Economics

This study seeks to evaluate second best quota agreements that do not include research and development elements in a situation where the member countries are heterogeneous. This paper compares contexts in which the assigned emission quotas are tradable against a context in which they are not. The authors argue that marginal costs of abatement vary across countries for the second best agreement where countries are heterogeneous. The researchers explain that abatement costs are influenced by research and development activities that are undertaken by all the firms in all of the participating countries and that for second-best optimum in countries that are heterogeneous, the abatement marginal costs vary across countries. They also argue that the second-best outcome cannot be attained in situations where the emission quotas are tradable.

In order to achieve the purpose of the study, the researchers first explain the gaps in the existing literature that caused them to conduct the study. The study is based on the findings of a research conducted by Golombeck and Hoel (2006), which concentrated on an international environment where countries which are identical are assigned emission quotas but where the agreement does not include research and development policies(Golomek  Hoel 2008 198). However, this study, unlike the one conducted by Golomek and Hoel which focused on identical countries, it seeks to examine the case of countries which are heterogonous. The study therefore developed out of insufficiency in literature on cases of heterogonous countries as the existing literature mostly concentrated on identical. This serves as a justification for the study.

This study  uses the standard economic theory which argues that a climate that is international has to address both negative as well as positive environmental externalities for it to attain the first-best outcome. The researchers are however quick to note that neither the EU quota nor the Kyoto agreement include elements concerning research and development investments. It is on this observation that the researchers decided to evaluate an international climate that does not also include research and development policies. The researchers explain that lack of the research and development policies in the international climate is a shortcoming symbolising an imperfection which might mean that welfare is lower in cases where quota trade is allowed than when this trade is not permitted.

This paper is divided in five sections. After the introduction is the second section which discusses the formal model the researchers used in their study. This model consists of identical firms but located in two countries that are different in size. The third section of the article discusses first-best social optimum which refers to the levels of research and development investments as well as abatements that minimize the total social costs in each of the firms. In the fourth section, the researchers examine an international agreements optimal design under the constraint that the agreement is not characterised by research and development policy elements. The researchers assume that the climate agreement is planned by the member countries with the intention of minimizing social costs. The international climate agreement s referred to as second best because of the fact that it has been devised under the constraint not to include research and development policy elements. This section also explains why the second best agreement cannot imitate the first-best agreement and why quotas should not be traded under the second-best agreement. The fifth and final section of the study discusses the how the model can be extended to other differences in countries other than size and the results attained using the formulas derived by the model.

Background
This study is built from Golombek  Hoel (2006), which concentrated international climate agreements in situations where member countries are identical and receive emission quotas with agreements that do not include policies on research and development. The current paper extends this study to eterogeneous countries. This study identified differences in size, technology diffusion abatement cost function and in assessment of climate damages. It however only focussed on difference in size where it draws from Golombek  Hoel (2006) that the second-best optimum for such a situation is characterised by abatement marginal costs surpassing the Pigovian level in all the participating countries. This conclusion is in relation to the fact that the agreement does not include research and development policies.

While the findings of Golombek  Hoel (2006), generalized that abatement marginal costs in heterogeneous countries for second best optimum should surpass the Pigovian level, this paper sought to specify exactly how these costs differed in the context of heterogeneous countries.  It is on the findings of this study on identical countries that the current research which focuses on heterogeneous countries was developed.

Theory of the Writer
This study draws its argument from the Coase theorem, which argues that tradable emission quotas yield efficiency despite the preliminary allocation of quotas. This is attributed to the fact that cost minimizing agents will ensure cost-effectiveness through trade until all marginal abatement cost differences between sources are done away with. According to the theorem, trade in emission quotas is advantageous both nationally and internationally if there exists an international agreement that regulates the emission of greenhouse gases into the atmosphere through quotas. Examples of such agreements are the Kyoto agreement allows the participating countries to trade in quotas but with some restrictions. The European Union quota trading scheme whose purpose is to help the European Union countries achieve the Kyoto commitments also permits different firms located in various European Union countries to trade in quotas.

One of the conditions for quota trade to be beneficial to the participating firms or countries is that any imperfections that might be existing elsewhere in the economy remain unaffected by trade in quotas otherwise quota trade might lower welfare. This paper therefore focuses on trade as opposed to no trade situations where countries have signed up an international climate agreement that allocates emission quotas to each of the participating countries.

It is important to note that in evaluating international climate agreements that allow member countries to trade in quotas against other contexts that do not allow trade, these authors base their arguments on the assumption that abatement costs are influenced by research and development activities all firms al the member countries undertake. This is simplified as abatement technologies tend to be endogenous. To be specific, the authors assume that the abatement costs of a firm are to a great extend affected by the investment it has put in its own research and development and to some degree by the research and development investments made by other firms, both local and foreign in the same industry.

This research focussed on various factors that make countries different from each including differences in diffusion of technology, differences in the size of countries, differences in how climate damages are evaluated and abatement cost function differences. The researchers concentrated mainly on the difference in country size as a factor which they then used to explain all the prepositions derived from its evaluation are also valid under the other mentioned differences.

The authors argue that the second-best optimum in countries that differ in size are typified by marginal costs of abatement that exceed the Pigovian level in all the participating countries. This argument is based on the findings of the study conducted by Golombek and Hoel (2006), which is the foundation of this research. This finding is turn associated with the fact that the climate agreement does not include research and development policies. Each of the participating countries will therefore overlook technology spillover to and from other countries and instead concentrate on an RD policy that provides less research and development than that which is socially optimal. In conceiving the second-best agreement, the participating countries consider that the stricter emission requirements imply that a country will have to undertake more research and development during the next stage. Setting the emission requirements that are so strict that they cause the marginal abatement costs to surpass the Pigovian level is therefore a way of compensating for domestic research and development subsidy that is too low.

Though Golombek and Hoel (2006) generalise that in second best optimum, marginal abatement costs have to surpass the Pigovian level, this is not the case in a context involving heterogeneous countries as the study seeks to explain that that marginal abatement costs generally vary across countries that are heterogeneous in a second-best optimum. This study also seeks to illustrate that it is not possible to conclude (it is not obvious) whether marginal costs of abatement should be highest in large countries or small ones.

The Model
The model used in this study is a static framework that disregards all kinds of uncertainties. The model is build from a study that involves only two countries domestic and foreign. The model considers two firms in the economy which are denoted as m  m which are identical, in this model, m is located within the mother country (is domestic) and m is located in the foreign country. The countries only differ from each in size which is represented by the total number of firms (Golomek  Hoel 2008 199). This model assumes that the domestic country is larger than the foreign country, mm. The findings of this factor (difference in size) will later be extended to other differences in countries where they will be proved to hold.

The authors acknowledge that all firms do invest in technology but ignore patents. They also argue that technology diffusion from a firm to other firms is not perfect in spite of technology spillover. Thus only (0    1) of another firm s research and development investments are useful for any firm. The researchers assume that for a particular domestic firm, its level of technology () is determined by its own investments in research and development (), the other firms  (in the same country) amount of  research and development investments and the amount firms in the other country have invested in research and development.
Y  X   (m   1)   m    ..1

In the above equation, an additive technology spillover structure is assumed where by   the assumption that a firm s technological level is dependent on the sum of all firms  research and development investments is corrected by technology diffusion parameters denoted as (). According to literature, this is the method that is used to standardise modelling spillovers.

The technology level of an individual foreign firm denoted as Y is likewise given by
Y  X   (m   1)   M   2
In the event there no environmental policies hence no abatement, emission levels in all the firms will be identical. This is denoted as E. By denoting abatement in every firm as a and in each domestic firm be a, actual emissions are given by the formulae E  a in domestic firms and E  a in foreign firms.

The model assumes that the abatement costs for all firms are dependent both on the technology level as well as the level of abatement of the firm. For domestic firms, abatement costs are denoted as c (a, y). It is also assumed that the properties of the function c (a, y) include ca (0, y)  0, c (0, y)  0, and ca (1, y).

In this analysis, the researchers assume that each country s emissions are set via international agreement. Because each country has identical firms, the emission levels per firm are given as 1m and 1m of the exogenously emission levels that have been set for the domestic and foreign country respectively. Research and development investments price is normalised to one. The researchers however assume that research and domestic investments are subsidised by the domestic government by a rate denoted as  while the government abroad subsidises by .

An individual domestic firm chooses research and development investments (X) in order to minimize its total cost of productionoperation. Taking other firms  expenditures on RD as given and its abatement as given (a1m), the firm minimizes its cost by
C (a, Y)  (1- ) X        ..3

Regarding X, the term in equation 3 is net research and development expenditures. Technology level denoted as Y is given by equation 1. Since all domestic tend to solve similar problem, the values they choose will be the same at equilibrium, (Xx and Yy).

The first order condition is given by
  cy (a, y)  1-           .4
A domestic s technology level is given by y y (a, ). This is based on the above equation which implies that technology of this firm is determined only by a and .

At equilibrium, it was found that X   and Y  y for domestic firms (in the home country) while in the foreign country X   and Y y (Golomek  Hoel 2008 201).
By solving equation 1 and 2, it was found that the values for  and  at equilibrium are
  hy  ky  6
 hy  ky   7,
Where k  k  0 and (for where for m  m) h  0 (Golomek  Hoel 2008 201).

The constants in equations 6 and 7 imply that since foreign firms have similar problems and assuming that foreign subsidy remains constant, a firms optimal technology level is not altered. In the event a rise in domestic subsidy increases a domestics firms optimal technology level by lets say one unit, to support the new level, RD investment in the domestic firm must increase by h. since increase in technology tends to increase the technology level of other firms in foreign countries through spillover, whereas at the same time the optimal technological level of foreign firms has not changed, research and development in every foreign firm decreases. From equation 7, this reduction is given by k  0 (Golomek  Hoel 2008 201).

The researchers acknowledge that greenhouse gas emissions is harmful to the environment. The environmental damage costs incurred by each country are determined by the total emissions from the two countries denoted as (m (E  a)  m (E  a)). This model also acknowledges that a large country will suffer more than a smaller one from climatic changes. The model uses the number of firms in a country to represent its size. The marginal damage experienced by each firm is assumed to be the same in both countries and is denoted as d. The marginal cost of damage in the domestic country is will be md while that in the foreign country will be md. The total cost of environmental damage in the home country is given by md m (E _ a)  m (E  a) while that in the foreign country is given as md m (E  a)  m (E  a).

The researchers used this model to explain the firstbest and second -best quota agreements under two models namely the first-best model and the second-best model respectively.

The First-Best Model.
This model is used to evaluate the first-best social model which refers to the model whose outcome minimize total social costs which include the research and development expenditures as well as environmental costs and the total abatement costs. The optimal result will be characterized by equal research and development expenditures as well as abatement levels in all firms. Based on this and using the already defined equations, the first best optimum is given by minimizing the equation
(m  m) c (a, y)    d m (E   a)  (E   a)         .equation 8.

With respect to technology and abatement levels in the two countries, and subject to equation 6 and the fact that y - y, the condition for the first-order with respect to abatement is given by
Ca (a, y)  (m  m) d ..equation 9.

Marginal abatements should therefore be equalized throughout the firms and the common value should be equal to that obtained by summing the marginal environmental costs of the two countries (domestic and foreign).

First order condition regarding technology level is given by
-cy (a, y)  h  k  1   (m  m - 1)-1               equation 10.
This equation implies that when technology level in all firms is increased, a firm s marginal benefits of  increased technology (-cy (a, y)) should be equal to that firm s  marginal costs of increasing technology which is equal to h  K because all firms invest in research and development whose price has been set to 1.

The researchers had earlier suggested that one way of implementing the first-best solution is by imposing a common tax, denoted by ((m  m ) d) and setting technology subsidy that is common to all countries. Using equation 4, the technology subsidy in both countries is gotten by
F  1   (h  k)  1- 1  (m  m - 10-1             . equation 11.

From this equation, it can be deducted that increase in technology level in all firms results in constant marginal costs of increasing technology level in any of the of the firms. This constant is (h  K). This implication reflects linear structure that characterises technology spillover functions in equations 1 and 2 (Golomek  Hoel 2008 202).
The Second Best Model

This involves pure quota agreements in which the climate agreements are not characterised by research and development elements. In this model, the researchers assume that both member countries have agreed to an international climate agreement that spells out emission quotas distribution between countries. It is also assumed that this agreement is second best in that the signatory members determine the emission quotas amount allocated to each country such that the total social costs are minimized based on behavioural constraints on firms as well as governments.

Each country goes on to maximise on its individual utility after the agreeing on the emission quotas and the allocated number of quotas. Each country will determine its domestic subsidy on technology depending on the response of domestic firms to the subsidy and the agreed upon emission level (explained by equation 5). In setting the domestic subsidy on technology, each government considers that each of the domestic firms refuses to acknowledge that is own research and development has a spillover effect on the technology levels of other localdomestic firms. Likewise all countries consider the fact each country will refuse to acknowledge the research and development spillover effects to foreign firms.

For a particular amount of emission quotas (a particular abatement level, a, a country s choice of subsidy for technology,  corresponds to choosing technology level y (based on equation 5). For a particular abatement, the domestic country minimizes
m c (a, y)     equation 12

Regarding its own level of technology which is subject to technology restriction expressed in equation 6 and using the expression for technology subsidy given above, the first order condition is expressed as
-cy (a, y)  h .equation 13

The research and development marginal benefits when only the domestic spillovers are considered should correspond to the marginal costs of research and development investments expressed as (-cyh-1  1). Based on equation 4, the optimal level of technology in each country can be implemented using the subsides
Q  1  h for domestic firms and Q  1  h

It had previously been proved that h  h  0 as m  m. The largest country will therefore have the largest subsidy. This is attributed to the fact increased technology level in the particular country benefit more firms domestically. The researcher came up with the following prepositions based on the second-best module and the equations derived using the module.

The largest country will have the highest equilibrium technology subsidy (Golomek  Hoel 2008 203).
From discussion of equation 7 and by comparing equations 14 and 15 with equation 11, k and k are negative hence technology subsidy will be lower than in the first-best optimum in both countries.