Business climate versus climate change: an estimation of negative externalities in dairy farm emission taxation
Thesis Bachelor of Science
Student: Mark Frederik Appel
10783245
Major Economics and Business Specialisation Economics and Finance Faculty of Economics and Business Universiteit van Amsterdam
1 Statement of Originality
This document is written by Mark Frederik Appel who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
2 Abstract
Whilst the agricultural sector produces 1.59% of the Dutch GDP in 2017, it was responsible for 9.8% of CO2 equivalent emissions in 2017. Nitrogen and phosphorus, besides carbon dioxide, are among the greenhouse gasses that are used in computing CO2 equivalent emissions. From 2015 to 2019, the Dutch government introduced a series of regulation to push down phosphorus and nitrogen emissions, leading to a national crisis and were met by nationwide protests from people active in the agricultural and construction industry, and their sympathisers. There has always been a substantial number of Dutch dairy farmers deciding to relocate abroad, which has been in a declining trend from the years 1980 to 2000, but has been increasing since.
Considering economic liberalisation has substantially decreased entry barriers, business migration has become more feasible over the years, even for more capital-intensive industries like the dairy industry.
This thesis opts to find a mathematical microeconomic model that studies output-based utility maximising decision making processes in an international setting, allowing firms to decide to set up their business abroad if that outcome is optimal to them. The scope of this thesis is to see how taxation may influence this decision making process and how output influences greenhouse gas emissions. Through this model, we can study whether at some point taxation may lead to adverse tax
consequences.
Whilst there are theoretical possibilities where tax increases indeed lead to higher emission outputs, in the context of migration between the Netherlands and Canada tax increases in the
Netherlands are not likely to result in net-negative outcomes. The model suggests that the incremental production of incumbent Dutch farmers is does not outweigh the decrease in domestic production. Keywords: business migration, dairy farms, Cournot decision making, negative externalities, Netherlands, emission tax, taxation, utility maximisation, globalisation, climate change
3 Table of Contents 1. Introduction 4 2. Methodology 10 3. Results 26 3.1 Empirical results 3.2 Theoretic modelling 4. Conclusion 32 5. Remarks 33 6. References 34 7. Appendix 38
4 Introduction
The Cournot model of competition, named after Antoine Augustin Cournot (1801–1877), is a microeconomic model that models how prices arise in a oligopolistic market when firms compete on the level of output they produce. Cournot first described the model in 1838 when describing a duopoly market for spring water. The model assumes perfect information and thus firms can develop a best response to whatever they expect their competitor to do. The model lies on six assumptions:
• There are 𝑛 > 1 firms and each firm 𝑖 produces a homogeneous product. • Firms do not collude.
• Firms firm 𝑖’s output 𝑞𝑖 has effect on the price market 𝑃(𝑄), thus firms have market power, unlike in original Bertrand competition, where firms compete in a race to the bottom until there is no profit from further lowering prices, thus at that prices equal marginal costs. • The number of firms 𝑛 is constant.
• All firms’ goal is profit maximisation through optimal output and they decide output simultaneously, thus no firm has a dominant position as in Stackelberg competition. • Firms have an understanding of their competitors’ cost function.
Some of these assumptions, especially the first, make Cournot competition an useful model for analysing output-decision making in a commodity market. Milk is not a completely homogenous product because the quality of milk is mostly determined by the nutrient contents inside milk. These quality levels differ result from variables like food input and cow characteristics, which correlates to inputs costs. Hemme et al. (2014) describes how any quality of milk is adjusted to ECM, energy corrected milk. ECM is converted so that any unit of ECM contains 4% fat and 3.3% protein.
The equilibrium value of production following from a Cournot competition model is also a Nash equilibrium in a simultaneous game, hence, all firms decide on output simultaneously and can not deviate for any higher profit, single-handedly. Cournot did not realise about the existence of the concept of the Nash equilibrium at the time, but described the outcome of his model as being stable. In his own words:
‘The state of equilibrium corresponding to the [optimal output] is therefore stable; i.e. if either of the producers, misled as to his true interest, leaves it temporarily, he will be brought back to it by a series of reactions’
5 The main practical issue of the Cournot model is the fact that it assumes that firms can
perfectly observe a relationship between price and market demand, described through a demand curve. However, on a smaller scale, one can theorise about an endless list of factors that affect demand. German philosopher Hans Albert (1963) argued that a demand curve is more of a metaphysical concept rather than real causal concept. The law of demand assumes a ceteris paribus condition thus a purely causal relationship between price and demand. However, consumer’s preferences are not fixed as the model assumes through the ceteris paribus condition.
Ordinary least squares regression (OLS) is a statistical method for estimating relationships between observations that are linear in their parameters. OLS minimises the squared deviations between the predicted value and the observed value and so describes a model that shows some kind of covariance, but not necessarily causality. OLS is at the core of econometric science of describing relationships. The law of supply and demand states that prices arise in a situation of market
equilibrium, thus market prices are market clearing. Therefore, it is impossible to infer relationships between supply or demand on one hand and price on the other hand, as only observing those two variables describes no causal relationship. Mathematicians Carl Friedrich Gauss and Andrey Markov developed four assumptions, now named the Gauss-Markov theorem, under which the coefficient(s) estimated through OLS is (are) the best linear unbiased estimator(s). Contrary to the theorem’s name suggests, Gauss and Markov did not develop the theorem together as Gauss’ work predates Markov’s work by nearly a century, according to Plackett (1949). OLS regression cannot identify unbiased coefficients of a system of simultaneous equations. Econometrists define this to be an issue of
endogeneity, because one explanatory variable (price) is correlated with an endogenous variable which resides in the error term.
Instrumental variable regression (IV regression) is a method where a endogenous variable is estimated using instrumental variables that are exogenous and relevant. Exogeneity means that those instruments have no significant covariance with the model’s error term in the explanatory equation and relevance means that those instruments have a significant covariance with the endogenous explanatory variables, conditionally on the other variables. The fitted values resulting from the first stage are thus exogenous and are used in estimating the second stage regression, assuming that the instruments affect the variable of interest through the fitted values from the first stage. There is a discussion on who should receive credit for the invention of instrumental regression (Stock and Trebbi, 2013), but Philip G Wright’s 1928 book “The Tariff on Animal and Vegetable Oils” is generally regarded as the basis of the method.
6 Discounted cash flow analysis (DCA) is a method used commonly in valuation when one deals with intertemporal cash flows. Investments typically involve payments upfront before revenues can be harvested in the future. Future cash flows are discounted according to how far in the future they are expected to flow in using a discount rate that is based on current profitability.
CO2-equivalent emissions (CO2e) follow from a method that weighs chemical compounds according to their global warming potency relative to carbon dioxide. The weighting of CO2e emissions are done at different timescales because of the differences in atmospheric lifetime of chemical compounds. In this thesis, all CO2e emissions will be considered at a 100-year timescale, as this is the case in most academic literature.
Motivation
Climate change is ever more a topic that receives more attention in contemporary politics, the Netherlands being no exception. Whilst the agricultural sector produces 1.59% of the Dutch GDP in 2017 [1], it was responsible for 9.8% of CO2 equivalent emissions in 2017 [2]. However, one must note that including the value added through further processing, the agricultural complex creates 6.4% of the Dutch GDP in 2018 [4]. Nearly half of all reactive nitrogen emissions (46%) is caused by the agricultural sector [5].
In 2018 the Dutch government introduced a phosphorus emission rights system, which is was announced in 2015, aiming to reduce phosphate emissions in the dairy industry. In 2015 a nitrogen reduction policy was introduced and in 2019 this regulation was ruled invalid, leading to a national crisis because construction projects suddenly were halted. Later that year the Dutch government introduced a new regulation aimed on reducing nitrogen emissions which were met by nationwide protests from people active in the agricultural and construction industry, and their sympathisers.
In the 1980s, around 300 Dutch families moved their dairy farm abroad annually, and this number dropped to about 30 per annum around the 2000s. Since the announcement of the phosphorus emission right system and the announcement of the nitrogen reduction policy, this number has
increased to about 75 families per annum [3]. Common are complaints about regulatory instability and the fear of having to invest to meet new regulatory standards, that are conceived to be ever-changing, but also administrative burdens. Many farmers announced they would emigrate, and offshore their businesses to countries with less hefty taxes on the agricultural sector, like Denmark, Germany, Canada and the United States, to name a few. There are agencies that specialise in helping Dutch farmers to migrate abroad – a clear sign that it is a common phenomenon.
7 One can assume that not only taxes are lower, but in general also land prices and labour costs are lower in the regions farmers migrate to, therefore, we can expect the migrated farmers would open larger scale businesses than they ran in the Netherlands. Logically, due to the lower emission costs and higher production, their businesses would emit more reactive nitrogen and other greenhouse gasses than they would have done initially, producing in the Netherlands.
The government argued that reactive nitrogen emissions damages biodiversity by creating an environment where certain plants thrive, and other plats die out. Whilst reactive nitrogen is partially absorbed by plants therefore mostly affects the environment on a local level, official estimates still argue that 32% of reactive nitrogen emission comes from abroad, and that the Netherlands exports 4 times more reactive nitrogen than the country imports. So, reactive nitrogen gasses also affect environments on an international scale. However, in this thesis, the focus will be on CO2e emissions by dairy farmers, as this measurement is a more complete measurement of global warming potency instead of measuring one specific chemical compound.
The conclusions of this thesis can be applied in a wider scale of outsourcing decisions. For decades, many western businesses have set up production plants in the developing world. These decisions were largely fuelled by cost-based decision making, albeit not per se due to environmental tax burdens, but also labour and capital costs. However, as climate change is an increasingly important topic in the world stage of politics, tax disparities between nations on environmental regulations will increase. There is even an incentive for developing nations not to set ambitious environmental fiscal policies, as this will make them less attractive for foreign producers, hindering their economic progression.
Climate change is a global problem, and relocating businesses to areas with less strict emission regulations cannot solve it. Besides hurting the domestic economy because the production moves abroad, causing famers to emigrate may also be counterproductive to the goal of the tax: reducing greenhouse gas emissions.
Research question
Can emission tax disparities lead to fiscal regulatory inefficiencies through offshoring decisions in the context of Dutch dairy farmers moving from the Netherlands to Canada?
8 Literature review
Dierickx, et al. (1988) describes a Cournot model that has been adjusted to allow for the effect of taxation. This adjusted Cournot model serves as the basis of the Cournot model we will use in this thesis. The model in this paper investigates for the effect of taxation considering that different firms have different marginal costs.
The paper states that excise taxation, being a constant added for all firms, reduces cost differentials across firms in contrast to ad valorem taxation. This suggests that ad valorem taxation is favourable to firms that have lower marginal costs, because the difference in marginal costs is what gives them a competitive advantage. Anyhow, firms with lower marginal costs can in some cases still increase profits due to a tax increase, because less competitive firms can fall out of business or have a more significant drop in output, leaving more residual demand for the competitive firms.
Increases in excise taxation can, through the same channel, thus also lead to a higher net prices. One market where we could expect this to happen is a market dominated by many, small producers, that have comparable but high marginal costs, and a few large producers with relatively low marginal costs. An increase in excise taxation can drastically reduce output for those smaller firms, reducing output to a level where the net price exceeds the net price before the increase in tax. In this case, larger, more efficient firms become more dominant in the market and their profitability increases.
In most countries, the dairy market is quite similar to the hypothesised one. In most countries, the market is dominated by many, small-scale producers but the difference being the existence of a few large producers.
Hemme et al., (2014) provides a clear overview of cost and performance indicators of dairy farms worldwide. The differences in typical herd sizes varies greatly between countries; large typical Russian farms have over 2443 dairy cows versus a large farm in Egypt only having five dairy cows.
Generally, the larger farms have higher levels of efficiency when it comes to milk yield per cow. Regardless of farm size, milk yield per cow in Western Europe and North America dominates milk yield in other areas of the world. An exception to this is Israel: the country’s large firms have the highest yield per cow at almost 12000 kg ECM per cow per year. Even small typical farms in Israel have levels of output that dominates milk output for many countries, even for herd sizes an order of magnitude larger.
The differences in total milk production costs per 100 kgs of ECM are less substantial worldwide, with two highly developed nations being an exception: the total costs per 100kgs of ECM in Norway and Switzerland both being more than double the worldwide trend. This is also due to significantly higher costs of labour in those countries. Those two countries also see the highest level of subsidies compared to other nations.
9 Non-milk returns are basically the income dairy farms have from receiving subsidies, selling manure that is used as fertiliser and returns on selling the cattle to be used in meat production. The latter, cattle returns, are significantly higher in developing nations. This is an indication that meat is more scarce in those countries, and that dairy cattle, albeit less preferred than beef cattle, is a more significant part of people’s diet in developing nations compared to developed nations. Feed costs are more significant in developing nations than in developed nations, where labour and depreciation are more significant.
Interestingly, the costs of milk production only shows us that in nearly all analysed countries the larger firms have a competitive advantage. That means that larger firms are hurt less by taxation effects. The world’s highest values are observed in small firms in Switzerland and Canada, the lowest costs are observed in small Armenian firms.
IFCN world dairy report (2013) and IFCN world dairy report (2014) allows us for more thorough comparison between countries. Most countries, including the Netherlands and Canada have observed increases in milk yield per cow. Both countries have seen a near halving of the number of dairy farms, whilst the average herd size nearly doubled in the Netherlands and increased by almost 50% in Canada. Milk prices in Canada are a lot higher and a lot more stable than in the Netherlands. Also, the farmer’s share of the final milk price is higher in Canada. Therefore, the ratio between the milk price and feed costs is more favourable in Canada. Milk yield per cow are relatively similar. Dairy farm profitability is worst in western Europe and best in Oceania.
Pennings, E., & Sleuwaegen, L. (2000) describes key determinants in what makes firm decide on international relocation. Firms in highly industrialised and open economies such, like the
Netherlands, are more likely to migrate, although it usually are more labour intensive firms. Firm size also has a positive effect on the likelihood of relocation. As we observe the dairy industry becoming more concentrated around fewer firms, we can expect more dairy farms to migrate in the future. There is an increase in firm migration, probably fuelled by more economies opening up and less restrictions to entering markets.
10 Methodology
From research bureaus, government agencies and other sources as listed in the reference section, data is gathered for estimating our model. Using our model, we can make predictions and see how parametric shifts affect the outcomes. We can test these outcomes against our hypothesis.
By researching average dairy farm sizes, herd size, and production levels in both the
Netherlands and Canada, an estimate of greenhouse emissions per production unit can be made in both countries. In Canada, these statistics are published by the Canadian Dairy Information Centre (CDIC) and the Dutch figures are published by Wageningen University’s Lifestock Research.
We can estimate net effects by allowing for migration in our model. Using some indifference point, we can allow for migration up to that point as a reaction to parametric shifts. Using derivatives we can do a more fundamental analysis of our model and using ceteris paribus conditions, we can compare the result from our mathematical analysis to the results from using real data to validate our findings.
Hypothesis
Because increases in taxation would lead to lower levels of output, we would expect higher taxation to lead to lower levels of output. Therefore, domestic tax increases will lead to lower levels of output in the home country. However, as taxation at home decreases farm profitability, relative to foreign dairy farms, domestic farmers would become more interested in migrating. Therefore, there will be migration up to the point where farmers are no longer profiting from migration. The farmers moving into the new country will follow a profit maximising strategy in their incumbent market.
This profit maximising strategy can lead to levels of production higher or lower than initially. Because it is expected that farmers would migrate to countries with lower costs, farmers will possibly set higher levels of output. This will increase emissions in the country they migrated to.
𝑡𝑎𝑥 ↑ → 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑜𝑢𝑡𝑝𝑢𝑡 > 0 → 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑛𝑒𝑡 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠 > 0
Higher levels of ad valorem taxation or excise taxation will cause firms to migrate. The change output in the foreign country after a new firm enters is higher than the change in output in the home country after one firm leaves. The change in the level of emissions in the foreign country after one new firm enters is higher than the change in emissions in the home country after that one firm leaves. The hypothesis from the model following from mathematical analysis would be:
{𝜕𝜖 𝜕𝑣, 𝜕𝜖 𝜕𝑒, 𝜕𝜖 𝜕𝑛} > {0,0,0}
11 The set of derivatives to the total emissions function with respect to ad valorem taxation, excise taxation and the number of firms is greater than a set of all zeros. In other words, all of those derivatives are positive. This implies that taxation affects emissions through two channels after an increase in taxation. Namely a non-migratory channel where firms that do not migrate increase output, suggesting {𝜕𝑞
𝜕𝑣, 𝜕𝑞
𝜕𝑒} > {0,0}, and a migratory channel where firms that do migrate result in higher output levels in their new foreign market, suggesting 𝜕𝑄
12 Introducing the variables
All variables are described in order of appearance. When used in the thesis, some subscripted items may be omitted if they are obvious from context or unspecified.
𝑄𝑐𝑜𝑢𝑛𝑡𝑟𝑦,𝑦𝑒𝑎𝑟 Total output
Subscript: 𝑐𝑜𝑢𝑛𝑡𝑟𝑦, 𝑦𝑒𝑎𝑟
The total amount of units supplied or demanded in a certain country, e.g. 𝑄𝐶𝐴,2016 denotes the amount of production units produced in Canada in 2016.
𝑞𝑖,𝑦𝑒𝑎𝑟 Firm-specific output Subscript: 𝑐𝑜𝑢𝑛𝑡𝑟𝑦, 𝑦𝑒𝑎𝑟
The total amount of units supplied or demanded in a certain country, e.g. 𝑄𝐶𝐴,2016 denotes the amount of production units produced in Canada in 2016.
𝑃𝑐𝑜𝑢𝑛𝑡𝑟𝑦,𝑦𝑒𝑎𝑟 Gross price
Subscript: 𝑐𝑜𝑢𝑛𝑡𝑟𝑦, 𝑦𝑒𝑎𝑟
The gross market price of one production unit in a certain country in a certain year, e.g. 𝑃𝑁𝐿,2015 denotes the price of one production unit in the Netherlands as observed in 2015.
𝛼 Alpha
Some constant, the y-intercept, that follows from a regression. 𝐸(𝑥) Expected value
A value, for example a mean value, that would be expected to be observed. 𝛽𝑘, 𝛾𝑘 Beta, gamma
Subscript: 𝑘
Some coefficient that follow from a regression. When there are 𝑘 > 1 coefficients present in a regression, then the subscript 𝑘 numbers the different coefficients.
𝜀𝑖, 𝑢𝑖 Error term Subscript: 𝑖
13 𝑞̃ 𝑖 Non-firm output
Subscript: 𝑖
This term aggregates the output of all firms other than firm 𝑖 𝑃̃𝑐𝑜𝑢𝑛𝑡𝑟𝑦,𝑦𝑒𝑎𝑟 Net price
Subscript: 𝑐𝑜𝑢𝑛𝑡𝑟𝑦, 𝑦𝑒𝑎𝑟
The net market price of one production unit in a certain country in a certain year. This is the marginal revenue of selling one production unit.
𝑣𝑐𝑜𝑢𝑛𝑡𝑟𝑦 Ad valorem taxation Subscript: 𝑐𝑜𝑢𝑛𝑡𝑟𝑦
A tax rate that is levied based on the value of the good in a certain country. 𝑒𝑐𝑜𝑢𝑛𝑡𝑟𝑦 Excise taxation
Subscript: 𝑐𝑜𝑢𝑛𝑡𝑟𝑦
A tax rate that is levied per production unit.
𝑅𝑖 Revenues
Subscript:𝑖
Firm 𝑖’s total revenues in an annum. 𝑟𝑖 Marginal revenues
Subscript:𝑖
Firm 𝑖’s marginal revenues, the first-order derivative of the total revenues.
𝐶𝑖 Costs
Subscript:𝑖 Firm 𝑖’s total costs in an annum. 𝑐𝑖 Marginal costs
Subscript:𝑖
14
𝐹𝑖 Fixed costs
Subscript:𝑖
Firm 𝑖’s costs, that do not depend on the level of output.
𝛱𝑖 Profit
Subscript:𝑖 Firm 𝑖’s total profit in an annum. 𝑞𝑖∗ Optimal output
Subscript:𝑖
Firm 𝑖’s production, following from Cournot profit maximisation.
𝛿𝑖 Discount rate
Subscript:𝑖
The discount rate firm 𝑖 faces, for discounting future cashflows.
𝑈𝑖 Utility
Subscript:𝑖
A function that expresses the amount of utility 𝑖 receives, from a certain outcome.
𝑚𝑖 Discount rate
Subscript:𝑖
The disutility a firm faces for migrating to another country. 𝜖𝑐𝑜𝑢𝑛𝑡𝑟𝑦 Discount rate
Subscript:𝑐𝑜𝑢𝑛𝑡𝑟𝑦
15 Introducing the model
There are 𝑛 firms where 𝑖 = (1,2, … , 𝑛) and aggregate demand 𝑄 is expressed through the inverse demand function:
𝑃 ≡ 𝑃(𝑄)
Where 𝑃 denotes the gross price of the commodity (raw milk) and 𝑄 denotes the quantity sold. Aggregate output 𝑄 is the sum of all firms 𝑖’s individual output 𝑞𝑖. All 𝑛 firms produce a homogenous commodity, raw milk. Whilst dairy farms produce a wide range of dairy products, they are all made of milk. So we assume in that case that any further processing is not done by the milk producing firm, as a processor can also buy milk on the market. Consider processing milk as an internal transfer sale. Because the quality of milk differs significantly, we correct the produced output to be measured in terms of Energy Corrected Milk (ECM). ECM standardises milk by assuming a standard of 4% fat content and 3.3% protein content.
𝑄 ≡ ∑ 𝑞𝑖 𝑛 𝑖=1
Total output 𝑄 and firm-specific output 𝑞𝑖 are measured in units of 100 kilogrammes ECM. Symmetry implies that milk producers face the identical profit functions relevant in decision making, so therefore, in equilibrium, they make the same decision, whilst expecting the competitors to do so to. Assuming symmetry between milk producers within the same country, it holds:
𝑞𝑖 = 𝑞𝑗 𝑓𝑜𝑟 𝑎𝑙𝑙 0 < [𝑖, 𝑗} ≤ 𝑛
As a result, it also holds that total production 𝑄 equals any firm 𝑖’s output scaled by the number of producers in a country 𝑛:
𝑄 ≡ 𝑛 ∗ 𝑞𝑖
We can estimate an inverse demand function 𝐷 through least-squares regression. However, before we apply any econometric analysis we must think about how we prevent endogeneity issues in our regression. Because prices are jointly determined by both demand and supply effects, if we were to observe equilibrium output and price, we cannot directly assume a price-demand relationship. Hence, if we would estimate a relationship through OLS, our independent variable (price) would be correlated with the error term, causing endogeneity. First we must estimate the price using only supply-side effects as instruments, in order to have an exogenous estimate of prices. Then we can use that estimated (exogenous) price to estimate a linear effect between price and demand.
16 The instruments that are used to estimate the price, which are believed to only affect output indirectly through the supply effect, are:
𝑐𝑜𝑤𝑠 More dairy cows directly affects milk production.
𝑎𝑣𝑡 High temperatures are negatively correlated in milk production (Yano et al., 2014). Could be endogenous because high temperatures are correlated with drinking.
𝑟𝑛𝑓 More rainfall leads to more grass for cows to eat. 𝑛 More dairy farms lead to more output.
𝑓𝑒𝑒𝑑𝑟 Higher feed prices lead to cows being fed less, so less milk production. 𝑙𝑎𝑛𝑑 Higher land prices lead to less space for cows and less milk production.
Stage 1:
𝑃𝑖 = 𝛾0+ 𝛾1𝑐𝑜𝑤𝑠 + 𝛾2𝑡𝑚𝑝 + 𝛾3𝑟𝑛𝑓 + 𝛾4𝑛 + 𝛾5𝑓𝑒𝑒𝑑𝑟 + 𝛾6𝑙𝑎𝑛𝑑 + 𝑢𝑖
We must perform an instrumental variable (IV) regression in order to separate supply effects from demand effects in our two-stage regression. So first, we estimate the price using exogenous variables.
Stage 2:
𝑄 = 𝛼 − 𝛽𝑇𝑆𝐿𝑆𝑃̂ + 𝜀𝑖
We regress the demand function using the fittest values from the first-stage regression to acquire 𝛽𝑇𝑆𝐿𝑆, the IV-coefficient.
However, in a case that IV regression cannot yield a relationship that is consistent with economic theory, we need to come up with rather ambiguous but sensible estimates of these parameters. To do that, we need to describe those parameters’ function in the model.
𝛼 is the constant in a linear demand model. Since for 𝑃 = 0 → 𝐸(𝑄) = 𝛼, this allows us to ask ourselves, how much milk would be demanded if milk were free? We assume that for 90% of the non-lactose intolerant population, milk consumption strictly dominates water consumption to the point where someone consumes 1 litre per day. We would use values for 2013 for estimating 𝛼. Thus, we can estimate 𝛼 as:
𝛼 = 365 ∗ 0.9 ∗ 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ∗ (1 − 𝑙𝑎𝑐𝑡𝑜𝑠𝑒 𝑖𝑛𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒%)
We can estimate 𝛽 by entering the farm gate price and quantity produced that year and find a linear relation, using 𝛼 as previously mentioned. 𝐸(𝑄) = 𝛼 − 𝛽𝑃 → 𝛽 =(𝛼 − 𝑄)⁄ . 𝑃
17 Assuming a linear relationship with 𝛽 > 0 , we may conclude a demand function
𝐸(𝑄) = 𝛼 − 𝛽𝑃 Therefore, we can express the inverse demand function:
𝑃(𝑄) =𝛼 − 𝑄 𝛽
We define the term non-firm output 𝑞̃ to be the total quantity produced by all firms other than 𝑖 firm 𝑖.
𝑞̃ ≡ ∑ 𝑞𝑖 𝑗 𝑛 𝑗=1
Where 𝑗 can take all values of 𝑖 except 𝑗 = 𝑖, so {𝑗 ∈ 𝑖|𝑗 ≠ 𝑖}
𝑞̃ ≡ 𝑄 − 𝑞𝑖 𝑖 → 𝑄 ≡ 𝑞̃ + 𝑞𝑖 𝑖
In this thesis we look at the impact of taxation in output-based decision making. Taxes come in two shapes: excise taxes 𝑒, levied per unit of output 𝑞 and ad valorem taxes 𝑣, levied per unit of currency of the unit of output’s net price 𝑃̃. Both types of taxation can be applied simultaneously, so we can describe the net price 𝑃̃ as:
𝑃̃ = 𝑃 1 + 𝑣− 𝑒 Where if [𝑣, 𝑒] < 0, we consider net-subsidies.
As we previously defined 𝑃(𝑄), we can find any firm 𝑖’s revenues 𝑅𝑖 as:
𝑅𝑖= 𝑞𝑖∗ 𝑃̃ = 𝑞𝑖( 𝑃(𝑄) 1 + 𝑣− 𝑒) 𝑅𝑖 = 𝑞𝑖( 𝛼 − 𝑄 𝛽(1 + 𝑣)− 𝑒) 𝑅𝑖 = 𝑞𝑖( 𝛼 − (𝑞̃ + 𝑞𝑖 𝑖) 𝛽(1 + 𝑣) − 𝑒)
18 Firm 𝑖’s marginal revenues 𝑟𝑖 is the first-order derivative with respect to firm 𝑖’s output 𝑞𝑖:
𝑟𝑖 = 𝜕𝑅𝑖 𝜕𝑞𝑖 = 𝜕 𝜕𝑞𝑖 (𝑞𝑖( 𝛼 − (𝑞̃ + 𝑞𝑖 𝑖) 𝛽(1 + 𝑣) − 𝑒)) = 𝛼 − 𝑞̃ − 2𝑞𝑖 𝑖 𝛽(1 + 𝑣) − 𝑒
We assume linear cost functions. We assume the marginal costs 𝑐 to be constant for all farmers according to the typical milk production cost (Hemme, 2014). Each firm 𝑖 faces fixed costs 𝐹𝑖 and country-specific typical production costs per 100 kilogrammes ECM 𝑐𝑗. We define the cost function:
𝐶𝑖 = 𝐹𝑖+ 𝑐𝑗𝑞𝑖 𝜕𝐶𝑖
𝜕𝑞𝑖 = 𝑐𝑗 Where 𝑐𝑗> 0.
Each firm 𝑖 faces a profit function 𝛱𝑖:
𝛱𝑖 ≡ 𝑞𝑖𝑃̃ − 𝐶𝑖 𝛱𝑖 = 𝑞𝑖( 𝛼 − (𝑞̃ + 𝑞𝑖 𝑖) 𝛽(1 + 𝑣) − 𝑒) − 𝐹 − 𝑐𝑗𝑞𝑖 𝛱𝑖 = 𝑞𝑖( 𝛼 − (𝑞̃ + 𝑞𝑖 𝑖) 𝛽(1 + 𝑣) − 𝑒 − 𝑐𝑗) − 𝐹
Profit is maximised once producing one incremental unit is no more profitable, so when: 𝜕𝛱𝑖 𝜕𝑞𝑖 =𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) + 𝑞̃ + 2𝑞𝑖 𝑖 𝛽(1 + 𝑣) = 0 → 𝛼 − 𝑞̃ − 2𝑞𝑖 𝑖 𝛽(1 + 𝑣) − 𝑒 = 𝑐𝑗 Profits are therefore maximised when marginal revenues 𝑟𝑖 equal marginal costs 𝑐𝑖. We find any firm’s optimal output 𝑞∗ using the symmetry assumption and expressing this equation in terms of 𝑞:
𝑞̃ + 2𝑞𝑖 𝑖= 𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) 𝑞̃ + 2𝑞𝑖 𝑖= (𝑛 + 1)𝑞∗
𝑞∗=𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1)
19 In order to find any firm’s optimised profit 𝛱∗ we substitute the optimal output 𝑞∗ into the profit function 𝛱𝑖: 𝛱∗= 𝑞∗(𝛼 − 𝑛𝑞 ∗ 𝛽(1 + 𝑣)− 𝑒 − 𝑐𝑗) − 𝐹 𝛱∗= (𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1) ) ( 𝛼 − 𝑛 [𝛼 − 𝛽(𝑐(𝑛 + 1)𝑗+ 𝑒)(1 + 𝑣)] 𝛽(1 + 𝑣) − 𝑒 − 𝑐𝑗 ) − 𝐹
In this thesis we will create a two-stage simultaneous game. In the first stage, a firm 𝑖 decides whether to relocate or not, i.e. whether to produce domestically or abroad. This requires the agent to form expectations about the inputs of the profit function at home 𝛱𝑖,ℎ𝑜𝑚𝑒 and the profit function abroad 𝛱𝑖,𝑎𝑏𝑟𝑜𝑎𝑑. If a firm decides to relocate, the firm migration costs 𝑚 > 0. If a firm decides not to relocate, 𝑚 = 0. Thus, a break-even value for 𝑚 can be found where 𝑈𝑖,ℎ𝑜𝑚𝑒= 𝑈𝑖,𝑚𝑖𝑔𝑟𝑎𝑡𝑒. This value for 𝑚 is the point where a farmer is indifferent on whether to migrate.
Migration costs 𝑚, or rather migration (dis)utility, encompasses all possible costs that a firm faces by migrating, but is also affected by the farmer’s own preferences regarding certain countries. For example, a Dutch dairy farmer might maximise profits by migrating to a certain country, but would receive large disutility because that country has certain factors the farmer dislikes. Those factors can contain cultural factors like language compatibility, legal factors like quality of law enforcement and protection of property rights and so forth. A farmer is expected to do a PESTEL-analysis (Ebbers, J., & Pruppers, R., 2012) of some sort to form a personal opinion on migration costs 𝑚.
Because agents expect to live for more than one period, they actually make an intertemporal choice. Therefore, the agent also has to form expectations on how many periods (𝑙 ≥ 1) to consider in discounting future cashflows. This can exceed a farmer’s expected lifetime (e.g. the agent has bequest motives, for example expects the business to be continued by the agent’s children after the agent’s death and these profits also provide utilities). The farmer expects a discount rate 𝛿.
The discount rate a firm 𝑖 faces, 𝛿, depends on the firm’s own expected return on assets. It makes sense that firms discount expected cash flows with the same rate as their own in order to compare any investment to their own current investment. As we expect 𝑛 equally sized firms, all with market share 1 𝑛⁄ , all firm’s return on assets in a year using aggregated data. The discount rate is a ratio of earnings before income and taxation (EBIT) and the total book value of the assets.
𝛿 = 𝐸(𝑟𝑎,𝑖) = 𝐸 (
𝑑𝑎𝑖𝑟𝑦 𝑠𝑒𝑐𝑡𝑜𝑟 𝐸𝐵𝐼𝑇 𝑑𝑎𝑖𝑟𝑦 𝑠𝑒𝑐𝑡𝑜𝑟 𝑎𝑠𝑠𝑒𝑡𝑠)
20 This leads to these following utility functions:
𝑈𝑖 = ∑ 𝑃𝑉(𝛱𝑖) 𝑙 𝑡=0 − 𝑚 𝑈𝑖 = ∑ ( 𝛱𝑖,𝑡 (1 + 𝛿)𝑡) 𝑙 𝑡=0 − 𝑚
As the number of farmers in a country 𝑛 affects the individual profits made in a country negatively, farmers will migrate to countries where they achieve higher utility up to the point that migration no longer increases there utility. Hence, they are indifferent. At this point, a migratory steady state has been achieved. This equilibrium is reached when utilities between the home country 𝐴 and the foreign country 𝐵 are equal:
𝑈𝑖,𝐴= 𝑈𝑖,𝐵 ∑ ( 𝛱𝑖,𝐴 (1 + 𝛿𝐴)𝑡 ) 𝑙 𝑡=0 = ∑ ( 𝛱𝑖,𝐵 (1 + 𝛿𝐴)𝑡 ) 𝑙 𝑡=0 − 𝑚
We can consider the expected profits as to be an annuity of income cash flows, so we can rewrite the formula using the annuity factor (Bodie et al., 2018 p.433). We define the annuity factor (or discount factor) 𝐷(𝛿, 𝑙) as the multiplying factor that, multiplied by one period’s profits 𝛱𝑖, equates to the sum of discounted profits ∑𝑙𝑡=0𝑃𝑉(𝛱𝑖).
𝛱𝑖,𝐴∗ 1 𝛿𝐴 [1 − 1 (1 + 𝛿𝐴)𝑙 ] = 𝛱𝑖,𝐵∗ 1 𝛿𝐴 [1 − 1 (1 + 𝛿𝐴)𝑙 ] − 𝑚 𝑚 = 𝛱𝑖,𝐵∗ 1 𝛿𝐴 [1 − 1 (1 + 𝛿𝐴)𝑙 ] − 𝛱𝑖,𝐴∗ 1 𝛿𝐴 [1 − 1 (1 + 𝛿𝐴)𝑙 ] 𝑚 = 𝐷[𝛱𝑖,𝐵− 𝛱𝑖,𝐴]
We assume the farms discount future profits in perpetuity so we can rewrite the annuity factor as: 𝐷(𝛿𝐴, 𝑙 → ∞) = lim 𝑙→∞( 1 𝛿𝐴 [1 − 1 (1 + 𝛿𝐴)𝑙 ]) = 1 𝛿𝐴 Therefore, the migratory steady state is reached when:
𝑚 = 1 𝛿𝐴 [𝛱𝑖,𝐵− 𝛱𝑖,𝐴] 𝑚 = 1 𝛿𝐴 [(𝑞𝐵∗( 𝛼𝐵− 𝑛𝐵𝑞𝐵∗ 𝛽𝐵(1 + 𝑣𝐵) − 𝑒𝐵− 𝑐𝐵) − 𝐹𝐵) − (𝑞𝐴∗( 𝛼𝐴− 𝑛𝐴𝑞𝐴∗ 𝛽𝐴(1 + 𝑣𝐴) − 𝑒𝐴− 𝑐𝐴) − 𝐹𝐴)]
21 Substituting 𝑁 = 𝑛𝐴+ 𝑛𝐵→ 𝑛𝐵 = 𝑁 − 𝑛𝐴 yields: 𝑚 = 1 𝛿𝐴 [(𝑞𝐵∗( 𝛼𝐵− (𝑁 − 𝑛𝐴)𝑞𝐵∗ 𝛽𝐵(1 + 𝑣𝐵) − 𝑒𝐵− 𝑐𝐵) − 𝐹𝐵) − (𝑞𝐴∗( 𝛼𝐴− 𝑛𝐴𝑞𝐴∗ 𝛽𝐴(1 + 𝑣𝐴) − 𝑒𝐴− 𝑐𝐴) − 𝐹𝐴)]
This equation allows us to find the number of farmers in a country 𝑛 as it is the variable that adjusts to shocks in demand factors, costs and taxation. The number of farmers in country A, 𝑛𝐴, for which the expression above holds is the steady-state population of producers 𝑛𝐴∗.
In the second stage, there is a migratory steady state and farmers will produce according to the Cournot equilibrium. CO2e emissions per 100 kilogrammes of milk are assumed to be a constant and therefore we can directly convert the optimal output into a predicted level of CO2e emissions at equilibrium level in country 𝑗, 𝜖𝑗:
𝜖𝑗= 𝜀 ∗ 𝑛∗∗ 𝑞∗
𝜖𝑗= (𝜀 ∗ 𝑛𝑗∗) (
𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛𝑗∗+ 1) )
Therefore, the total emission output 𝐸 in both countries 𝐴 and 𝐵 in equilibrium equals: 𝐸(𝑡) = 𝜖𝐴+ 𝜖𝐵
22 Data collection
In order to estimate a milk demand curve in both countries, data has been sourced from IFCN reports, national statistics bureaus and research bureaus. For the first stage of the IV-regression, the following observations are gathered. For the Netherlands, the temperature is an average of five weather stations around the country and rainfall is measured at the Royal Dutch Meteorological Institute (KNMI) in De Bilt. The feed ratio is a ratio between the national milk price and the feed costs as reported by IFCN. Land price is the price in euros of one hectare of suitable farm land as reported by IFCN. Prod measures milk production in million tonnes ECM.
The same methodology is applied for gathering the data on Canada. However, because Canada is much larger than the Netherlands, temperature and rainfall data have been selected for the city of Toronto. That decision has been made because Toronto is in Ontario, the Canadian province with the highest density of dairy farms [7]. Land prices are expressed in Canadian Dollars.
23 Table 1: Instrumental data for the Netherlands
Country: The Netherlands
Year Prod Cows Temperature Rainfall Farms Feed ratio Land price 1996 11,71 1504076 10 5757 39000 1,9 29360 1997 11,7 1545821 10 7435 37500 2,15 33353 1998 11,69 1485367 10,1 12396 36000 2,4 37346 1999 11,73 1477649 10,1 9015 32733 2,15 35873 2000 11,77 1470483 10,1 9324 29466 1,9 34400 2001 11,635 1433202 10,2 10389 27925 2,1 34050 2002 11,5 1419716 10,2 9240 26393 2,3 33700 2003 11,565 1413166 10,2 6127 25002 2,15 30850 2004 11,63 1466134 10,3 8594 24329 2 28000 2005 11,655 1489071 10,3 8729 23527 2 28630 2006 11,68 1478635 10,3 8071 22301 2 29260 2007 12,005 1469720 10,4 9511 21313 1,75 34130 2008 12,33 1483991 10,4 8805 20746 1,5 39000 2009 12,485 1552919 10,4 7769 20268 1,55 40000 2010 12,64 1572287 10,5 8253 19805 1,6 41000 2011 12,62 1621767 10,5 9090 19247 1,5 44000 2012 12,68 1744827 10,5 8783 18682 1,2 46000 2013 13,25 1693804 10,6 8272 18665 2014 1621914 10,6 8729 18581 Source [10] [9] [8] [7], [13] [7] [7]
24 Table 2: Instrumental data for Canada
Country: Canada
Year Prod Cows Temperature Rainfall Farms Feed ratio Land price 1996 7,39 1237200 7,3 631 23823 2,2 4010 1997 7,52 1231100 7,8 688 22649 2,5 4578 1998 7,65 1184000 10,3 1111 21571 2,8 5146 1999 7,68 1156700 9,6 909 20581 3,2 5413 2000 7,70 1103400 8,4 955 19368 3,5 5679 2001 7,73 1091000 9,7 1015 18679 3,2 6022 2002 7,75 1083900 9,6 954 17931 2,9 6365 2003 7,81 1065500 8,1 683 16970 2,9 6851 2004 7,87 1054900 8,4 912 16224 2,9 7336 2005 7,77 1041400 9,2 843 15522 3,3 7739 2006 7,66 1019100 9,9 822 14660 3,7 8142 2007 7,77 997500 9,2 985 14036 3,5 8768 2008 7,88 984700 8,4 886 13587 3,2 9394 2009 7,91 965600 8,2 805 13214 3,5 9855 2010 7,94 966200 9,7 878 12971 3,7 10315 2011 8,11 965600 9,3 844 12762 2,7 11259 2012 8,33 965400 10,6 946 12557 2,3 14038 2013 8,18 968200 8,7 812 12267 2014 7,39 959400 7,7 846 12007 Source [12] [11] [10] [7], [12] [7] [7]
In Canada, carbon emissions are set to rise from $15 per tonne CO2e emissions to $30 in 2022. Therefore, for simplicity’s sake, it has been averaged to $22.50 per tonne CO2e emission.
25 In the European Union, carbon emissions are regulated through an emission rights trading system, and the price of emission rights are about $27.50 per tonne CO2e.
Table 3: characteristics of dairy farm emissions (source: [14], [18], [19])
Country Emissions per 100 kg of milk Tax per tonne CO2e Tax per 100kg milk
Netherlands 140 kg CO2e $27.50 $3.85
Canada 105 kg CO2e $22.50 $2,3625
In the Netherlands, we observe a steep decline in farm profitability since the introduction of the phosphate emission rights. Because these emission rights are considered intangible assets on the balance sheet, they have had significant impact on dairy firm valuation and therefore greatly reduced the return on assets.
Table 4: EBIT and assets of average dairy farm, discount rates in the Netherlands and Canada, 2018 (source: [21], [22]
Country Dairy sector EBIT Dairy sector assets Return on assets
Netherlands € 64.700 € 4,562,010 1.42%
26 Results
Empirical results
Unfortunately, the instrumental regression was unable to find unbiased estimators for a demand function in both the Netherlands as Canada. That is my conclusion, because both models expected a positive value of 𝛽, suggesting that output and price are positively correlated. Besides the two examples below, all possible combinations of instruments have been tried and also extra variables for the second stage model such as GDP, number of households and the population have been tried to see if a model that corresponds to theory could be found, without positive result. The same model as used by Altarawneh (2015) also did not find a negative relationship between output and price.
IV regression for the Netherlands
IV regression for Canada
Unfortunately, no sensible result however can be inferred from the Cournot model using real data, because the marginal costs exceed the farm gate price in both Canada as the Netherlands.
Therefore, for both countries, 𝑞∗= 0. Even when subsidies are taken into account, marginal costs still exceed farm gate prices. This is confirmed by other case studies [20].
27 Theoretic modelling
Due to the complex nature of milk production and a lack of publicly available data, one can infer more sensible data from mathematical analysis of the model. We will use chosen values in order to see different outcomes of the model and look at derivatives.
Given the fact that although Canada has a population greater than the Netherlands, the Netherlands still has a higher milk production and consumption than Canada, we can expect the Netherlands to have a higher value for 𝛼. Given the fact that the Netherlands exports a larger proportion of her milk, we can expect a steeper demand curve because it that market is more
competitive, therefore we select a higher value for 𝛽 in the Netherlands. These values are also chosen, so what if the prices in both countries were to equal the respective country’s marginal costs, the quantities produced are similar to what is observed in reality. Zero migration costs are assumed. Therefore, we assume the following demand parameters:
Table 5: Chosen values for alpha and beta
Variable Netherlands Canada
𝛼 250,000,000 200,000,000
𝛽 2,200,000 1,500,000
Marginal costs are like observed but rounded. Initially, ad valorem taxes are assumed to be equal. Excise taxes are based off the CO2e tax per 100kgs ECM. The number of farmers are rounded for each country.
Table 6: Chosen parameter values
Variable Netherlands Canada
𝑐 50 75
𝑒 5 2.5
𝑣 0.2 0.2
𝛿 0.014 0.018
28 We can use our model to see how these parameter values would lead to market Cournot equilibria. Hence, if migration was impossible, then this would be the two equilibria in both countries. These inputs lead to the following outputs:
Table 7: Initial disequilibrium
Variable Netherlands Canada
𝑞 5.665 5.041
𝑄 104.794.335 60.494.959
𝑃 € 66,00 € 93,00
𝑃̃ € 50,00 € 75,00
𝛱 € 12,15 € 14,12
These initial values do not lead to any equilibrium value, so we must solve for our steady-state condition in order to begin with an equilibrium. This leads to the following situation:
Table 8: Initial steady-state
Variable Netherlands Canada
𝑛 17.951 12.549 𝑞 5.838 4.821 𝑄 104.794.162 60.495.179 𝑃 € 66,00 € 93,00 𝑃̃ € 50,00 € 75,00 𝛱 € 12,91 € 12,91
29 Now we will introduce an increase in excise taxation in the Netherlands, increasing excise taxation from €5,- per 100 kgs ECM to €10,- kgs ECM. There is no other change in taxation in either country. This shock in excise taxation in the Netherlands leads to the following steady-state
equilibrium:
Table 9: Post-shock steady-state
Variable Netherlands Canada
𝑛 16.946 (-1005) 13.554 (+1005) 𝑞 5.405 (-433) 4.463 (-358) 𝑄 91.594.595 (-13.199.567) 60.495.537 (+358) 𝑃 € 72,00 (+6) € 93,00 𝑃̃ € 50,00 € 75,00 𝛱 € 11,07 (-1.84) € 11,07 (-1.84)
We observe that this increase in excise taxation has led to an overall decrease in milk production whilst many farmers have migrated to Canada. The tax increase has decreased farm profitability in the Netherlands directly and in Canada in directly, through migration. We can compare the outcomes before and after the shock in excise tax in the Netherlands.
Table 10: Excise tax effect on emissions (million kgs CO2e)
Netherlands Canada Total
Before After Before After Before After
Emissions 14.671 12.823 6.352 6.352 21.023 19.175
It is clear that because of the tax increase, the production in the Netherlands decreased which decreases the emission of CO2e gasses. The increase of production in Canada was so minimal that it had no significant effect on emissions.
However, if we start from the steady-state as in table 8 and instead of a tax increase in the Netherlands, there is an ad valorem tax decrease in the Netherlands and an excise tax increase in Canada. The ad valorem taxation in the Netherlands drops to 15% and the excise tax in Canada increases to $7.5.
30 Table 11: Post-shock steady-state
Variable Netherlands Canada
𝑛 19.667 (+1.716) 10.833 (-1.716) 𝑞 5.636 (-202) 4.754 (-67) 𝑄 110.844.364 (+6.050.202) 51.495.246 (-8.999.933) 𝑃 € 63,25 (-€2,75) € 99,00 (+€6) 𝑃̃ € 50,00 € 75,00 𝛱 € 12,56 (-0.35) € 12,55
The simultaneous decrease of taxation in the Netherlands and increase of taxation in Canada, has led to migration of farmers from Canada to the Netherlands. Milk prices rose in Canada, contrary to the Netherlands. Total global milk output has decreased, despite the increase of production in the Netherlands. This is visible in table 12.
Table 12: Combined tax effect on emissions (million kgs CO2e)
Netherlands Canada Total
Before After Before After Before After
Emissions 14.671 15.518 6.352 5.407 21.023 20.925
When a firm enters a foreign market, the amount of firms at home declines by one and the number of foreign firms increases by one, ceteris paribus. Thus, by analysing the emission function we can have a better understanding of the effect of a migrating dairy farmer.
𝜕𝜖 𝜕𝑛= 𝜕 𝜕𝑛((𝜀 ∗ 𝑛) ( 𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1) )) = 𝜀 ∗ ( 𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1)2 )
We can infer that when migrating to a country with higher values 𝛼 and lower values for 𝛽, i.e. more (residual) and less steep demand, the net effect to greenhouse gas emissions will be positive (positive in the sense that it increases global emissions), ceteris paribus. Migrating to countries with lower marginal costs, excise taxes and ad valorem taxation, will, ceteris paribus, lead to higher global emissions because firms will produce higher levels of output in their profit maximising strategy.
31 Moving to a country with more dairy farms, ceteris paribus, will have a decrease net global emissions. However, each new incumbent firm will have less impact on overall emissions. On the contrary, if the only difference between countries is output per unit of production 𝜀, higher levels of taxation will lead to firms migrating to countries with lower levels of emissions. This would mean less global emissions. 𝜕𝜖 𝜕𝑒= 𝜕 𝜕𝑒((𝜀 ∗ 𝑛) ( 𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1) )) = −𝛽 ∗ 𝜀 ∗ 𝑛 ∗ (1 + 𝑣) (𝑛 + 1) 𝜕𝜖 𝜕𝑣 = 𝜕 𝜕𝑣((𝜀 ∗ 𝑛) ( 𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1) )) = −𝛽 ∗ 𝜀 ∗ 𝑛 ∗ (𝑐𝑗+ 𝑒) (𝑛 + 1)
We can infer that following from the model, that an increase in taxation leads to lower emissions, ceteris paribus. This is because with higher taxation, firms decrease their output in a profit maximising strategy. 𝜕𝛱∗ 𝜕𝑒 = 𝜕 𝜕𝑒( 𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1) ) ( 𝛼 − 𝑛 [𝛼 − 𝛽(𝑐(𝑛 + 1)𝑗+ 𝑒)(1 + 𝑣)] 𝛽(1 + 𝑣) − 𝑒 − 𝑐𝑗 ) − 𝐹 =𝛼((𝑛 − 1)𝑣 2+ 2(𝑛 − 1)𝑣 − 2) − 2𝛽(1 + 𝑣)(𝑐 + 𝑒)(𝑛𝑣(𝑣 + 2) − 1) (𝑛 + 1)2
The effect of an increase in excise taxation on profit becomes less effective the more dairy farms a country has. This has to do with an important property of the Cournot model, namely that prices converge towards marginal costs as the number of producers increases. Given the sizes of the numbers, in most cases we will observe 𝜕𝛱
∗
𝜕𝑒 < 0. This effect is of importance, because it confirms that higher excise taxation lowers domestic profit which makes migration again more attractive to
domestic firms. 𝜕𝛱∗ 𝜕𝑣 = 𝜕 𝜕𝑣( 𝛼 − 𝛽(𝑐𝑗+ 𝑒)(1 + 𝑣) (𝑛 + 1) ) ( 𝛼 − 𝑛 [𝛼 − 𝛽(𝑐(𝑛 + 1)𝑗+ 𝑒)(1 + 𝑣)] 𝛽(1 + 𝑣) − 𝑒 − 𝑐𝑗 ) − 𝐹 =−𝛼 2− 2𝛼𝛽(𝑐 + 𝑒)(𝑛 − 1)(1 + 𝑣) + 𝛽2(𝑐 + 𝑒)2(𝑛(3𝑣2+ 6𝑣 + 2) − 1 𝛽(𝑛 + 1)2
32 Conclusion
The Cournot model with adjustments for taxation allow for mathematical analysis that give clear conclusions. There are two main effects coming from the taxation. In most scenarios, tax increases will decrease global greenhouse gas emissions, because firms decrease their level of production in their homeland and therefore will emit less greenhouse gasses. On the other hand, there will be farmers that migrate. Because they migrate, they will likely increase total output in that country. In most cases the first effect with outweigh the other. However, there certainly are some possible situations where indeed higher taxes can lead to higher global gas emissions.
If the foreign country has higher levels of greenhouse gas emissions per unit of production and also facilitates cheaper production, in that case we can expect a net increase of global greenhouse gas emissions, because the incumbent farmers will have higher levels of output in the new equilibrium.
Anyhow, further analysis is required before we can conclude whether the tax income is sufficient in offsetting the negative externalities. Mathematical analysis shows a clear trade-off between profitability on one hand and emission taxation on the other hand. If globally reducing emissions is a priority, countries with generally higher levels of emissions per unit of output 𝜀 should have taxes as an equilibrating force to reduce output, but should be wary that those taxes cause firms to migrate or shut rather.
Thus, the Cournot model of competition allows for thorough analysis and adjustments of parameters. It also shows that when dairy farmers migrate to countries with less producers, the effect on total emissions is greater. The answer to the research question therefore is no. It is certainly
possible that fiscal disparities can lead to negative externalities through offshoring decisions, however, in the context of Dutch dairy farmers migrating to Canada, this is not the case.
33 Remarks
As stated, the direct conclusions from the model is clear. However, a shortcoming of the model is that it assumes number of firms to be constant. In each country we see a downward trend in the number of dairy farms. Lower profitability logically results in less firms in the industry, as it increases opportunity costs.
Also, this Cournot model assumed equal marginal costs within countries. However, due to economies of scale, natural circumstances, availability of technology and other factors, marginal costs vary greatly between dairy producers (Hemme et al, 2014). Additionally, one must note that the model assumes constant costs, which do not hold, certainly on the short run. In a general sense, especially developing markets can profit from having low levels of taxation, as it attracts more firms to enter their market. This development has been going on for decades for larger manufacturing businesses, which are more labour intensive than dairy farms. However, as tax disparities grow on a global scale, especially on the environmental scale, firm migration becomes more attractive. This process takes place while due to globalisation entry barriers decrease, making firm relocation significantly more attractive.
34 References
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38 Appendix
Description of variables
Variable Description
Prod Milk produced in one annum, million tonnes ECM
Pop Population, in millions
Farmprice The farm ‘gate price’, the gross price a farmer charges for 100 kgs ECM
Cons Milk consumption in one annum, million tonnes ECM
Households Number of households in a country
Compric Price of one litre of milk in a shop
Gdp Gross Domestic Product of a country, observed in a year
Cows Number of cows in a country, observed in a year
N Number of dairy firms in a country
Rnf Rainfall, millimetres, average in a year
Tmp Temperature, measured in degrees Celsius, averaged of a year
Feedr Price-to-feed-cost ratio, a measure of feed costs
39 Data for the Netherlands
year Prod pop farmprice cons households compric gdp 1996 11,71 15,5 29,74 7,73 6580000 0,66 604106 1997 11,7 15,6 31,03 7,99 6640000 0,675 662503 1998 11,69 15,7 32,76 8,25 6700000 0,69 720900 1999 11,73 15,8 30,60 8,595 6750504 0,6 744594 2000 11,77 15,9 30,60 8,94 6801008 0,51 768288 2001 11,635 16,0 33,19 8,795 6867636 0,56 794167 2002 11,5 16,2 31,90 8,65 6934263 0,61 820046 2003 11,565 16,2 30,60 8,06 6991772 0,605 876464,5 2004 11,63 16,3 29,31 7,47 7049280 0,6 932883 2005 11,655 16,3 29,31 7,59 7097684 0,6 988297,5 2006 11,68 16,4 28,88 7,71 7146088 0,6 1043712 2007 12,005 16,4 32,76 7,99 7194145 0,65 1038697,5 2008 12,33 16,5 33,62 8,27 7242202 0,7 1033683 2009 12,485 16,5 25,00 7,74 7314173 0,67 1059789,5 2010 12,64 16,6 31,03 7,21 7386144 0,64 1085896 2011 12,62 16,7 35,34 7,69 7443801 0,67 1108508 2012 12,68 16,8 33,19 8,13 7512824 0,71 1120600 2013 13,25 16,8 38,79 8,36 7569371 0,76 1138132 2014 15,5 29,74
40
year cows n rnf tmp feedr land cows
1996 1504076 39000 630,858 10 1,9 29360 1504076 1997 1545821 37500 688,424 10 2,15 33353 1545821 1998 1485367 36000 1110,78 10,1 2,4 37346 1485367 1999 1477649 32733 909,186 10,1 2,15 35873 1477649 2000 1470483 29466 955,26 10,1 1,9 34400 1470483 2001 1433202 27925 1014,639 10,2 2,1 34050 1433202 2002 1419716 26393 954,343 10,2 2,3 33700 1419716 2003 1413166 25002 682,813 10,2 2,15 30850 1413166 2004 1466134 24329 912,234 10,3 2 28000 1466134 2005 1489071 23527 842,997 10,3 2 28630 1489071 2006 1478635 22301 822,388 10,3 2 29260 1478635 2007 1469720 21313 984,716 10,4 1,75 34130 1469720 2008 1483991 20746 885,563 10,4 1,5 39000 1483991 2009 1552919 20268 805,326 10,4 1,55 40000 1552919 2010 1572287 19805 877,644 10,5 1,6 41000 1572287 2011 1621767 19247 843,74 10,5 1,5 44000 1621767 2012 1744827 18682 945,839 10,5 1,2 46000 1744827 2013 1693804 18665 811,993 10,6 1693804 2014 1621914 18581 845,794 10,6 1621914
41 Data for Canada
year prod pop farmprice cows n rnf tmp feedr Land
1996 7,39 29,57 55,99 1237200 23823 631 7,3 2,2 4010 1997 7,52 29,85 53,92 1231100 22649 688 7,8 2,5 4578 1998 7,65 30,12 55,30 1184000 21571 1111 10,3 2,8 5146 1999 7,68 30,39 55,76 1156700 20581 909 9,6 3,2 5413 2000 7,70 30,65 58,29 1103400 19368 955 8,4 3,5 5679 2001 7,73 30,98 60,60 1091000 18679 1015 9,7 3,2 6022 2002 7,75 31,31 61,06 1083900 17931 954 9,6 2,9 6365 2003 7,81 31,61 64,06 1065500 16970 683 8,1 2,9 6851 2004 7,87 31,90 64,29 1054900 16224 912 8,4 2,9 7336 2005 7,77 32,22 68,43 1041400 15522 843 9,2 3,3 7739 2006 7,66 32,53 69,82 1019100 14660 822 9,9 3,7 8142 2007 7,77 32,87 73,50 997500 14036 985 9,2 3,5 8768 2008 7,88 33,20 74,42 984700 13587 886 8,4 3,2 9394 2009 7,91 33,58 75,81 965600 13214 805 8,2 3,5 9855 2010 7,94 33,96 76,96 966200 12971 878 9,7 3,7 10315 2011 8,11 34,30 79,26 965600 12762 844 9,3 2,7 11259 2012 8,33 34,70 78,34 965400 12557 946 10,6 2,3 14038 2013 8,18 35,10 79,72 968200 12267 812 8,7 0 2014 959400 12007 846 7,7
42 Marginal costs per country, for 100kgs ECM
Region Country
MC/100 kg ECM
Western
Europe
Netherlands $ 52,39 Switzerland $ 97,61 UK $ 38,24 Ireland $ 37,50CEEC
and ME
Israel $ 54,60 Ukraine $ 32,17 Belarus $ 24,26Africa
South Africa $ 43,01Nigeria $ 24,26
