Uncertainty and Policy Choice: Carbon Tax or Emissions Trading Scheme

Abstract

As we explained in Chaps. 1 and 3, regulations, taxation, or any policy instruments could maximize social surplus if policymakers have perfect information about the demand curve, supply curve, and marginal external cost curve. In reality, however, governments do not have perfect information and therefore can mistakenly determine the optimal level of production, emissions, or an environmental tax, resulting in a decrease in social surplus. In this chapter, we consider which policy option is desirable—environmental taxes (we take a carbon tax as an example) or emissions trading schemes—to mitigate a decrease in social surplus in the presence of uncertainty due to imperfect information.

Chapters 1 and 3 explained that it is possible to abate CO₂ emissions to an optimal level either by an environmental tax (or a carbon tax) or an emissions trading scheme, and that the level of the tax and the price of the permit will equal at the optimal abatement/emissions level. In Chaps. 1 and 3, it is assumed that the government knows the optimal emissions level and thus optimally sets the level of the tax or the number of permits to issue because it has perfect information regarding the CO₂ demand and marginal external costs thereby identifying these functions correctly.

In reality, however, governments do not have perfect information and therefore have to predict the functions based on imperfect information and make decisions accordingly. In this chapter, we examine which type of measure is best suited in the presence of uncertainty due to imperfect information. In particular, we consider policy instruments that control prices (e.g., a carbon tax) or quantities (e.g., an emissions trading scheme) in terms of efficiency in resource allocation.¹

1 Policy Choice and Total Social Surplus Under Perfect Information

Before addressing the issue of uncertainty caused by imperfect information, we review the outcomes of implementing a carbon tax and an emissions trading scheme when the government has perfect information. We start with the case of implementing a carbon tax. Figure 4.1 shows the CO₂ demand curve (D^*) and the marginal external cost curve (MEC^*), with CO₂ price² (P) on the vertical axis and the amount of CO₂ emissions (X) on the horizontal axis.

Fig. 4.1

Optimal carbon tax under perfect information

As shown in the figure, social surplus is maximized at point B and the optimal level of emissions is X^*. When the government does not implement any environmental measure, CO₂ price is equal to zero and CO₂ will be emitted up to X₀. The optimal level of the tax to reduce emissions to X^* is t^*. In this case, the consumer surplus (CS^*) of carbon emissions, the revenue raised by the tax (T^*), and the external cost (EC^*) would be

$${{\text{CS}}}^{*}=\mathrm{ area\, ABC}, {{\text{T}}}^{*}=\mathrm{ area\,}{{\text{OCBX}}}^{*}, {{\text{EC}}}^{*}=\mathrm{area\,}{{\text{OBX}}}^{*}$$

Thus the social surplus (SS^*) would be

$${{\text{SS}}}^{*}= {{\text{CS}}}^{*}+{{\text{T}}}^{*}- {{\text{EC}}}^{*}=\mathrm{area\,OAB}$$

By using Fig. 4.2, let's consider the case the government adopts an emissions trading scheme. To achieve the emissions level X*, the government needs to issue X* units of permits that allow one unit of emissions per permit. We assume that this is an auction type system meaning that there is no initial allocation of the permits to each firm.

Fig. 4.2

Emissions trading scheme under perfect information

Figure 4.2 is similar to Fig. 4.1, but it shows a demand curve for emissions permits (D^*) and the marginal external cost curve (MEC^*) with the price of the permits (P_e) on the vertical axis and the quantity of the permits (X) on the horizontal axis. S^* is the permit supply curve. A firm must own one permit for one unit of CO₂ emissions, so the demand for one unit of emissions corresponds to the demand for one permit. Therefore, the demand price of the permit equals that of CO₂, and accordingly, the permit demand curve in Fig. 4.2 is identical to the CO₂ demand curve in Fig. 4.1. In a similar vein, the marginal external cost curve in Fig. 4.2 is identical to that in Fig. 4.1.

As shown in Fig. 4.2, the supply of and the demand for the permits are in equilibrium at point B. The equilibrium price of the permits is P_e^*. The consumer surplus (CS_e^*), the revenues from the sale of the permits (T_e^*), and the external cost (EC_e^*) are

$${{\text{CS}}}_{{\text{e}}}^{*}=\mathrm{area\,ABC}, {{\text{T}}}_{{\text{e}}}^{*}=\mathrm{area\,OCB}{{\text{X}}}^{*},\mathrm{ E}{{\text{C}}}_{{\text{e}}}^{*}=\mathrm{area\,OB}{{\text{X}}}^{*}$$

Thus the social surplus (SS_e^*) is

$${{\text{SS}}}_{{\text{e}}}^{*}={{\text{CS}}}_{{\text{e}}}^{*}+{{\text{T}}}_{{\text{e}}}^{*}-{{\text{EC}}}_{{\text{e}}}^{*}=\mathrm{area\,OAB}$$

By comparing the surpluses in Figs. 4.1 and 4.2, we obtain:

$${{\text{CS}}}_{{\text{e}}}^{*}={{\text{CS}}}^{*},{{\text{T}}}_{{\text{e}}}^{*}={{\text{T}}}^{*},{{\text{EC}}}_{{\text{e}}}^{*}={{\text{EC}}}^{*},{{\text{SS}}}_{{\text{e}}}^{*}={{\text{SS}}}^{*}$$

Also, it is clear that the level of the carbon tax and the price of the permits are the same:

$${\text t}^{*} = {\text P}_{\text e}^{*}$$

2 Loss of Social Surplus Due to Imperfect Information on the MEC Curve

Now we consider a case where the government has perfect information on the CO₂ demand function and imperfect information on the marginal external cost function. Figure 4.3 resembles Fig. 4.1, but the only difference is that Fig. 4.3 has MEC¹. Suppose that the government incorrectly estimates that MEC¹ is the true marginal external cost curve and therefore mistakenly considers that the optimal amount of CO₂ emissions is X¹ to maximize the predicted social surplus.

Fig. 4.3

Loss of surplus due to imperfect information on external costs

Suppose also that the government imposes a carbon tax and sets the level of the tax to t¹ to abate emissions to X¹. In this case, the consumer surplus (CS¹), the carbon tax revenue (T¹), and the external cost (EC¹) will be

$${{\text{CS}}}^{1}=\mathrm{area\,AFE}, {{\text{T}}}^{1}=\mathrm{area\,OFE}{{\text{X}}}^{1},\mathrm{ E}{{\text{C}}}^{1}=\mathrm{area\,OG}{{\text{X}}}^{1}$$

Thus, the total social surplus (SS¹) is

$${{\text{SS}}}^{1}={{\text{CS}}}^{1}+{{\text{T}}}^{1}-{{\text{EC}}}^{1}=\mathrm{area\,OAEG}$$

and the loss of the social surplus (ΔSS¹) due to the imperfect information is

$$\Delta \text{SS}^{1}=\text{SS}^{1}-\text{SS}^{*}=\text{area}\,\text{BEG}$$

Next, we examine the case in which the government introduces an emissions trading scheme to achieve the same emissions level (X¹). For this purpose, the government should issue X¹ units of permits. The CO₂ demand function in Fig. 4.3 can be interpreted as the demand curve for the permits just like the one in Fig. 4.2, if the CO₂ price (the quantity of emissions) on the vertical (horizontal) axis is replaced with the permit price (the quantity of the permits supplied/demanded). S¹ represents the supply curve for the permits. We can see that at point E, the equilibrium price of the permit is t¹, i.e., identical to the case when the carbon tax is adopted. The consumer surplus (CS_e¹), the revenue from the permit sales (T_e¹) and the external cost (EC_e¹) are

$${{\text{CS}}}_{{\text{e}}}^{1}=\mathrm{area\,AFE}, {{\text{T}}}_{{\text{e}}}^{1}=\mathrm{area\,OFE}{{\text{X}}}^{1},\mathrm{ E}{{\text{C}}}_{{\text{e}}}^{1}=\mathrm{area\,OG}{{\text{X}}}^{1}$$

Hence, the social surplus (SS_e¹) is

$${{\text{SS}}}_{{\text{e}}}^{1}={{\text{CS}}}_{{\text{e}}}^{1}+{{\text{T}}}_{{\text{e}}}^{1}-{{\text{EC}}}_{{\text{e}}}^{1}=\mathrm{area\,OAEG}$$

and the loss of the social surplus (ΔSS_e¹) due to the imperfect information is

$$\mathrm{\Delta S}{{\text{S}}}_{{\text{e}}}^{1}={{\text{SS}}}_{{\text{e}}}^{*} - {{\text{SS}}}_{{\text{e}}}^{1}=\mathrm{area\,BEG}$$

As shown above,

$$\mathrm{\Delta S}{{\text{S}}}^{1}=\mathrm{\Delta S}{{\text{S}}}_{{\text{e}}}^{1}$$

In sum, when the government has imperfect information on the marginal external cost function, the loss of the social surplus would be the same regardless of whether a carbon tax or an emissions trading scheme is implemented.

3 Loss of the Social Surplus Due to Imperfect Information on the CO₂ Demand Function

Next, we consider a case where the government has perfect information on the marginal external cost function and imperfect information on the CO₂ demand function. This is the case where the government incorrectly estimates that D² is the true CO₂ demand function, as shown in Fig. 4.4 (i.e., Fig. 4.1 plus D²). Here, the government mistakenly assumes that the optimal amount of emissions is X².

Fig. 4.4

Loss of the social surplus due to imperfect information on CO₂ demand curve

Suppose a carbon tax is introduced to abate emissions to X². Then the level of the tax set by the government would be t² to maximize the predicted social surplus. Because the true CO₂ demand function is D*, the emissions level is X³. Therefore, the consumer surplus (CS²), the carbon tax revenue (T²), and the external costs (EC²) are

$${{\text{CS}}}^{2}=\mathrm{arae AGE}, {{\text{T}}}^{2}=\mathrm{area\,OEG}{{\text{X}}}^{3},\mathrm{ E}{{\text{C}}}^{2}={{\text{areaOHX}}}^{3}$$

The social surplus (${{\text{SS}}}^{2}$) is

$${{\text{SS}}}^{2}={{\text{CS}}}^{2} + {{\text{T}}}^{2} -\mathrm{ E}{{\text{C}}}^{2} =\mathrm{ area\,OAGH}$$

and the loss of the social surplus ($\mathrm{\Delta S}{{\text{S}}}^{2}$) due to the imperfect information is

$$\mathrm{\Delta S}{{\text{S}}}^{2}={{\text{SS}}}^{*}-\mathrm{ S}{{\text{S}}}^{2}=\mathrm{area\,BEH}$$

If an emissions trading scheme is chosen to achieve the same emissions level, the government issues X² permits. As in Fig. 4.3, the CO₂ demand function in Fig. 4.4 can be interpreted as the permit demand curve if the CO₂ price (the quantity of emissions) on the vertical (horizontal) axis is replaced with the permit price (the quantity of the permits supplied/demanded). S² represents the supply curve for the permits just like S¹ in Fig. 4.3. The equilibrium price of the permit is P_e² at point F. The consumer surplus (CS_e²), the revenue from the sale of the permits (T_e²), and the external cost (${{\text{EC}}}_{{\text{e}}}^{2}$) are

$${{\text{CS}}}_{{\text{e}}}^{2}=\mathrm{arae AIJ}, {{\text{T}}}_{{\text{e}}}^{2}=\mathrm{area\,OIJ}{{\text{X}}}^{2}, {{\text{EC}}}_{{\text{e}}}^{2}=\mathrm{area\,OF}{{\text{X}}}^{2}$$

The social surplus (SS_e²) is

$${{\text{SS}}}_{{\text{e}}}^{2}={{\text{CS}}}_{{\text{e}}}^{2} + {{\text{T}}}_{{\text{e}}}^{2} +{\mathrm{ EC}}_{{\text{e}}}^{2} = \text{area OAB} - \text{area BFJ}$$

and the loss of the social surplus (Δ${{\text{SS}}}_{{\text{e}}}^{2}$) in the absence of perfect information is

$$\Delta {{\text{SS}}}_{{\text{e}}}^{2}={{\text{SS}}}_{{\text{e}}}^{2}-{{\text{SS}}}_{{\text{e}}}^{*}=\mathrm{area\,BFJ}$$

4 Loss of the Social Surplus: The Slopes of the MEC Curve and the CO₂ Demand Curve

The relationship between ΔSS² and $\Delta {{\text{SS}}}_{{\text{e}}}^{2}$ depends on the slopes of the marginal external cost curve and the CO₂ demand curve. We examine how the loss of the social surplus changes in accordance with the shapes of these curves. We start with the marginal external cost curve.

(1) The MEC Curve and the Loss of Total Social Surplus

To examine how the size of the surplus loss varies with the slopes of the marginal external cost curve, we compare the difference between the loss incurred by adopting a carbon tax and the loss incurred by implementing an emissions trading scheme when the marginal external cost curve is MEC* and MEC**, respectively, as shown in Fig. 4.5.

Fig. 4.5

MEC curves and loss of total social surplus

Fig. 4.6

CO₂ demand curves and loss of total social surplus

We first consider the case where a carbon tax is chosen over an emissions trading scheme. As discussed above, if the marginal external cost curve is MEC^*, the social surplus loss caused by the government incorrectly estimating that D² is the true CO₂ demand function is area BGH. Similarly, the loss that occurs when the curve is MEC^** is area MGK. Since area MGK > area BGH, the steeper the slope of the curve, the greater the loss. Next, let's consider the case where an emissions trading scheme is adopted instead of a carbon tax. If the curve is MEC^*, the social surplus loss is area BFJ. Likewise, if it is MEC^**, the loss is area MFJ. Since area BFJ > area MFJ, the steeper the curve, the smaller the loss.

(2) The CO₂ Demand Curve and the Loss of Total Social Surplus

We now turn to the CO₂ demand curve and examine how the shape of the curve affects the size of the loss in the social surplus. Similar to what we did in 1), we compare the difference between the loss incurred by having a carbon tax imposed and that by having an emissions trading scheme implemented when the CO₂ demand curve is D^* and D^**. First, we examine the case where a carbon tax is adopted. As we have seen, if the CO₂ demand curve is D^*, the loss caused by the government incorrectly assuming D² as the true CO₂ demand curve is area BGH. Similarly, the loss that occurs when the demand curve is D^** is area KGH. Since area KGH > area BGH, the flatter the curve, the larger the loss.

In the case where an emissions trading scheme is chosen, if the CO₂ demand curve is D^*, the loss is area BFJ. Similarly, the loss is area KMF if the demand curve is D^**. Since area KMF < area BFJ, the flatter the curve, the smaller the loss in surplus. As we can see from Fig. 4.7, if the absolute value of the slope of the marginal external cost curve equals that of the CO₂ demand curve, then the loss from the carbon taxation equals the loss by the implementation of an emissions trading scheme.

Fig. 4.7

Equivalence of carbon tax and emissions trading scheme

To conclude, if the absolute value of the slope of the marginal external cost curve is greater than that of the CO₂ demand curve, the surplus loss from the taxation is greater than the loss from the adoption of an emissions trading scheme. In this case, it is desirable to choose an emissions trading scheme over a carbon tax to minimize the loss in social surplus. Conversely, if the absolute value of the slope of the marginal external cost curve is less than that of the CO₂ demand curve, the loss arising from choosing an emissions trading scheme is greater than the loss arising from choosing a carbon tax. Therefore, it is desirable to choose a carbon tax over an emissions trading scheme.

Box 4.1 Climate Adaptation Measures: Making Agriculture More Resilient to Climate Change Risks

Climate change has significantly impacted agriculture and food production. For example, rising temperatures lower crop yields in high-temperature regions and increase yields in colder regions. More frequent and intense hurricanes cause more severe flooding which results in reduced crop production. Strategies and actions to mitigate the impacts of climate change are adaptation measures. Agricultural adaptation practices include the development of crop varieties resistant to extreme temperatures and switching to crops that thrive at high temperatures.

While the average annual temperature has been increasing, temperatures and precipitation fluctuate every year. Some years have high temperatures and heavy rainfall, while others experience low temperatures and little rain. Agricultural yields may suffer from high temperatures in the previous year and flood damage this year, or may not suffer any significant damage at all in a different year. If the temperature increase is greater than the projected increase, farmers who choose crops that match the projection will suffer reduced yields. Similarly, if the temperature is lower than the projection, farmers who choose crops that match the projection may lose profits due to inappropriate crop choices. Thus, short-term weather fluctuations cause yield and damage fluctuations.

Mitigating these damage or risk fluctuations is an integral part of the adaptation measures. For example, the diversification of cultivation areas reduces risks. Likewise, growing crops that suit various temperatures, such as planting high- and moderate-temperature-tolerant crops, reduces the risk of income fluctuations for farmers. Cultivating crops at different times of the year is also effective in reducing climate risks such as high temperatures and flooding. However, these practices are more feasible for large-scale farmers, but not for small-scale farmers.

Smart agricultural technologies, such as robotics and ICT, can also mitigate climate risks. However, larger-scale and younger farmers are more likely to be engaged in smart farming as small-scale farmers are not likely to afford fixed costs associated with technology and equipment, and it may be challenging for aging farmers to learn the skills necessary for smart farming. In addition, the benefits of acquiring hard-won skills and technology are small if they have no successors. Thus, those farmers are not likely to be engage in them.

These are the challenges that farmers in Japan face today. The majority of Japanese farmers are small-scale, part-time, and aging farmers with few successors. The entry of large-scale farmers must be encouraged to increase agricultural profitability and influence younger generations to enter the farming industry. It will also reduce the number of part-time farmers. Establishing institutional mechanisms that guide the industry to reduce risks and facilitate farmers’ adoption of climate-smart practices is also important.

Cooperation among farmers is also the key to effective agriculture adaptation. Farmers, including those located in different regions, can cooperate to increase crop diversity across locations and to reduce their income risk by sharing total income. Nearby farmers can adopt smart farming, if they can establish a cooperative structure to share the devices and facilities for smart farming. As a collaborative farming group, they can also utilize financial instruments such as weather derivatives and disaster insurance. If insurance companies offer group policies with reduced premiums (or if the government subsidizes policy premiums), small farmers gain better access to these climate-adaptive instruments as part of their adaptation measures.