensate the fishermen.

The effect of this policy on the plantations’ profits is similar to the effect of the tax, but the fishermen do better because they, rather than the government, receive payment from the plantations.

Diagnosis and treatment in the case of chlordecone

When we identified 38,000 tons as the Pareto-efficient level of output in our model, we assumed that growing bananas inevitably involves Weevokil pollution. So our diagnosis was that too many bananas were being produced, and we considered policies for reducing production. But that was not the case in Guadeloupe and Martinique, where there were alternatives to chlordecone. If alternatives to Weevokil were available, it would be inefficient to restrict output to 38,000 tons, because if the plantations could choose a different production method and the corresponding profit-maximizing output, they could be better off, and the fishermen no worse off.

The use of chlordecone was the problem, not the production of bananas.

The market failure occurred because the price of chlordecone did not incorporate the costs that its use inflicted on the fishermen, and so it sent the wrong message to the firm. Its low price said: ‘Use this chemical; it will save you money and raise profits’, but if its price had included the full external costs of its use, it might have been high enough to have said: ‘Think about the downstream damage, and find an alternative way to grow bananas.’

In this situation, a policy requiring the plantations to compensate the fishermen would have given them an incentive to find production methods that caused less pollution and could, in principle, have achieved an efficient outcome.

But the other two policies would not do so. Rather than taxing or regulating banana production, it would be better to regulate or tax the sale or the use of chlordecone, to motivate plantations to find the best alternative to intensive chlordecone use.

A tax on a unit of chlordecone equal to its marginal external cost would make the price of chlordecone equal to its marginal social cost. It would be sending the right message. Plantations would then choose their production method and banana output taking into account the full costs of chlordecone, reducing its use or switching to a different pesticide. As with the banana tax, the profits of the plantations and the pollution costs for the fishermen would fall, but the outcome would be better for the plantations, and possibly the fishermen also.

Chlordecone was first listed as carcinogenic in 1979. Its external costs were much higher than in our case of Weevokil, damaging the health of islanders as well as the livelihood of fishermen. In fact, the marginal social cost of any bananas produced with the aid of chlordecone was higher than their market price. So, had the plantation owners been required to fully compensate those harmed, they would have stopped using chlordecone altogether. But this did not occur. Finally in 1993, its use was legally prohibited. The pollution turned out to be much worse than anyone had realised, and is likely to persist in the soil for 700 years. In 2013, fishermen in Martinique barricaded the port of Fort de France until the French government agreed to allocate $2.6 million in aid.

Unfortunately, none of these remedies was used for more than 20 years in the case of chlordecone, and the people of Guadeloupe and Martinique are still living with the consequences. In 1993, the government finally recognized that the marginal social cost of chlordecone was so high that it should be banned altogether.

In The Economy 2.0: Macroeconomics, we return to the many inefficient and unfair outcomes that arise in the economy. We ask why these persist, if the government can implement policies that would correct the situation.

There are limits to the effectiveness of Pigouvian taxes, regulation, and compensation in solving pollution problems. Just as in Coasean bargaining, marginal social costs are difficult to measure. While firms’ marginal private costs may be known, it is harder to measure marginal social costs to either individuals or to society as a whole. So it is difficult for the government to find a Pareto-efficient outcome, or distribute compensation fairly. And governments may favour the more powerful group (the plantation owners in our case), imposing a Pareto-efficient outcome that is also unfair.

Great economists Arthur Pigou

Portrait of Arthur Pigou

Arthur Pigou (1877–1959) was one of the first neoclassical economists to focus on welfare economics, which is the analysis of the allocation of resources in terms of the wellbeing of society as a whole. Pigou won awards during his studies at the University of Cambridge in history, languages, and moral sciences. (There was no dedicated economics degree at the time.) He became a protégé of Alfred Marshall. Pigou was an outgoing and lively person when young, but his experiences as a conscientious objector and ambulance driver during the First World War, as well as anxieties over his own health, turned him into a recluse who hid in his office except for lectures and walks.

Pigou’s economic theory was mainly focused on using economics for the good of society, which is why he is sometimes considered as the founder of welfare economics.

His book Wealth and Welfare was described by Schumpeter as ‘the greatest venture in labour economics ever undertaken by a man who was primarily a theorist’, and provided the foundation for his later work, The Economics of Welfare. Together, these works built up a relationship between a nation’s economy and the welfare of its people. Pigou focused on happiness and wellbeing. He recognized that concepts such as political freedom and relative social status were important.1 2

Pigou believed that the reallocation of resources was necessary when the interests of a private firm or individual diverged from the interests of society, causing what we would today call externalities. He suggested taxation could solve the problem: Pigouvian taxes are intended to ensure that producers face the true social costs of their decisions.

The online version of Keynes’s The General Theory allows you to search for his critique of Pigou.

Despite both being heirs to Marshall’s new school of economics, Pigou and Keynes did not always agree. Keynes’s work, The General Theory of Employment, Interest and Money, contained a critique of Pigou’s The Theory of Unemployment, and Pigou was similarly critical in response.

Although overlooked for much of the twentieth century, Pigou’s work paved the way for much of labour economics and environmental policy. Pigouvian taxes were largely unrecognized until the 1960s, but they have become a major policy tool for reducing pollution and environmental damage.

Exercise 10.3 Pigou’s ideas and environmental policy

Read Sections 1 to 3 of the article, ‘Pigou in the 21st Century: A Tribute on the Occasion of the 100th Anniversary of the Publication of The Economics of Welfare’, which summarizes Pigou’s contributions to economics. Refer to specific examples of Pigouvian taxation from Section 3 (Germany’s carbon price reform and the EU Emissions Trading Scheme (ETS)) when answering the following questions.

  1. What challenges have policymakers faced when implementing Pigouvian taxes in practice?
  2. Why might the tax that is actually implemented not exactly satisfy the theoretical requirements proposed by Pigou (that is, producers facing the true social costs of their decisions)?

Exercise 10.4 Comparing policies

Consider the three policies of regulation, taxation, and compensation arrangements discussed above. Use the criteria of Pareto efficiency and fairness to evaluate the strengths and weaknesses of each policy.

Question 10.4 Choose the correct answer(s)

The graph shows the MPC and MSC of robot production for the factory situated next to a dormitory for nurses who work night shifts.

In this diagram, the horizontal axis shows output, denoted Q, ranging from 0 to 140. The vertical axis shows costs in dollars, ranging from 0 to 600. Coordinates are (output, costs). There are two upward-sloping straight lines that start from the point (0, 100), labelled marginal social cost and marginal private cost. The marginal social cost lies above the marginal private cost at all points. A horizontal line corresponding to a price of $340 intersects the marginal social cost curve at a quantity of 80 and intersects the marginal private cost curve at a quantity of 120. At a quantity of 120, the marginal social cost is $460. A horizontal line corresponding to a price of $260 is the after-tax price. It intersects the marginal private cost curve at a quantity of 80.
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The market for robots is competitive and the market price is $340. The initial output is 120, but the government uses a Pigouvian tax to reduce this to the efficient level of 80. Read the following statements and choose the correct option(s).

  • Under the Pigouvian tax, the factory’s surplus will be $6,400.
  • The required Pigouvian tax is $120 per robot.
  • The nurses are at least as well off as they would be under Coasean bargaining.
  • The nurses obtain no benefit from the imposition of the Pigouvian tax.
  • The Pigouvian tax lowers the after-tax price to $260. The factory’s surplus is the area above the MPC line and below the line for a price of $260 = 0.5 × 80 × (260 – 100) = $6,400.
  • The Pigouvian tax has to lower the after-tax price from $340 to $260, so it is $80.
  • Under a Coasean bargain that involved a payment from the factory to the nurses, as well as a reduction in noise, the nurses would be better off.
  • The nurses do not receive a payment, but they benefit from the noise reduction.

Extension 10.4 Pigouvian taxes

In this extension, we continue to analyse the model constructed in Extension 10.2 of the external effects of pollution. We determine the Pigouvian tax, and consider its distributional consequences.

In Extension 10.2, we showed that the profit-maximizing plantation owner chooses banana output, Qp, so that the marginal private cost is equal to the market price:

\[C^{\prime}_p(Q_p)=P^W\]

But at the Pareto-efficient output, Q*, the marginal social cost is equal to the market price:

\[C^{\prime}_p(Q^*)+C^{\prime}_e (Q^*)=P^W\]

Suppose that the government could impose a tax of x units of money for each ton of bananas produced. The plantations’ total cost of producing Q tons of bananas is now \(C_p(Q) + xQ\). Differentiating with respect to Q, the marginal cost incurred by the plantations is now \(C^{\prime}_{p}(Q) +x\): taxes raise the marginal cost of production. As before, the owner chooses output so that the marginal cost is equal to the price, but since the marginal cost has changed, so does the choice of output. The plantations will produce \(Q^{\dagger}\), where:

\[C^{\prime}_{p}(Q^{\dagger}) + x=P^W\]

Since the private marginal cost \(C^{\prime}_p(Q)\) is an increasing function of Q, \(Q^{\dagger}\) is smaller than Qp if x is positive—and the higher the tax, the lower the output produced.

Comparing this equation with the previous one, we can understand how the government could achieve Pareto efficiency. If the tax, x, is set equal to \(C^{\prime}_e(Q^*)\), then the plantations will choose \(Q^{\dagger}\) so that:

\[C^{\prime}_{p}(Q^{\dagger}) +C^{\prime}_e(Q^*)=P^W\]

But this equation is satisfied when \(Q^{\dagger}=Q^*\). So the tax rate \(x^*=C^{\prime}_e(Q^*)\) induces them to choose the Pareto-efficient level of output.

This is the Pigouvian tax rate: it is equal to the marginal external cost (MEC) at the Pareto-efficient output level. It addresses the externality problem and achieves Pareto efficiency by changing the marginal costs faced by the banana plantations, so that they take into account the full social costs of their decisions—including the costs they impose on others.

The Pigouvian tax is illustrated in Figure 10.4 above, although it is explained slightly differently there. An alternative way of thinking about how it works is to say that it changes the price that the plantations obtain for their bananas, rather than their costs. Then they will choose their output so that their marginal private cost is equal to the after-tax price \(P^W-x^*\). So again they choose Q*, because:

\[C^{\prime}_p (Q^*)= P^W-x^*\]

Distributional effects: Who gains and who loses?

In the absence of a tax, the plantations maximize profits at \(Q=Q_p\). The effect of the tax is to lower the after-tax price they receive per ton; they reduce output to Q* and their profits are lower than before.

The fishermen gain: the reduction in banana output reduces pollution, increasing the profits from fishing.

And the government gains too: it receives revenue, \(x^*Q^*\).

There is an important point to understand here. If the government imposes the tax, x*, banana output will be reduced to the Pareto-efficient level. However, this change is not a Pareto improvement—the plantations are worse off than before. You can check that the total gains (to the government and fishermen) outweigh the loss to the plantations. This means that, in principle, the gainers could compensate the losers and still be better off. But unless they do so, the tax policy will not be welcomed by the plantations.

Exercise E10.2 Pigouvian taxation

Consider the toy manufacturer in Extension 10.2, with cost function, \(C(Q) = 2Q^2 + 2Q + 5\), for Q units produced, and generating external costs \(\frac{1}{6}Q^3 + \frac{1}{2}Q^2\). The world price for premium toys is $50 per unit.

  1. Calculate the required Pigouvian tax, and illustrate how the tax leads to Pareto efficiency on a diagram showing the marginal social and private costs.
  2. Calculate the overall effect on profit for the manufacturer, and compare it with the gains resulting from the policy (the tax revenue, and the reduction in pollution).
  1. Arthur Pigou. 1912. Wealth and Welfare. London: Macmillan & Co. 

  2. Arthur Pigou. (1920) 1932. The Economics of Welfare. London: Macmillan & Co.