Partial equilibrium theory

Consider a profit maximizing price taking firm. The transformation function: f(x1, x2,..., x1, e) = 0 (9.1)

describes the technologically efficient input output options available to the firm (where a positive value for xi indicates an output and a negative value indicates an input) and e is the associated level of emissions.

It is assumed that a firm may adjust outputs and inputs to reduce emissions in one of three ways. First, 'tail end' cleaning technologies may be available (scrubber technologies) that will allow the firm to reduce the emissions associated with a given vector of outputs. Typically, such technologies will require the use of more of some inputs (and not less of other inputs) so that the total cost of producing the given output vector will be higher. Second, it may be possible to substitute lower emission for higher emission inputs (for example, natural gas for coal as an energy source) to produce the given outputs. If the initial vector of inputs were chosen optimally to produce a given vector of outputs such substitution will increase total production costs. Third, the use of some inputs resulting in emissions (and presumably some other inputs if they are not to be redundant) may be reduced resulting in a reduction in some outputs and net revenue (if the initial output input combination was optimal).

Suppose that a tax of t per unit of emissions is introduced. The problem of the firm is to maximize net revenue subject to equation 9.1. Forming the Lagrangean:

where pi represents the price of output/input i, the following first order conditions of interest are obtained:

The shadow price, may be interpreted as the price of an additional unit of emissions. The term, df/de, represents the marginal physical product of emissions. Thus, the term, df/de, can be interpreted as the marginal cost of reducing emissions and is more commonly called the marginal cost of abatement. Equation 9.3 shows that the optimal level of emissions is determined by the condition that the marginal cost of abatement equals the tax rate.

The total cost of abatement is the difference between the net revenue of the firm when emissions are unconstrained and net revenue when emissions are constrained given that outputs and inputs are adjusted optimally in both situations. It would be expected that total costs of abatement would increase with the level of abatement (the smaller the value of e). Indeed, it would be expected that total costs would increase more than proportionately with the level of abatement. There are likely to be limits on emission reductions possible through scrubber technologies and substitution options. Once these limits are exhausted the firm has no option other than to reduce output. Thus, the marginal cost of abatement would be expected to increase with the level of abatement.

If all emission sources face a uniform tax on emissions and equate their marginal costs of abatement to the tax rate, marginal costs of abatement will be equalized across emission sources. This is, of course, the condition for the total costs of abatement to be minimized. Thus, as discussed in Chapter 8, a uniform tax on emissions is one of the policy instruments that uses market forces to achieve a least cost solution to the problem of achieving a given level of abatement. Since it is unlikely that the level of abatement resulting from a given tax rate will be known with certainty, some experimentation with the tax rate may be required to achieve the desired level of abatement.

Economy-wide studies

Two basic types of models known as 'bottom up' and 'top down' models have been used to study the impact of carbon taxes at the economy level. 'Bottom up' models contain detailed information about technological options in the energy sector but there is limited interaction with the rest of the economy. For example, in the simplest models, demand is totally unresponsive to changes in price. The model is solved simply for the least cost method of supplying a given quantity of energy. Imposing carbon taxes alters the contribution of different types of energy to the least cost supply. However, the total quantity of energy demanded remains fixed even though carbon taxes have altered the total cost of supply (and the supply price).

The assumption that demand is not responsive to price has been relaxed in more recent model developments. However, there is still much less interaction with other sectors of the economy than in 'top down' models. 'Bottom up' models are often solved using linear programming or non-linear programming techniques to minimize (discounted) energy system costs.

'Top down' models are usually computable general equilibrium (CGE) models and allow for more extensive interaction between different sectors of the economy. It is assumed that consumers make purchase decisions to maximize their welfare while firms make production decisions to maximize profits. All prices are variable and an equilibrium consists of a set of prices that ensures that demand for all goods is equal to their supply. Such models are usually solved using one of a number of methods for the numerical solution of a set of simultaneous equations. Modelling of technological options in the energy sector is much less detailed than in 'bottom up' models. Technological options are usually modelled based on a production function estimated from historical data where it is assumed that different inputs can be smoothly substituted for one another.

In a partial equilibrium framework, the costs of abatement are measured by the loss in net revenue for a firm. In general equilibrium models it is common to use a broader measure of the change in economic welfare. Abatement may alter the income of a representative consumer and change relative prices resulting in a change in the optimal consumption bundle. In some cases Hicksian equivalent variation has been used as a welfare measure but it has been more common to use the change in Gross Domestic Product (GDP) as a general purpose measure. Results from 'bottom up' models are often converted into a GDP equivalent form to allow comparison with the results from 'top down' models.

A general finding of both types of models is that the total cost of abatement, no matter how measured, tends to increase more than proportionately with the level of abatement. Such a finding is in line with theoretical expectations as discussed above.

It is also often found that 'bottom up' models yield lower welfare losses in attaining given abatement targets than 'top down' models. For example, to stabilize carbon dioxide emissions at 1990 levels, estimates from 'bottom up' models for a number of economies suggest a loss of GDP in the range of 0.5 per cent to 1 per cent. Estimates from 'top down' models for a given economy are usually somewhat larger although most estimates seldom involve more than a 2 per cent loss in GDP.

To understand the reasons for these difference in results, it is important to note that it is widely conceded that 'bottom up' models tend to be over-optimistic compared with observed performance about the speed of adoption of newer technologies in response to changes in relative costs. Such models do not appear to capture adequately the various sources of inertia that may slow shifts towards less costly technologies. These sources of inertia are probably better captured in 'top down' models since the speed of adjustment is based on historical estimates. On the other hand, the assumption in many 'top down' models that inputs can be smoothly substituted for one another can imply the use of unobserved technologies.

It also seems probable that some of the flow through effects of higher energy prices captured by 'top down' models but not by 'bottom up' models add to welfare losses. For example, higher energy prices will affect the relative prices of goods and services according to energy intensity resulting in changes in production patterns that may be a further source of welfare loss.

The strength of 'bottom up' models is in their technological detail and illustration of technological possibilities. 'Top down' models are probably better at capturing the relationship between economic aggregates, which would include economic welfare losses in response to imposing a carbon tax.

International repercussions


The economy level models considered in the previous section were closed models in the sense that any international repercussions of imposing carbon taxes were ignored. However, taking account of international repercussions may modify estimates of the size of the carbon tax and welfare losses incurred in achieving a given level of abatement. Policy proposals to reduce the risk of global warming involve simultaneous abatement by a large number of economies. In particular, the Kyoto Protocol proposes simultaneous abatement by the group of so-called Annex I countries that essentially consists of all developed countries (see Chapter 5). International repercussions of such simultaneous abatement could be of a considerable order of magnitude.

A basic theoretical point to make in considering international repercussions is that imposing a carbon tax to achieve an emission target alters the production possibility set for an economy. Some input output combinations that are technologically feasible may no longer be economically feasible since they violate the overall emission constraint implied by the carbon tax. The impact of a carbon tax on the production possibility set is analogous to that of negative technological progress.

A standard graphical device used to illustrate determining international equilibrium in a two good, two input, two country world involves the use of the production possibility sets for the two economies. If the production possibility set of either economy changes, the terms of trade change resulting in welfare changes in both economies. Since a carbon tax alters production possibility sets, changes in the terms of trade is an avenue for the international transmission of the effects of abatement.

If the overall international repercussions of abatement are to improve the terms of trade for an abating economy, welfare losses will be smaller than if the terms of trade were unchanged while the converse also applies. The terms of trade of non-abating economies may also be affected by abatement in Annex I countries. Impacts of Annex I abatement on the group of the Organization of Petroleum Exporting Countries (OPEC) and the possible response by OPEC has been a topic of special interest as discussed below.

Annex I abatement may also alter relative rates of return on capital in different economies resulting in changes in the pattern of international capital flows. Such changes in international capital flows may also result in welfare changes. In many studies it has been assumed that capital is not mobile internationally. It has been suggested that changes in international capital flows are likely to be related to changes in the terms of trade. Thus, results obtained under the assumption of no international capital mobility may serve as a reasonable first approximation to the more realistic case where capital is internationally mobile. Some support for this assumption is given by results from most of the few studies that have considered international capital mobility.

Empirical results

The international repercussions of abatement have been assessed with a number of models of the global economy using various regional aggregations. These models are exclusively 'top down' CGE models.

It is useful to consider simulation results for the international repercussions of single economies abating before turning to results for the more complex interactions that occur when a number of economies abate simultaneously. These results show that the large industrial economies of the United States, the European Union and Japan all experience an improvement in their terms of trade when they impose carbon taxes to achieve an abatement target. Such an improvement in the terms of trade reduces the welfare losses from abatement. These economies are net exporters of manufactures and net importers of fossil fuels. Carbon taxes result in higher energy prices that push up the prices of exported manufactures while reduced demand for fossil fuels results in lower import prices.

The Annex I economies that are net exporters of fossil fuels and net importers of manufactures, such as Australia and the former Soviet Union, suffer a deterioration in their terms of trade when they abate, which increases welfare losses. Domestic abatement reduces domestic demand for fossil fuels, which increases supplies to the export market, resulting in lower export prices and a deterioration in the terms of trade.

When all Annex I economies simultaneously abate (at the same individual levels as in the case just considered) it would be expected that combined welfare losses would be increased. Imposing carbon taxes would simultaneously reduce production possibilities in a number of economies, narrowing the scope to exploit gains from specialization through trade. Simulation results do confirm that the sum of losses in real GDP for all Annex I countries is larger under simultaneous abatement than under unilateral abatement.

There are two immediate factors that are apparent in explaining these increased welfare losses under simultaneous abatement. First, Annex I countries are significant importers of manufactures from other Annex I countries. Thus, simultaneous abatement by all Annex I countries raises the price paid for imported manufactures. Second, the fossil fuel exporting Annex I countries now face reduced demand in export markets as well as at home, resulting in lower fossil fuel prices. Of course, such lower prices are beneficial to importing countries and not all Annex I countries are worse off under simultaneous compared with unilateral abatement. However, collective welfare losses for the Annex I region are higher under simultaneous abatement than under unilateral abatement.

Non-Annex I impacts

The impact of Annex I abatement on non-Annex I economies is important for the economic welfare of non-Annex I economies. It is also important for the environmental effectiveness of Annex I abatement policies due to the problem of emission leakage. Emission leakage is said to occur when reduced emissions from Annex I countries are partly offset by increased emissions from non-Annex I countries. Results on these impacts are available from simulations with a number of models under various abatement strategies.

The main conclusion from these studies is that the impact of Annex I abatement on non-Annex I welfare is predominantly adverse. Combined non-Annex I welfare losses increase the more severe the level of Annex I abatement.

As discussed above, Annex I abatement results in a decline in the price of imported fossil fuels and a rise in the price of exported manufactures. The nonAnnex I countries with the heaviest dependence on exported fossil fuels such as the Middle East and Indonesia suffer the greatest deterioration in their terms of trade and welfare losses under Annex I abatement. South Korea and Brazil are among the most favourably placed non-Annex I economies, being net importers of fossil fuels and net exporters of non-ferrous metal and iron and steel products. The latter products are highly emission intensive in production in Annex I economies and their price throughout the world rises markedly under Annex I carbon taxes. Under milder levels of Annex I abatement, such as that involved under the Kyoto targets, South Korea and Brazil and a few other non-Annex I countries have been found to experience mild welfare gains in various model simulations.

Emission leakage

Emission leakage is usually measured as 100 times the increase in non-Annex I emissions divided by the reduction in Annex I emissions. It may result from both the production of more emission intensive goods and the use of more emission intensive production techniques in non-Annex I countries. Production of more emission intensive goods may be for both own consumption and export to Annex I countries. More emission intensive production techniques may be adopted in response to lower prices for fossil fuels resulting from Annex I abatement.

Estimates of the degree of emission leakage vary widely among models. Estimates tend to be higher, the higher the elasticity of substitution assumed between imports and domestic production. The higher the elasticity of substitution the smaller the reduction in Annex I final consumption of emission intensive goods as greater substitution of non-Annex I for domestic production occurs. High elasticities of substitution also tend to result in larger declines in fossil fuel prices and greater use of emission intensive production techniques in non-Annex I countries. Nevertheless, there are some significant differences between estimates of emission leakage even among models with similar assumptions about the elasticity of substitution for reasons yet to be fully explored.

Resolving the issue of the most appropriate assumptions about elasticities of substitution between domestic production and imports involves some difficult problems. Commodities identified in CGE models are usually aggregates of many sub-commodities. Since the sub-commodity composition of a given commodity may differ significantly between countries the assumption of imperfect substitution between domestic production and imports for the aggregated commodity may often be reasonable. However, even if the initial estimate of the elasticity were appropriate it may not be appropriate for all of the simulation if in reality the sub-commodity composition of the aggregate would change markedly under the conditions assumed in the simulation.

It would be possible to reduce the extent of the above problem by working with more finely disaggregated commodities. However, the computational burden of solving CGE models tends to increase exponentially with the number of commodities. Furthermore, the need to ensure that the model is consistent with its database may constrain feasible values for elasticities of substitution. There is also the problem that under high elasticities of substitution it is possible in a simulation that a model may shift all of world production to one country.

A general finding of the various studies is that the degree of emission leakage tends to increase with the level of Annex I abatement. Such a result would be expected from the economy level non-linear relationship between total costs of abatement and the level of abatement. As the level of abatement increases and there is increasing reliance on output reduction relative to input substitution to reduce Annex I emissions, there would be stronger incentives for emission intensive production in non-Annex I countries. There would be increased incentives to displace Annex I production and to use emission intensive techniques due to lower fossil fuel prices.

The results discussed above are derived from models where it is assumed that an exogenously given rate of technological change is unbiased (that is, affects all inputs equally). In particular, it is usually assumed that there is an exogenously given rate of so-called autonomous energy efficiency improvement. It is also assumed that all world markets are perfectly competitive. These assumptions have been modified in a number of studies and the impact on model results is now considered.

The induced innovations hypothesis

The induced innovations hypothesis maintains that technological change is biased and that bias is related to movements in relative input prices. It is argued that the greatest profit opportunities exist for economizing on the use of inputs where relative prices have risen the most. Thus, technological change should be biased towards those inputs where relative prices have increased and biased away from inputs where relative prices have fallen.

Since a carbon tax would increase the relative price of energy, the induced innovations hypothesis implies that technological change would be biased towards economizing on the use of energy inputs. Although only the bias and not the overall rate of technological change is affected, simulation results show that the improvement in energy efficiency can significantly reduce welfare losses in meeting abatement targets. In fact, in some simulations of CGE models under the induced innovations hypothesis, welfare losses have been of a similar order to those obtained with bottom up models.

The difficulty with the induced innovations hypothesis is that attempts to test it using historical data have produced mixed results. Alternatives to the induced innovations hypothesis are that technical progress follows a path determined entirely by scientific and technological imperatives or that technical progress is a purely random process as evidenced by the number of 'accidental' discoveries. It may be objected that the extent to which scientific and technological imperatives are followed and the extent to which accidental discoveries are converted into working technologies will be influenced by profit opportunities. Nevertheless, it may be that there is sufficient randomness in the process of technical progress that it often makes it difficult to detect the patterns implied by the induced innovation hypothesis.

A related problem is that it is not simple to devise a conclusive test for the hypothesis given available data. Some of the most recent studies using more sophisticated methodologies have been relatively favourable to the hypothesis. However, it cannot be said that the hypothesis either receives overwhelming support or is decisively rejected by the weight of empirical studies.

OPEC response

Oil is probably the market where assumptions about the nature of world competition are most important in the context of climate change policies. The standard assumption in many CGE models of price taking behaviour by producers in the world oil market may appear questionable. In the past OPEC appears to have had some success in controlling production to influence the world price of oil. Nevertheless, in recent years a number of 'fringe' producers have emerged that have reduced OPEC's share of world oil production.

In various CGE model simulations of the impacts of Annex I abatement policies under the price taking assumption, the OPEC group of nations are usually found to suffer the largest welfare losses among non-Annex I countries. Such a result stems from the heavy dependence of OPEC nations on oil for export revenue. There clearly would be an incentive for OPEC to attempt to restrict production to force up prices to curb the loss in export revenue. However, the ability of OPEC to control prices may be limited by competition from fringe producers. To the extent that OPEC was successful in stemming the loss in oil revenue, it would reduce its own welfare losses and increase those of Annex I countries. Such a result follows since a favourable movement in the terms of trade for one group of countries represents a deterioration in the terms of trade for its trading partners.

The possible nature of an OPEC response to Annex I abatement has been studied mainly using models specifically constructed to examine this problem. It is usually assumed that OPEC seeks to maximize discounted net revenue from oil over some time horizon. The main finding is that while competition from the fringe reduces OPEC's market power, OPEC does have some power to stem the loss in oil revenue provided cartel discipline can be maintained. There would be incentives to break cartel discipline in a falling market. However, on the level of political economy, it has been suggested that Annex I abatement would be seen as a hostile act by OPEC and this could strengthen the resolve to maintain cartel discipline. Some have attributed the apparent greater cartel discipline shown by OPEC during 2000 and 2001 partly to the threat of abatement action by Annex I economies.

The most successful strategy for OPEC would be to expand the cartel to include the non-OECD fringe producers (some of the countries of the former Soviet Union and a number of developing countries). These countries would also suffer significant oil revenue losses under Annex I abatement and so have an incentive to join the cartel. It does not seem plausible to assume that OECD fringe producers could be induced to join the cartel given that most of these producers have received a high level of government assistance to increase production with the aim of weakening OPEC's market power.

While any successful OPEC cartel strategy would tend to increase welfare losses for Annex I countries, there would also be other side effects. One of these would be that the higher world price for oil would reduce the growth of consumption in non-Annex I countries and so reduce the amount of emission leakage.

The impact of possible OPEC strategies has not been studied using global CGE models mainly because many of the solution techniques used are not consistent with modelling the exercise of market power. Thus, all of the quantitative global ramifications of possible OPEC strategies have not been fully explored. This remains a challenge for future research.

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