Regulating gasoline retail markets: The case of Germany

Wittmann, Nadine Article Regulating gasoline retail markets: The case of Germany Economics: The Open-Access, Open-Assessment E-Journal Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Wittmann, Nadine (2014) : Regulating gasoline retail markets: The case of Germany, Economics: The Open-Access, Open-Assessment E-Journal, ISSN 1864-6042, Kiel Institute for the World Economy (IfW), Kiel, Vol. 8, Iss. 2014-33, pp. 1-33, https://doi.org/10.5018/economics-ejournal.ja.2014-33 This Version is available at: https://hdl.handle.net/10419/102722 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/3.0/ Received March 31, 2014 Published as Economics Discussion Paper April 10, 2014 Revised September 21, 2014 Accepted September 25, 2014 Published October 9, 2014 Licensed under the Creative Commons License - Attribution 3.0 Vol. 8, 2014-33 | October 09, 2014 | http://dx.doi.org/10.5018/economics-ejournal.ja.2014-33 Regulating Gasoline Retail Markets: The Case of Germany Nadine Wittmann Abstract In 2011, price peaks in retail gasoline prices caused public outrage and attracted the attention of German regulatory agencies. After having examined the market, competition authorities concluded that tacit collusion existed but could not easily be prosecuted under given competition law. In several other countries, various types of regulatory schemes are implemented to tackle tacit collusive behavior, e.g., there are price ceilings established in Luxembourg or per day limits of price increases given in Austria. However, research has found that none of them has led to satisfactory results. Hence, the following paper proposes a different regulatory approach, i.e., the implementation of corrective taxes. Results show that a specially tailored tax on price successfully manages to render collusion an unprofitable business by collecting marginal profits and that the inherent vice of the gasoline retail market, i.e., the transparency that enables tacit—and therefore non-prosecutable—collusion, could be turned into a regulatory virtue as it becomes a powerful means to help successfully tackle imperfect competition and to bring about a more efficient market outcome. JEL Q48 D42 D43 Keywords Gasoline retail market; regulation; market structure and antitrust; collusion Authors Nadine Wittmann, TU Berlin, Germany, [email protected] Citation Nadine Wittmann (2014). Regulating Gasoline Retail Markets: The Case of Germany. Economics: The Open-Access, Open-Assessment E-Journal, 8 (2014-33): 1—33. http://dx.doi.org/10.5018/economicsejournal.ja.2014-33 www.economics-ejournal.org 1 1 Introduction In today’s globalized economy, mobility is a crucial aspect of most people’s everyday lives on both a professional and personal level. Many people still rely on cars to satisfy their demand for transportation.1 Although the number of cars that run either partially (i.e. hybrid technologies) or totally on alternative energy sources is increasing steadily, the vast majority still relies entirely on fossil fuel based technologies.2 Hence, the retail market for gasoline is a very important economic sector to most industrialized nations and any irregularities or turbulences draw a lot of attention from the general public, policy makers, and researchers alike (Haucap and Mueller 2012). European nations in general and Germany in particular is certainly no exception to that. E.g., with well above 500 cars per 1000 people Germany is among the world’s top 12 nations in terms of car ownership.3 Also, the German gasoline retail market experienced significant price peaks in 2011, which triggered in-depth investigations by German regulatory authorities (Bundeskartellamt 2011). Possible measures and regulatory actions to be taken are still under consideration (Bundeskartellamt 2013) which makes the German gasoline retail market an extremely interesting showcase for the analysis presented in this paper. Regarding the characteristics of the market in general, there is a vast strand of literature dealing with numerous aspects of the retail gasoline market. A lot of publications examine the characteristics of the demand side, such as elasticity of demand (Dahl 2012, Brons et al. 2008), using various methods and looking at various countries, e.g. North America (Lau et al. 2012, Park and Zhao 2010, Nicol 2003), South America (Hofstetter and Tovar 2008), China (Lin and Zeng 2013), the Middle East (Ben Sita et al. 2012), or Europe (Pock 2010). Overall, the common denominator is that demand for gasoline is inelastic (Haucap and Mueller 2012). So far, there exist a total of well over 240 empirical gasoline demand studies that examine over 70 countries (Dahl 2012). With respect to diesel, there are another 60 studies dealing with over 55 countries. Dahl (2012) examined whether income and own-price elasticity differ across nations. While her data analysis showed that differences among countries exist, it nonetheless _________________________ 1 http://www.huffingtonpost.ca/2011/08/23/car-population_n_934291.html 2 http://data.worldbank.org/indicator/IS.VEH.PCAR.P3/countries/1W?display=default 3 http://www.electricdrive.org/index.php?ht=d/sp/i/27132/pid/27132 www.economics-ejournal.org 2 rendered important results as certain pattern emerged that allowed for estimating elasticity values for over a hundred nations. Moreover, Dahl also derives policy implications regarding the implementation of environmental and fuel mix policy measures in the retail gasoline market. Dahl’s findings underpin those of Pock (2010) who also found that changes in diesel car usage do affect demand in the gasoline retail market, and therefore also influence the own-price and income elasticity levels of the latter. Dahl (2012) also found that price elasticity increased with prices of both gasoline and diesel fuel. A paper by Nicol (2003) examines the elasticity of demand with respect to Canada and the United States. Naturally, one has to differentiate between different types of income elasticity, while the most common ones analyzed are own-price and income elasticity (Nicol 2003). Moreover, introducing the time aspect into the model set, Noel’s results show a significant difference between short and long run elasticity. In general, most empirical studies agree on a short (long) run own-price elasticity of around –0.26 (–0.86) regarding in the gasoline retail market (Nicol 2003). While the empirical model of Nicol (2003) does not contradict these results, it nonetheless finds significant proof of the fact that the exact level of both own-price and income elasticity of households differs across both household types and countries. These findings are certainly in line with standard economic theory which states that heterogeneous agent models render different results than a standard homogeneous agent models (Kirman 2006). Moreover, another important aspect that was identified by Pock (2010) with respect to estimating gasoline demand in Europe is that of an increase in diesel car usage. With respect to empirical data analysis such trends have to be taken into account in order to render non-confounded results. Pock’s analysis shows that the surge in diesel cars across Europe led to an overestimation of both income and own-price elasticity. With respect to the US retail market for gasoline, Park and Zhao (2010) focus on an empirical data analysis of post 2000 data. In their model setup price elasticity depends on the time horizon, budget constraints, as well as the economic characteristics of the good in question, i.e. whether it is necessary to economic subsistence or a luxury product, and whether substitutes are easily at hand (Park and Zhao 2010). Within their model set, time is not a relevant variable. This stems from the fact that their data is fixed by month and that substitution possibilities are hard to come by in the short run. Overall, Park and Zhao (2010) find that welfare could be increased by a shift from income to gasoline taxation and that deadweight loss for the most part www.economics-ejournal.org 3 depends on own-price elasticity. Lin and Zen (2013) analyze elasticity of demand in the Chinese gasoline market. Aside from calculating estimates for own-price and income elasticity whose ranges also comprise the estimates given by Nicol (2003) they also calculate the so called vehicle miles traveled elasticity (Lin and Zen 2013) which ranges somewhere between –0.882 and –0.579. In China, fuel taxes have been increased in 2009 and now also include agents that were previously exempted from the tax scheme, such as airlines and the army (Lin and Zen 2013). In their model setup, they find that demand seems slightly more elastic with respect to gasoline demand for transportation than other purposes. With respect to income elasticity of gasoline demand, Ben Sita, Marrouch and Abosedra (2012) analyze Lebanon data. They find that both government revenues and environmental standards do not benefit from a flat excise tax. Their model expresses gasoline demand as a function of structural changes that affect consumption, price and income. In doing so, they find that long run elasticity levels are higher than identified otherwise and conclude that structural changes have a significant effect on the demand for gasoline as they appear to affect people’s economic behavior substantially (Ben Sita, Marrouch, Abosedra 2012). On the whole, it can be said that the general consensus across publication is that demand for gasoline is rather inelastic (Havranek et al. 2012, Haucap and Mueller 2012). With respect to empirical findings regarding then general workings of gasoline retail markets, the following findings are of great interest. Polemis and Panagiotis (2013) examine how gasoline price fluctuate in the EU and whether price changes are asymmetric, i.e. prices are more likely to, e.g., increase than decrease. In the course of their analysis they find that for most EU countries, the gasoline market is still dominated by a small number of large and international corporations that explicit a very high level of vertical integration (Polemis and Panagiotis 2013). Their analysis focuses on 11 EU countries, i.e. “Austria, Belgium, Finland, Greece, France, Germany, Ireland, Italy, Netherlands, Portugal and Spain” (Polemis and Panagiotis 2013, p. 426). It is assumed that the existence of asymmetric price volatility is a result of tacit collusion being prevalent within the gasoline retail market (Borenstein et al. 1997). In the course of their analysis, Polemis and Panagiotis find that asymmetric price changes are especially prevalent within the wholesale market in which positive retail price increases are passed on to consumer prices virtually instantly while price remain fairly sticky in the face of www.economics-ejournal.org 4 a decrease in wholesale prices. According to their analysis, policy measures which foster competition within the wholesale segment of the gasoline retail market would also pose a remedy regarding asymmetric price volatility. Garcia (2013) also researched price asymmetries in the market for gasoline using a Meta regression analysis. Aside from EU markets, his analysis also incorporates, among others, the North American hemisphere as well as Australia. Nonetheless, his findings are in line with those of Polemis and Panagiotis (2013) who also identify that the asymmetries occur mostly and most prominently with respect to the retail market segment. Moreover, he also identifies the lack of competition as the primary source of the problem. The Meta analysis conducted by Brons et al. (2008) also examines the price elasticity of gasoline demand along with other important elasticities such as mileage per car. Their analysis shows that the latter is inelastic and values are in line with those identified by others such as Nicol (2003). They also identify differences in elasticity levels between countries which stem from structural differences such as infrastructure and availability of car substitutes such as public transportation. The paper by Lau et al. (2012) focuses on the Canadian Research market and looks at how price regulation affects the retail market for gasoline. Their analysis shows that price regulation leads to a significant reduction in price volatility within the market which is also a good indicator on whether regulating price manages to successfully, i.e. negatively, affect tacit collusion within the market. Hence, with respect to the supply side of the retail market for gasoline, the general consensus is that the gasoline retail market is likely to suffer from a lack of competition and an oligopolistic market structure and non-prosecutable tacit collusion (Garcia 2013, Haucap and Mueller 2012, Andreoli-Versbach 2011, Bundeskartellamt 2011). Therefore, several countries have taken different regulatory measures in order to fight this economically undesirable status quo. However, it appears as though none of these measures have proven successful (Berninghaus et al. 2012, Haucap and Mueller 2012), i.e. neither have markets become significantly more competitive and less collusive nor has asymmetric price volatility been abolished (Polemis and Panagiotis 2013, Bettendorf et al. 2003). Hence, it seems as though, so far, regulation authorities do not have any feasible instrument available, to adequately address this problematic state of affair. However, the model presented in the following section might be an option which could help to do away with the problem in question. The paper is structured www.economics-ejournal.org 5 as follows: Section 2 presents the formal structure of the proposed regulatory scheme and Section 3 contains a numerical example. Section 4 takes a critical look at the proposed regulatory scheme and findings presented in Section 2 using additional literary sources. Section 5 contains some concluding remarks. 2 The Model As has been shown in the previous section, seminal research identifies the following set of crucial characteristics inherent to the gasoline retail market: Inelastic demand, imperfect competition and tacit collusion. However, before the formal analysis conducted in this section can commence, three important aspects have to be introduced. Firstly, it is important to note that the core of the proposed regulatory tax scheme presented in the following section draws from findings by M.A. Adelman (1978). In his paper on the constraints on the world oil monopoly price he proposes that oil importing nations could successfully tackle the OPEC cartel by implementing a tax rate proportional to price. Whenever prices rise, the tax rate is adapted accordingly and the cartel is thereby deprived of the desired rise in revenue, which otherwise would have taken place due to a sufficiently inelastic demand function. In addition, a recent paper, Vetter (2013a) generates valuable findings which proof that variable tax rate schemes on sales prices can indeed increase welfare in markets that exhibit certain types of imperfect competition. As is to be seen shortly, the results of the following sections serve as additional verification of Vetter’s results. Secondly, the design of the proposed regulatory scheme adheres to the findings of Buchanan (1969) who has shown the importance of market structure in designing optimal regulation. The results of a recent paper by Kverndokk and Rosendahl (2011) also validate the importance of Buchanan’s findings with respect to the oil market and transport sector in general. In particular, Kverndokk and Rosendahl found strong evidence that, in the presence of market power, effects on the oil market resulting from regulating the transport sector differ significantly from those under perfect competition. Thirdly, it is important to keep in mind what the regulatory scheme is supposed to accomplish. The proposed scheme is not meant to generate government income, i.e. a predictable stream of revenue to the government as discussed in Madowitz and Novan (2013). Also, it is not meant as a measure to internalize the negative effects of fossil fuel consump- www.economics-ejournal.org 6 tion, e.g. the energy tax, as in Fisher et al. (1996). Rather, it is meant as a measure to successfully correct and prevent market distortions that stem from the exertion of market power as in Adelman (1978). 2.1 Demand The inverse demand function, denoted with D: p(x), is assumed to take the common downward-sloping form regarding the connection between price p and quantity demanded x (Vetter 2013a), i.e. : (), () 0 D px px x ∂< ∂ (1) with ( ), 0,px x ≥ and is also assumed to stem from a strictly monotonically decreasing demand function, x(p), with () 0, xp p ∂< ∂ which has also been used by Schendel and Balestra (1969) in their paper on price wars and rational behavior in gasoline markets. However, in order to better illustrate the outcomes and analysis to come, a set of two exemplary demand functions, Di, with { , },i I II∈ is introduced, which differ in terms of their elasticity to further illustrate the importance of the latter with respect to market outcomes 2 : 1 : II I II II II D p a bx Dp a x s = − = − (2) with , , 0 and , , , 0. I II I II abs x x p p >≥ Hence, in addition to portraying the standard linear demand curve, there is a second one that holds more elasticity within the upper price range and at the same time more inelasticity within the lower price range than a standard linear demand curve and thereby better manages to emulate some of the empirical findings on gasoline retail markets (Dahl 2012). In addition, to further facilitate comparability of market outcomes, the two representative demand functions do not only share the same reservation price at a eurocent/l (ct/l) but also the same maximum quantity demanded in case of a price equal to zero, i.e. 0, i p= that is denoted with sat x liters per period—e.g. per www.economics-ejournal.org 7 week—which means that the two are connected mathematically through the following identity . sat x bs ≡ In general, the former assumption is meant to illustrate a situation in which there is a point at that, although price is zero, demand does not increase any more, as, intuitively speaking, a consumer has only so much distance to travel to work and only so much spare time to make road trips and so forth. Hence, other exogenous variables would have to change first that could then cause the demand curve to shift outward. Price elasticity of demand, i.e. , with { , }, () i i xp E i I II px p ∂ = ∈ ∂ is given by ,. 2( ) I II DD EE pp ap ap −− −− = = (3) Within the entire price range [ ) 0,pa∈ ct/l, DII is more inelastic than DI. The unitary elastic point is reached at 2 a ct/l for DI and 2 3 a ct/l for DII. On the whole, demand within retail gasoline markets has proven to be rather inelastic (Haucap and Mueller 2012, Schendel and Balestra 1969). However, it is certainly not perfectly inelastic along the entire range of the demand function. Rather, elasticity increases as the price rises (e.g. Adelman 1978) which is also in line with the findings of Dahl (2012) that have been presented in Section 1. Intuitively speaking, when gasoline prices are low, consumers’ behavior, e.g. patterns of car usage, will not change significantly when prices fluctuate marginally. Once a significantly higher price level is reached, however, demand becomes increasingly more elastic with respect to price changes, because now people might more often choose to go by foot or take the bike instead of their car, as the opportunity cost of taking the car, just to get to the bakery around the corner, have become considerably higher. And, at the very end, i.e. a price approaching the reservation price, consumers start to switch almost entirely to using public transportation or to a car that runs on a different type of fuel. A graphical illustration along with a numerical example is presented in Section 3. www.economics-ejournal.org 14 AO.4 How does that come about? Through charging inflated wholesale prices, wholesale gas suppliers cause free gas stations to set the wrong tax rate with respect to any set of retail price and retail quantity supplied. Hence, the actions of the latter result in an act of tax evasion which is, in contrast to the economic aspect of this strategic behavior (Bundeskartellamt 2011), a prosecutable tax offence (see Footnote 4). Figure 2 illustrates the point made: With wholesale gasoline suppliers charging actual costs, c, the market equilibrium is characterized by point B in Figure 2 and a resulting actual regulatory tax rate of zero. Billing , free cc> however, leads to inflated marginal costs and results in a different gasoline retail market equilibrium which is represented by point A in Figure 2. The shaded rectangle represents the tax volume evaded and its height equals the per unit tax rate evaded in point A. Figure 2: Tax Evasion Caused By Inflating Marginal Cost _________________________ 4 http://www.gesetze-im-internet.de/ao_1977/__370.html (German version) or http://www.gesetzeim-internet.de/englisch_ao/englisch_ao.html#p2106 (English version). 5 10 15 20 25 30 50 100 150 200 250 A B H MCINFLATED MCACTUAL DII TEVADED www.economics-ejournal.org 15 Table 2: Tax Evasion Caused By Inflating Marginal Cost Equilibrium Results Scenario Charging c (Figure 2: Point B) Charging free cc> (Figure 2: Point A and H) Market price (pc vs. pfree) DI, DII (19) (1 ) E ct τ +< − (1 ) (1 ) E ct C ττ +∆ + −− (20) Quantity supplied (xc vs. xfree) DI (21) (1 ) (1 ) E act b τ τ − −− > − (1 ) (1 ) (1 ) E act C bb τ ττ − −− ∆ − −− (22) DII (23) () (1 ) 1 (1 ) E act C ss τ ττ − −− ∆ − −− (24) Tax rate paid D I = D II 0 (25) 0 5 (26) Tax rate due DI = DII C∆ 6 (27) Evaded tax volume DI = DII Cx free ∆× (28) Table 2 presents the results of the analysis with respect to scenario DI in a concise manner. Equations (19) and (20) illustrate that inflating marginal cost leads to higher prices which results in lower quantities demanded as shown by (21) to (24). The level of tax evasion is given by (28). Due to the transparency inherent to both the gasoline wholesale and retail market segment such a tax evasion can be both easily detected and prosecuted. Hence, the expected payoff Exp Π from charging inflated wholesale prices becomes negative, i.e. ( )0 Exp free free free free fine cx cx f χ Π= − + < (29) _________________________ 5 Solving cartel t P MC= − leads to (1 ) 0. (1 ) E cartel E ct C t ct C ττ + +∆ = − − − +∆ ≡ − 6 Inserting xfree, from (T2.IV), into (1 ) () cartel E free t ct px τ = − × −− renders (1 ) (1 ) ( (1 ) ) E cartel E act C t ab ct b τ ττ − ×−− ∆ = − × −× −− − − . cartel tC⇒ ≡∆ ( ) (1 ) 1 E act s τ τ − −− > − www.economics-ejournal.org 16 with 1 χ → including a non-negative fine for committing tax fraud, i.e. 0. fine f> Thereby, competition is fostered while collusive actions and profit skimming are successfully confounded in all, i.e. both retail and wholesale sectors of the gasoline market. Lastly, regarding the feasibility and applicability of the approach, it can also be stated, that the proposed regulatory tax scheme appears quite applicable, as commonly used gas station software7 8 typically combines all aspects of business management, back office and point of sale issues and also allows for a flexible _________________________ 7 Relevant websites on gas station software in German: http://www.infordata-oase.de/produkte/winoase/sondermodule-winoase.html http://www.ratio-elektronik.de/de/kassensysteme.php http://www.bungalski.de/prospekt.pdf http://www.mum-edv-service.de/index.php/produkte/tankstellen-raststaetten-software http://www.xsitesoftware.ca/site/home http://download.cnet.com/Gas-Station-Software/3000-2067_4-176906.html http://www.ratio-elektronik.de/de/kassensysteme.php http://www.bungalski.de/prospekt.pdf http://www.mum-edv-service.de/index.php/produkte/tankstellen-raststaetten-software 8 Relevant Websites on gas station software in English: http://www.xsitesoftware.ca/site/home http://download.cnet.com/Gas-Station-Software/3000-2067_4-176906.html Quote: “Store purchases, fuel sales, fuel purchases, price adjustments or shortage, paid-outs, assets, complete employee, customer, and vendor management. Inventory tracking by department, item, and category. Flexible taxing system which allows you to tax items differently. Keep track of each of your fuel pumps and tanks, by storing information about their location, model, and capacity. Optionally associate a pump and a tank with each fuel grade, for keeping track of fuel inventory, and better tracking of which tank and/or pump produces the most sales. The Agnitech gas station software is intended to be used as a back-office software to keep track of historical data of everything from store sales and purchases, fuel sales and purchases, payments, receivables, daily assets, etc. […] It tracks all activity that takes place at the gas station, from tracking fuel sales by category, fuel purchases, store sales and purchases, tracking store sales by department and by countable products. It also tracks all payments made to vendors and other payees, it tracks the daily assets by shift and by day. It allows you to instantly generate reports that show you what you have and what you should have. It also generates fuel reconciliation reports, historical reports of everything that happened during any period of time, and much much more.” (Source: http://download.cnet.com/Gas-Station- Software/3000-2067_4-176906.html Access Date: September 2014). www.economics-ejournal.org 17 taxing system (see Footnote 8). Hence, the proposed regulatory tax scheme is equally simple to implement as the well-known and well-functioning VAT scheme as the information problem is passed onto the economic agent that actually holds all the necessary information, i.e. the suppliers of the gasoline retail market. This results from the fact that, through standard management and back office software or basic profit margin spread-sheets, gasoline retailers generally have perfect information (see Footnotes 7 and 8) on their unit cost structure and price setting and the absolute value of subtracting the two simply renders . cartel t At most, it could mean that some new lines of code need to be added to the already existing software system or the profit margin spreadsheet used. Relevant data sets could then be sent over periodically to regulation authorities and be evaluated softwarebased as well. Hence, regulation authorities can isolate and focus on prosecuting irregularities such as positive tax rates, falsely calculated tax rates or inflated wholesale prices which result in tax evasion while gasoline retailer, for the most part, only need to make sure that their software or spreadsheet works correctly and to decide whether they want to engage in unit cost pricing or collect taxes for the government instead of cartel profits. On the whole, the reason why tacit collusion can be upheld so easily within the gasoline retail market is that market agents’ behavior in general and market prices in particular are highly transparent and readily observable at almost negligible cost (Haucap und Mueller 2012, Bundeskartellamt 2011). In addition, not only retail market structures but also data on wholesale prices and suppliers cost structures are accessible to regulation authorities (Bundeskartellamt 2011 and 2013). Through the proposed regulatory tax scheme, this inherent vice of the gasoline retail market, i.e. the transparency that enables tacit—and therefore nonprosecutable - collusion, is turned into a regulatory virtue as it becomes a powerful means to successfully tackle imperfect competition. This is also in line with findings of Vetter (2013a), who identifies information deficits as one of the most crucial issues when it comes to the practicability of variable tax rate schemes, such as a digressive tax rate. www.economics-ejournal.org 18 3 Numerical Example The analysis now proceeds by presenting further results and discussion based on a numerical example. These findings provide additional grounds that validate the results and discussion of the previous sections. Overall, they illustrate particularly well how market outcomes depend on the elasticity of demand with respect price but also that the proposed tax scheme functions successfully either way. Naturally, numerical results with respect to optimal prices and quantities presented in this section depend on the exemplary numbers chosen. However, as has been shown by (16) the proposed tax scheme renders the desired results even in the general model setup of (1), (4) and (5), thereby the main findings with respect to the desired effect of the proposed tax scheme do not suffer from a loss of generality. 3.1 Demand Representative demand functions are chosen in accordance with (2). Reservation price is assumed at 2.50€/l, i.e. 250ct/l9 and xsat is set around 31 liters per period, e.g. per week,10 i.e. 2 250 7.91 , 1/ 4 250. I I II II D xD x=− =−+ (30) Price elasticity of demand, as in (3), can be expressed as [ ) , with 0,250 . 250 2(250 ) I II DD pp p p EE p = ∈ −− = − − (31) _________________________ 9 Taking the Green parties 1998 proposal of 5 D-Mark per liter of gasoline as a vivid and well known example which, to-date, whips up significant outrage among German car owners. http://www.spiegel.de/auto/aktuell/kraftstoffpreis-warum-benzin-viel-zu-billig-ist-a-553489.html 10 Given an average weekly amount of kilometers driven by German car owners of around 14000 . . 270 52 . . km p a km weeks p a week ≈ (http://de.statista.com/statistik/daten/studie/2579/umfrage/durchschnittlich-pro-jahr-mit-kfz- gefahrene-kilometer/) and given an average fuel consumption of 8.5l/100km per car (http://www.upi-institut.de/iaa.htm) renders an average demand of around 23 l/week. Therefore, assuming a maximum quantity demanded of 31 l/week appears well justified. www.economics-ejournal.org 19 Hence, within the entire price range between zero and 250ct/l of gasoline, DII is more inelastic than DI. The unitary elastic point is reached at 125ct/l for DI and 166.67ct/l for DII which is illustrated by Figure 3. Figure 3: Price Elasticity of Demand 3.2 Supply Relevant cost structures and tax rates are chosen according to (4) combined with real live numbers, presented by German competition authorities in their final sector analysis report (Bundeskartellamt 2011) unit cost of input equals 45, 65.45, 0.16 ( ), { , }. 110.45 0.16 ( ) EU ii i c t t p p x i I II MC p x τ = = = = ∀= ⇒= + (32) The cost and demand structure of this numerical model are shown in Figure 4. Both representative demand functions, DI and DII, are sketched along with resulting marginal cost curves, MCI and MCII. The latter include unit cost of input (c) as well as energy tax (tE) and VAT in case of both scenarios. Section 3.3 and 3.4 are based on the settings illustrated in Figure 4, given demand and supply structures as characterized by (30) and (32). 50 100 150 200 250  4  3  2  1 D II D I www.economics-ejournal.org 20 Figure 4: Demand and Cost Structures 3.3 Results without Regulation against Collusive Behavior As has already been elaborated upon in more detail in Section 2, in the absence of collusion a standard Bertrand oligopoly outcome with zero companies’ profits emerges. If, however, a collusive cartel is established successfully, profits become positive and are maximized according to the standard profit maximizing condition that marginal revenue (MR) 2 3 250 15.82 , 250 4 I II II I MR MR x x−−= = (33) equals marginal cost (MC) as shown by (32). Table 3 presents a comprehensive overview over the results of the four different scenarios presented so far, i.e. scenarios DI and DII given either non-collusive or collusive market outcome. In case of a non-collusive Bertrand oligopoly, both DI and DII render the same market price but, naturally, the more inelastic demand in case of DII results in a higher quantity demanded. 5 10 15 20 25 30 50 100 150 200 250 D I DII MC I tE c MC II VAT I VAT II www.economics-ejournal.org 21 Table 3: Equilibrium Results of Bertrand Oligopoly and Collusion Equilibrium Results Non-collusive Bertrand oligopoly Collusive Cartel facing DI Collusive Cartel facing DII Quantities and Price: (Q*,P*) [Q* in liters, P* in eurocent/liter] Scenario DI: (15.0, 131.3) Scenario DII: (21.79, 131.3) (6.85,195.82) (11.85, 214.89) Suppliers’ Profits П*= 0 П* = 371.49 П* = 832.77 Consumers’ Rent CSDI = 890.18 CSDII= 1724.52 CSDI= 627.31 CSDII = 277.38 Tax revenue E I T = 981.75, U I T = 313.22 E II T =1426.16, U II T =454.87 E I T = 448.33 U I T =213.28 E II T =775.58 U II T =404.89 Aggregate Welfare Scenario DI: 2185.15 Scenario DII:3605.55 DI:1660.41 DII:2290,62 Welfare Loss – –24% –34.5% Once collusion is successfully accomplished, prices rise and quantity is reduced in both cases. Again, both effects are relatively more severe in case of the more inelastic scenario DII. Moreover, it is extremely interesting to see how prominent the effects of the difference in demand functions come up in these numbers. Although both reservation price and maximum quantity demanded are completely identical for both DI and DII, the difference in inelasticity of demand DI and DII has a significant effect on price levels and rents, which is in line with standard microeconomic theory. In the non-collusive Bertrand oligopoly, quantity demanded as well as consumer rents are significantly higher in case of a more inelastic demand function, i.e. DII. However, once a collusive cartel is established, supplier’s profits rise tremendously—at the expense of consumer rents and tax revenue. This effect is especially prominent in case of inelastic demand where consumer rents decrease by over 83% and tax revenue decreases by 45% (energy tax)/ 11% (VAT). These findings are in line with those of Park and Zhao (2010) as www.economics-ejournal.org 22 has been mentioned in the introduction. Hence, this example clearly shows that a successful regulation of such a retail gasoline cartel would entail a substantial welfare gain to society as a whole. Figure 5 and Figure 6 are meant to further illustrate the setups and results presented in Table 3. Figure 5: Demand DI and Resulting Marginal Revenue and Marginal Cost Figure 6: Demand DII and Resulting Marginal Revenue and Marginal Cost 5 10 15 20 25 30  200  100 100 200 5 10 15 20 25 30  200  100 100 200 MCI DI MRI AI BI CI MCII DII MRII AII BII CII www.economics-ejournal.org 23 Points CI and CII represent equilibrium results in case of a non-collusive Bertrand oligopoly. Points AI and AII represent equilibrium market outcomes in case of a collusive cartel. Cartel’s profits are sketched by the rectangular shape. Welfare losses of collusion are easily identified as the area between the lines connecting points AI, BI, and CI in Figure 5 and AII, BII, and CII in Figure 6. 3.4 Regulating Collusive Behavior Now, the proposed regulatory policy scheme that has previously been introduced in Section 2.4 is applied to the numerical setup of Section 3.3. As has been elaborated upon before, its implementation is meant to drive the collusive cartel into the Bertrand oligopoly outcome represented by both (9), (11), and (13) of Table 1 and column two of Table 3. The optimal tax rate set according to (15) in combination with the information given by (30) and (32). Hence, the following equations render the functions which determine the appropriate tax rate in each of the two representative demand scenarios: 2 ((1 0.159) 45 65.45) ((1 0.159) 45 65.45) ((1 0.159)( , ,250 , 7.91 ) 45 65.45) ((1 0.159)( 1/ 4 {0,31.63}. 250) 45 65.45) cartel I cartel II cartel I cartel II I I II I II II t t t t xx p p x x − −− − −− − = = ⇒ =− −− ∀ += ∈ − − −− (34) Figure 7 illustrates the respective functions which may serve to facilitate the understanding of the results presented in Table 4 and Table 5. Figure 7 depicts demand and marginal cost structures as well as optimal tax rates of both scenarios DI and DII. Point AI (AII) represents the equilibrium market outcome in case of demand scenario DI (DII). The former characterizes both the Bertrand oligopoly result, as given by column two in Table 3, as well as the case of the collusive cartel, regulated by the tax rate given by (34). www.economics-ejournal.org 30 References Adelman, M.A. (1978). 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