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Optimizing Social Welfare with Low Cost Carriers Entering Airline Markets

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vol. 21 mar ‘13

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The inventory routing problem: A two-phase approach The Impact of Expectation Feedback Systems on the Reaction of Market Price to Large Unanticipated Shocks Expectations in a Nonlinear Real Estate Model

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by: dr. ir. Sander van Triest When I was a student, I followed three courses on Operations Research. Quite aptly, they were named Operations Research I, Operations Research II, and Operations Research III. Now, this was long ago, when courses were many and academic years were divided into trimesters. I would follow 5 or 6 courses per trimester, so the credits per course were lower – not more than 3 or 4 ‘modern’ ec’s. I vaguely remember something with the Simplex method, dynamic programming, and even integer programming. I also remember that my course grade dropped with every next course, and so it was a good thing that there was no Operations Research IV. Now, this is not as bad as it seems. I studied Industrial Engineering (‘Technische Bedrijfskunde’), Operational Research III was an elective, and anyway I gradually drifted into the field of accounting, where I now do my teaching and research. In this field, complexity is not in modelling but in implementation. Accountants do not perform complex valuations of pension liabilities, nor do they calculate the optimal scheduling of a multi-stage supply chain. However, accountants do want to make sure that the results of a valuation or scheduling exercise are used in ways which contribute to reaching the goals of an organization. To this end, we (for I nowadays tend to view myself as an accountant rather than an engineer) try to identify ways in which we can develop performance measures that help in making the right decisions, sometimes in the form of a profit number, sometimes in terms of unit costs, sometimes in a balanced approach including measurements of customer satisfaction or product returns. Of course, it depends on your point of view what the ‘right’ decision is for a business, or any organization.

Which brings me to the point of this preface. In practice, models and numbers are not neutral entities. They are used in practical situations, where there are many stakeholders who all have their own interests. The tools of the econometric trade help in making decisions, and they can have a very real impact, as we know from the current discussion on pensions.

Just as important, they can help in understanding and improving business practice. They are used by researchers in all kinds of fields – accounting being very much one of those – to test theories and so develop new knowledge. To do so, these tools should be used wisely. It is at this point that there is a challenge for both developers and users of these tools. In my field of research, approaches using instrumental variables are quite popular. The mechanics of IV estimation are complex (at least for non-econometricians), but any good statistics package enables researchers to perform them. However, the quality of the instrument used often is assessed purely on statistical grounds: if the regression diagnostics are ok, then the instrument is valid. Rarely, if ever, is any thought given to the underlying theoretical process which would enable an instrument to be correlated with the independent variable of interest, while not being correlated with the dependent variable. Econometricians may not always realize that others are not as good as they are in understanding the limits of econometric models, and that the powerful tools that they develop can be dangerous in the hands of lesser mortals.

So for an econometrician, Operations Research I, II, and III may be excellent names for courses, given their resemblance to xi notations, but spare a thought for outsiders who are not necessarily as good in abstract thinking but do want to use econometric tools anyway – and in the right way.

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78 Optimizing social welfare with low cost carriers entering airline markets

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by: Joep Lustenhouwer Airline markets have recently changed due to the entering of so called “low cost carriers”. These market entries can either be beneficial for social welfare or not. This article considers how social welfare can be optimized by a government that can choose to allow entry or not and that can set a maximum flight frequency in an airline market. The possibility of entry deterrence by incumbent airlines is taken into account.

Expectations in a nonlinear real estate model

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by: Taek Bijman The real estate market shows cyclic behavior. The cycle could be caused by the economic cycle. Most research has modeled the market using a small number of economic fundamentals, but these fundamentals fail to explain the market fully. For this reason it cannot be confirmed whether the real estate cycle is fully caused by the economic cycle or not. It may be that there is an endogenous cause for the cycle. Cobweb dynamics may be an endogenous explanation, however there is little evidence whether agents on the market form myopic expectations. In general there is little research on the behavior of agents in the real estate market. The aim of this article is to investigate the effect of expectations of agents on the real estate market

An application of market power theory in bilateral oligopoly markets to the EU gas production and distribution industry

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by: Yukihiko Funaki, Harold Houba and Evgenia Motchenkova In this note we apply the theory developed in Funaki et al. (2012) for analysis of the EU gas production and distribution industry. We analyze several examples that fit the current structure of the European gas production and distribution market and derive important policy implications, which may help improving the EU bargaining power and reduce the market power of existing gas suppliers.

The inventory routing problem A two-phase approach

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by: Jacob Kooijman The aim of this thesis is to develop a heuristical approach for the inventory routing problem. We will propose a two-phase approach to solve the problem. A novelty of the approach is the use of volume delivery optimization while optimizing the route schedule by means of column generation.

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BSc - Recommended for readers of Bachelor-level MSc - Recommended for readers of Master-level PhD - Recommended for readers of PhD-level

The impact of expectation feedback systems on the reaction of market price to large unanticipated shocks

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by: Te Bao Expectation formation plays a central role in modern economic modeling. Bao et al (2012) study how the expectation feedback system influences the behavior of individual expectations and market price after the fundamental price experiences large unexpected shocks. We find markets with negative expectation feedback quickly converge to the new fundamental, while markets with positive expectation feedback do not converge, but show underreaction in the short run and overreaction in the long run. A heterogeneous agent model explains these differences in aggregate outcomes.

Puzzle

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Facultive

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Optimizing Social Welfare with Low Cost Carriers Entering Airline Markets by: Joep Lustenhouwer Airline markets have recently changed due to the entering of so called “low cost carriers”. These market entries can either be beneficial for social welfare or not. This article considers how social welfare can be optimized by a government that can choose to allow entry or not and that can set a maximum flight frequency in an airline market. The possibility of entry deterrence by incumbent airlines is taken into account.

Introduction The once heavily regulated airline industry, has seen major deregulation all over the world in the last four decades. This has allowed low cost carriers (LCCs) to successfully enter airline markets. Successful examples of low cost carriers are Ryanair, Easyjet and Air Asia.

Several studies concluded that the uprising of LCCs has had a positive effect on consumer welfare, due to the lower prices offered by both the LCCs themselves and the full service carriers (FSCs) facing LCC competition.

This however, does not necessarily mean that market entry by LCCs has had positive effects on social welfare as well. The increase in consumer welfare could be offset by cost inefficiencies occurring in markets run by multiple airlines or by a negative impact on social welfare of undesirable flight frequencies. And even if deregulation in the airline industry has had an overall positive effect on social welfare, this does not imply that every route entered by low cost carriers has positively contributed to social welfare.

The subject of this article is the role of the government in improving social welfare in airline markets faced with possible market entry of LCC’s. As mentioned above LCC market entry could be beneficial for social welfare in some cases, but not so in other cases. The government could try to improve social welfare by not allowing market entry when entry would lead to a decrease in social welfare. This however, brings the potential problem that the existence of such entry regulation could lead to a reduction rather than an increase in social welfare. That could happen if incumbent FSCs strategically use the existence of entry regulation to alter their entry deterrence strategies in a socially undesirable way. The possibility of a negative effect of entry regulation on social welfare was proposed in a more general setting by Kim (1997, 2003). Kawasaki (2008) applied this model on an airline market setting, where an incumbent firm can deter entry by means of its flight frequency. He concluded that entry regulation can be either profitable or harmful to society depending on the amount of differentiation between the incumbent airline and the entrant.

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Another way the governments could intervene in airline markets faced with possible LCC entry is by setting maximum flight frequencies. By doing so, the government could restrict the possibility for incumbents to deter entry with high flight frequencies when it is socially desirable that LCCs do enter the market. This government interference can furthermore not be misused by incumbent airlines, since setting a maximum flight frequency gives the government a first mover advantage, which they lack when applying entry regulation.

The goal of this study is to provide insight in the effect of both entry regulation and the introduction of a maximum flight frequency on social welfare when a LCC considers entering an airline market with a FSC monopolist. In order to accomplish this, I follow Kawasaki (2008) by constructing a simple airline model with price competition and differentiated costs for the incumbent and the entrant. This model is used in a three stage entry deterrence game as performed by Kawasaki (2008).

The model in this article differs from that of Kawasaki (2008) in two aspects. While both differences concern the consumer types used in the model, they arise for different reasons. The first difference arises because this study looks specifically at an LCC entering a market with a FSC monopolist rather than a setting where both airlines are, on average, valued equally. Research has indicated that passengers using LCC differ from those using FSCs and that LCCs entering airline markets both

Joep Lustenhouwer Joep Lustenhouwer obtained his bachelor’s degree in Econometrics (cum laude) at the University of Amsterdam (UvA). In addition to his studies, Joep also served as a full-time board member of the VSAE. He is currently enrolled in the master’s degree programme in Econometrics at the UvA, while also following courses for the MPhil programme at the Tinbergen Institute.

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steal customers from the full service carriers and draw from costumers who did not fly before. To accurately model price competition, this study therefore requires three types of consumers rather than two.

The second difference arises because in this article the assumption that all consumer type groups are equally large is relaxed. By making the consumer type group sizes variable, this study analyses the effect of different group size ratios on the conclusions following an analysis in line with Kawasaki (2008).

The model The market under consideration is a connection between two cities. Assume that that there are three types of consumers who potentially want to travel from one of these two cities to the other. These consumer types differ in how much they value service. Type A values service so much that it is hard for an LCC to steal them away from the incumbent FSC, type B is an easier target for the LCC and type C values service so little that it is not profitable for a monopolist FSC to target this type of consumer by lowering prices. These different valuations of service are expressed in the utility functions of the consumers by the amount of extra utility (α, β, γ, with α > β > γ) the consumers gain from using a full service airline (airline 1). When the passengers use a low cost carrier (airline 2), no extra utility is granted for all consumer types.

Assume furthermore that consumers lose utility when aircrafts do not depart at consumers’ preferred departure times. The larger the difference between an actual departure time and a consumer’s preferred departure time the more utility is lost. The model in this article follows Kawasaki (2008) by modeling the positive effect of flight frequency on consumer utility linearly. The utility functions of the three consumer types are given by Ui, with i=A,B,C. (1) Where R is the utility consumers gain from using an airline, S(i) is the extra utility gained from using a full service airline (S(i)=α for i= A; S(i)= β for i= B and S(i)=γ for i = C), and f1 and f2 and p1 and p2 are the frequencies and prices of airline 1 and airline 2. The number of consumers belonging to consumer type A, B and C are given by a, b and c respectively.

In line with Hassin and Shy (2004) and Kawasaki (2008), airlines costs are in this article assumed to rise quadratic with flight frequency and are given by (2) Doganis (2001) shows that LCCs with the lowest costs operate at 40 - 50% of an average FSC. This study assumes that the FSC’s per flight costs are t times as high as the LCC’s. Formally:

(3) The sequence of actions undertaken by the two airlines is the following. In the first stage airline 1, who is already operating in the market, chooses its flight frequency, which is not as easily changed as its price. Next, airline 2 decides if it wants to enter the market. If airline 2 does not enter the market, airline 1 decides on a monopoly price in stage three. If airline 2 does enter the market it needs to choose a flight frequency. Airline 1 and airline 2 subsequently simultaneously decide on prices with both the flight frequency of airline 1 and of airline 2 in mind.

The government can intervene in this sequence of actions in two ways. First, they can, in stage two, decide not to let airline 2 enter the market when it wants to.

Secondly, the government can set a maximum flight frequency which takes effect before the first stage.

To see the effect of the government’s actions on social welfare the model is solved using backward induction.

First optimal prizes are determined both in case of a monopoly of airline 1 and in case of a duopoly. In the duopoly case the optimal flight frequency of airline 2 is determined as well. With these results, the conditions on the frequency of airline 1 under which airline 2 wants to enter the market and under which the government will allow are derived. Finally airline 1’s profit maximizing flight frequency is determined, using this information.

Results and analysis It turns out that the government will, under mild assumptions, always allow airline 2 to enter the market when it wants to. Solving the model without maximum flight frequencies furthermore results in three qualitatively different regions of combinations of α and β (the service valuing parameters of consumer type A and B). In the first region (region 1) airline 2 does not enter and airline 1 uses its monopoly price and optimal monopoly flight frequency. In the second region (region 2) airline 2 does not enter the market, and airline 1 uses an entry deterring flight frequency, together with its monopoly price. In the third and last region (region 3) the market is a duopoly and both airlines use their duopoly price and frequency.

With this result together with expressions for social welfare in all three regions the effect of a maximum flight frequency on social welfare can be analyzed. Social welfare can be influenced by a maximum flight frequency in two ways. First, a maximum flight frequency hinders airline 1 in its ability to deter entry of airline 2 with a high flight frequency. This means that for some combinations of α and β where, without a maximum flight frequency, it was optimal for airline 1 to deter entry, this is no longer possible and a duopoly arises. Region 2 therefore becomes smaller and region 3 becomes larger. This will result in higher social welfare at the relevant levels of α and β when duopoly social welfare is higher than monopoly social welfare.

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Secondly, a maximum flight frequency may restrict the actions of one or both airlines in the duopoly situation, forcing them to use a lower flight frequency than they otherwise would have chosen. In most cases one would expect this to result in lower social welfare since lower than profit maximizing flight frequencies will result in less utility for the consumers as well as lower profits.

It may however be the case that when one airline needs to lower its frequency the profit of the other airline will increase enough to offset this negative effect on social welfare.

In order to get some insight in the effect of a maximum flight frequency on social welfare for different combinations of α and β and to see how this effect changes as a, b and c change some numerical examples are useful.

In this article only the example where all consumer type groups are equally large is explicitly outlined. In the numerical analysis the following assumptions are made.

First, one would expect that utility from flying (R) is at least as high as the extra utility gained from getting more service (α), and that α always is considerably larger than β. So set R = 10 and look at α between 0 and 10, and β between 0 and 7. Secondly c1 and c2 are assumed to be 2 and 1 respectively. Lastly assume a+b+c=3. It it of interest for this study to vary the ratios of a, b and c but not the total number of consumers.

All consumer type groups of equal size

Figure 1: Social welfare when all consumer type groups are of equal size In Figure 1 social welfare is plotted against α and β, for : a=b=c=1. Here social welfare in region 1 is represented by the dark plane and social welfare in region 2 by the curved plane. The triangular area is region 3. Social welfare is there represented by the upper plane. The part of the upper plane that is not in the triangular area represents what social welfare would be in the monopoly area (region 1 and region 2), if the market was a duopoly rather than a monopoly. It can clearly be seen form Figure 1 that, with this costumer type distribution, a duopoly is always better for social welfare than a monopoly.

A maximum flight frequency that restricts the flight frequency that can be chosen by airline 1 to deter entry, would thus improve social welfare in that part of region 2 that then becomes part of region 3. In other words, a maximum flight frequency can for some combinations of α and β cause a duopoly to arise, where otherwise a monopoly with lower social welfare would have existed.

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As long as the maximum flight frequency does not restrict the airlines’ actions in region 3 or airline 1’s action in region 1, the level of social welfare in those regions is not changed. In this example the entry deterring flight frequency (f1Det) of airline 1 is the highest frequency considered in the model at the relevant combinations of α and β. The second highest frequency is the duopoly frequency of airline 2 (f2Duo). f2Duo thus is the second variable that will be affected as the maximum flight frequency is lowered. This means that as the maximum flight frequency is higher than f2Duo, but lower than f1Det, social welfare might be improved and is definitely not worsened. It turns out a lower maximum flight frequency worsens social welfare in region 2. This implies that a maximum frequency of f2Duo would always be good and a lower maximum flight frequency will only be beneficial if the market is in region 2 and definitely not in region 3.

Changing the ratios of the consumer group size (a, b and c) results in qualitatively different properties of the 3 regions with respect to social welfare. The conclusions that can be drawn from the complete analysis are the following. First of all, we saw that whether or not social welfare can be improved by a maximum flight frequency depends on the service valuing parameters α and β. However, if the maximum flight frequency is set to the highest not entry deterring flight frequency that can be optimal for the airlines, social welfare is not harmed. Whether or not social welfare is improved at this maximum flight frequency depends on airline 1’s entry deterring frequency which in turn depends on α and β.

If α and β are such that airline 1 wants to use its entry deterring flight frequency, and this flight frequency is higher than the maximum flight frequency, social welfare will be improved.

A note of caution needs to be taken here though. If there are very few consumers who start flying when the LCC enters the market (type C), compared to the consumers who already fly with the monopolist (type A and B), a maximum flight frequency below airline 1’s entry deterring frequency could be harmful for social welfare.

This is the case because then social welfare in duopoly is lower than in monopoly for some combinations of α and β.

If there are enough consumers of type C, the maximum flight frequency should in most cases be set to the frequency airline 2 will use when it enters the market. If airline 1 however, would keep a relatively large market share (a lot of costumers of type A), the maximum flight frequency should be set at the frequency airline 1 chooses when it has the market to itself and does not need to worry about deterring entry.

If the maximum flight frequency mentioned above is not low enough to keep airline 1 from deterring airline 2 from entering the market, α and β are such that a lower maximum frequency is needed to improve social welfare.

If however, the maximum frequency is set lower than necessary to keep airline 1 from deterring entry, social welfare will be below optimal.

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Finally, the more consumers there are of type C, the more social welfare will be improved by preventing airline 1 to deter airline 2’s entry. It is then thus more important for the government to intervene.

References Brueckner, J. K. (2004), “Network Structure and Airline Scheduling”, Journal of Industrial Economics, 52, 291–312.

Brueckner, J. K. and Girvin, R. (2008), “Airport Noise, Airline Service Quality, and Social Welfare”, Transportation Research Part B 42, 19-37.

Brueckner, J. K. and Zhang, Y. (2001), “A Model of Scheduling in Airline Networks: How a Hub-andSpoke System Affects Flight Frequency, Fares and Welfare”, Journal of Transport Economics and Policy, 35, 195–222.

Daraban, B. and G. Fournier (2008), “Incumbent Responses to Low-Cost Airline Entry and Exit: A Spatial Autoregressive Panel Data Analysis”, Research in Transportation Economics, 24, 15-24.

Doganis, R. (2001), “The Airline Business in the 21st Century”, Routledge, 29 London, New York.

Gillen, D.W. and Morrison W.G. (2003), “Bundling, Integration and the Delivered price of air travel: Are low cost carriers full service competitors?”, Journal of Air Transport Management, 9, 15-23.

Hassin O. and Shy O (2004), “Code-Sharing Agreements and Interconnections in Markets for International Flights”, Review of International Economics, 12(3), 337–352.

Kim, J., (2003), “Limit Pricing Through Entry Regulation”, Hitotsubashi Journal of Economics, 44 (1), 1-13.

Morgan, P. B. and Shy, O. (2000), ”Undercut Proof Equilibria”, Mimeo, State University of New York at Buffalo and University of Haifa.

O’Connell, J.F. and Williams, G. (2005), “Passengers’ Perceptions of Low Cost Airlines and Full Service Carriers: A Case Study Involving Ryanair, Aer Lingus, Air Asia and Malaysia Airlines”, Journal of Air Transport Management 11(4), 259-272.

Schipper, Y., Nijkamp, P. and Rietveld, P. (2003), “Airline Deregulation and External Costs: A Welfare Analysis”, Tranportation Research Part B 37, 699-718.

Schipper, Y., Nijkamp, P. and Rietveld, P. (2007), “Deregulation and Welfare in Airline Markets: An analysis of Frequency Equilibria”, European Journal of Operations Research, 178, 194-206.

Southwest Airlines Co. History by Date, the Fight to Fly. Requested on May 1st, 2012 via http://www.swamedia. com/channels/By-Date/pages/1966-to-1971 Warnock-Smith, D. and Potter, A. (2005), “An Exploratory Study into Airport Choice Factors for European LowCost Airlines”, Journal of Air Transport Management 11, 388-392.

Windle, R. and Dresner, M. (1999), “Competitive Responses to Low Cost Carrier Entry”, Transportation Research Part E 35, 59-75.

Hotz, V. J., and Xiao, M. (2005), “Strategic Information Disclosure: The Case of Multi-attribute Products with Heterogeneous Consumers”, Economic Inquiry.

Huse, C. and Evangelho, F. (2007), “Investigating Business Traveler Heterogeneity: Low-Cost vs Full Service Airline Users?” Transportation Research Part E: Logistics and Transportation Review 43, 259e268.

Kawasaki A. (2008), “Entry Regulation and Strategic Entry Deterrence in the Airline Market”, Journal of Political Economy, 75(1) , 57-81.

Kim, J. (1997), “Inefficiency of Subgame Optimal Entry Regulation”, Rand Journal of Economics, 28(1), 2536.

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Expectations in a Nonlinear Real Estate Model by: Taek Bijman The real estate market shows cyclic behavior. The cycle could be caused by the economic cycle. Most research has modeled the market using a small number of economic fundamentals, but these fundamentals fail to explain the market fully. For this reason it cannot be confirmed whether the real estate cycle is fully caused by the economic cycle or not. It may be that there is an endogenous cause for the cycle. Cobweb dynamics may be an endogenous explanation, however there is little evidence whether agents on the market form myopic expectations. In general there is little research on the behavior of agents in the real estate market. The aim of this article is to investigate the effect of expectations of agents on the real estate market

Introduction As argued by Wheaton (1999), an endogenous real estate cycle should not occur if agents behave rational.

Rationality may be a too strong assumption since it assumes that the agents have perfect knowledge about the market. Research in other asset markets has focused on bounded rationality and adaptive beliefs, and experiments have shown that agents switch between heterogeneously bounded rational forecast rules (Hommes, 2011). While bounded rationality may be a good method to model the expectations of agents, it has an important drawback.

Bounded rationality does not prescribe a rule how agents form their expectations.

The model developed by Wheaton (1999) is one of the few general models that describes the beliefs that might occur in the real estate market and the implication for the dynamics of the system. The model is quite restricted, since it investigates the real estate market under rational expectations and naive expectations separately. In this article the model developed by Wheaton is adapted to include heterogeneous expectations. The model used consists of both nonlinear demand and supply curves.

Furthermore the model is extended by an empirical characteristic of the real estate market, namely that the rents occurring on the market adjust with the difference between the actual vacancy rate and a long term equilibrium rate (natural vacancy rate). The model is investigated for different belief benchmarks: three homogeneous benchmarks and a heterogeneous case.

Model The real estate market exhibits different characteristics from other asset markets. Like most asset markets, the price is determined by demand and supply. However unlike most asset market, the real estate market differs in three aspects. The first aspect regards the asset. The real estate asset is a durable good. Durable goods are most often modeled in a stock-flow framework (Rosen & Smith 1983). The second aspect regards the fact that in general the real estate market does not clear. Most often there

Taek Bijman Taek Bijman recently finished his Master of Science in econometrics at the University of Amsterdam. During his studies he contributed to several VSAE committees which included the Aenorm. This article is summary based on his master thesis which was supervised by prof. dr.

Cars Hommes and dr. ir. Florian Wagener

exists excess supply, since there exist vacant objects in the market. The third aspect regards the real estate market as a whole. The real estate market is actually a system existing of three interrelated markets, with different agents. The first market is the space market where landlords and space users (tenants) determine the rents and the occupancy rate. The second market is the asset market where supply and demand determine the property market value. The third market is the construction market where developers add new real estate stock. A graphical representation (4-Quadrant model) of these interrelated markets has been developed by DiPasquale and Wheaton (1992).

The model assumes that the space is rented according to a nonlinear demand function. The demand (Dt) for space will depend on the current rent (rt) with constant elasticity (-β1) and where a1 is constant scaling factor: (1) The supply is modeled using a stock-flow framework.

The stock of space (St) at time t is determined by the existing stock at time t-1 reduced by depreciation and demolition of existing space at a constant rate (δ) and the construction of new space (Ct-n) started at t-n. A lag of n periods reflects the time it takes to construct new space and implies that agents will have to forecast the future price n periods ahead. Furthermore it is assumed that the asset price depends on the rate of construction (Ct-n/ St-1) instead of the absolute level of construction. The rate of construction is a nonlinear function of the expected asset

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price (pte) at time t-n with constant elasticity (β2) and a scaling factor a. The evolution of the stock of space is therefore governed by (2) The construction market will depend on the expected future price, while the rental market is determined by the rental price. Both markets are connected through the investment market and it is assumed that the asset price is determined by the discounting the current market rents with constant yield (y). Therefore the price is determined as follows: (3) The market does not need to clear and therefore demand and supply does not need to be equal. The temporary equilibrium in the market is therefore determined by (4) where the Vt denotes the percentage of vacant space.

Empirically it has been shown that there exists an inverse relationship between rents and vacancies (Rosen and Smith 1983). The rents at time t will be determined by the rents at time t-1 and the difference between the contemporaneous vacancy rate Vt and the natural vacancy rate V. If the contemporaneous vacancy rate is higher than the natural vacancy rate, landlords will lower the rents. If the contemporaneous vacancy rate is lower than the natural vacancy rate rents landlords will increase the rents. Expressing the rental adjustment equation for the contemporaneous vacancy rate results in: (5) where ϑ is an adjustment parameter that denotes the speed at which the rents will adjust.

Combining equations (1) to (5) the evolution of the price is governed by (6) To close the model, the beliefs pte in equation (6) need to be defined. In case of homogeneous beliefs the beliefs pte needs to defined. However in case of heterogeneous beliefs the model needs to be adapted.

Heterogeneous beliefs Since in this model it is assumed that only the developers have expectations about the future price the heterogeneous beliefs can be incorporated in the evolution of space function (equation (2)). The evolution of space is determined by the fraction ηh,t of agents of type h that use forecast rule fh. The evolution of the price (equation (6)) is therefore changed to: (7) It is assumed that fractions are determined at the start of every period t by a discrete probability distribution as introduced by Brock and Hommes (1997). A sensible fitness measure for the real estate market would be the past squared prediction error minus the information costs.

Beliefs In the model real estate developers can have different beliefs about the expected future price (pte). In this article three homogeneous expectations benchmarks and a single type of heterogeneous beliefs are investigated: • Agents with rational expectations (perfect foresight can predict the future price with 100% accuracy. Agents are assumed to be informed of the past prices and the underlying real estate model (pte = pt).

• Agents with naive expectations base the prediction on the last observed price. Naive expectations or myopic expectations are a relatively simple rule that can be obtained quite easily (pte = pt-n).

• Agents with trend following expectations are agents that extrapolate the trend g from past prices. Past prices are assumed to be easy to obtain. Since studies have shown that past prices are linked to the current market price, extrapolating the trend may be a decent method to predict the future price (pte = pt-n + gn (pt-n - pt-n-1)).

• The heterogeneous model investigated is a system consisting of two belief types. An interesting case to investigate consists of a costly sophisticated predictor (rationale expectations) versus a freely available simple predictor (naive expectations).

Investigating the dynamics of a system involves investigating the stability of the fundamental equilibrium (steady state). The real estate model assumes no exogenous shock and therefore there exists a fundamental equilibrium price which is the same for all three homogeneous benchmarks, namely p* = (δ/a)1/β2.

As can be seen from the price equation (equation (6) and (7)) the stability conditions cannot be explicitly derived. However stability conditions and price dynamics can be investigated numerically1 since at each period, the

1. The software that is used for the numerical analysis is the E&F Chaos program. For more information: Diks, C., Hommes, C.H., Panchenko, V. & van der Weide, R. (2008). E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics. Computational Economics, 32, 221-244.

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price pt is uniquely defined, since the supply function is a strictly increasing function in pt and the demand function is a strictly decreasing function in pt.

Results Numerical simulations show that when agents exhibit rational expectations the price converges to the fundamental price. However under the two other homogeneous belief types and in the heterogeneous case the price dynamics can become more complex.

There are several common results regarding the price dynamics for both the two homogeneous belief types and the heterogeneous case. The common results will be discussed next. Afterwards different results regarding the price dynamics for the two homogeneous belief types and the heterogeneous case will be discussed.

Common results The stability of the fundamental equilibrium depends on the depreciation rate δ, the ratio between the demand and supply elasticity (β2/β1), the natural vacancy rate V and the speed of adjustment parameter ϑ. Apart from these parameters stability will depend on the construction lag n. These parameters not only affect the stability of the system, the parameters can influence the amplitude and duration of the cycle as well.

A higher depreciation rate or elasticity ratio can shift the stable equilibrium to an unstable equilibrium. This is economically sensible since a higher depreciation rate implies that every period the price would depend heavily on the newly created constructed real estate stock. This would be a classic example of a cobweb cycle. Furthermore a higher elasticity ratio can shift the stable equilibrium to an unstable equilibrium. A higher fraction would imply a more elastic supply or less elastic demand. Elastic supply would increase instability since developers are more inclined to adjust the supply on basis of past prices. Less elastic demand increases instability since buyers cannot adjust easily to the changing supply. For a construction lag of 1 a primary period doubling bifurcation occurs in which the steady state loses its stability and a period 2 cycle is created. Further

Figure 1. Bifurcation diagram under naive expectations with construction lag n=1 w.r.t. depreciation rate δ. Other parameters: a=0.01, β1=0.2, β2=4, V=0.

bifurcations lead to chaotic behavior (figure 1). For higher construction lags a primary Hopf bifurcation occurs in which a quasi-period cycle is created. Figure 2 shows examples of a quasi-periodic cycle. Further bifurcations lead to chaotic behavior as well.

When the natural vacancy rate is assumed to be equal to 0, an increase of the construction lag decreases the stability of the system. For a construction lag of 1 an increase in the natural vacancy rate increases the stability of the system, while an increase in the speed of the adjustment parameter has a destabilizing effect. For larger construction lags the effect of the natural vacancy rate and the speed of adjustment parameter on the stability of the system is not always clear.

Different results For agents using naive expectations an increase in the natural vacancy rate increases the amplitude and duration of the cycle. Furthermore the amplitude and the duration of the cycle increases with the depreciation rate and the construction lag as is shown in figure 2.

Figure 2. Time series under naive expectations with construction lag n=2 and for different natural vacancy rates (V=0.05 (black), V=0.15 (blue)). Other parameters: δ=0.12, a=0.01, β1=0.2, β2=2, ϑ=0.3.

Trend following expectations have, with the trend adjustment coefficient g, an additional parameter compared to naive expectations that can influence the stability of the system. The trend adjustment coefficient has a destabilizing effect on the fundamental equilibrium.

Depending on the trend adjustment coefficient, the trend followers can be split-up in two groups: strong trend followers (g>1) and weak trend followers (0<g<1). For a construction lag of larger than 1 an increase in the construction lag decreases the stability of the system and the type chaotic behavior that can occur depends whether the agents exhibit strong trend following behavior or weak trend following behavior. Strong trend following expectations can lead to strange attractors with fractal structures as shown in figure 3. However weak trend following expectations lead to strange attractors without fractal structures. For strong trend following expectations the natural vacancy rate has stabilizing effect on the fundamental equilibrium, while for weak trend following expectations the natural vacancy rate

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only has a stabilizing effect when the construction lag is equal to 1.

Figure 3. Phase plot (pt-1, pt) under trend following expectations for construction lag n=3, δ=0.065, a=0.01, β1=0.2, β2=2, V=0, g=1.5.

The heterogeneous case has two additional parameters that can have an effect on the stability of fundamental equilibrium; the cost of rational expectations C and the intensity of choice parameter γ. An increase of the cost of rational expectations and in the intensity of choice parameter has a destabilizing effect on the fundamental equilibrium.

The heterogeneous case has introduced fractions that can exhibit dynamical behavior. Like the price dynamics, chaotic behavior can be obtained for the fractions as well. The phase plot (figure 4) shows a strange attractor with an asymmetric structure. As is shown by Brock and Hommes (1997) a model with linear supply and demand curves leads to a symmetric strange attractor, while a model with a linear supply curve and nonlinear demand curve and obtained an asymmetric strange attractor (Goeree and Hommes, 2000). The asymmetric strange attractor seems to be caused by fact that the real estate model has both nonlinear supply and demand curves.

Conclusion and summary The real estate market exhibits cyclic behavior. This article gives an insight in the possible dynamics that can be caused endogenously. Under rational expectations the model will reach a stable fundamental equilibrium price and other dynamics are not obtained. However under the other two homogeneous benchmark beliefs (naive expectations and trend following expectations) and the heterogeneous belief benchmark (costly rational expectations versus freely available naive expectations) complex dynamics are obtained, these include (quasi-) periodic and chaotic behavior. Real estate cycles can be driven by animal spirits or (heterogeneous) expectations.

The findings are quite robust for the different belief benchmarks.

References Brock, W.A. & Hommes, C.H. (1997). A Rational Route to Randomness. Econometrica, 65, 1059–1095.

Brock, W.A. & Hommes, C.H. (1998). Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model. Journal of Economic Dynamics and Control, 33, 1912–1928.

DiPasquale, D. & Wheaton, W. C. (1994). Housing Market Dynamics and the Future of Housing Prices.

Journal of Urban Economics, 35, 1–27.

Goeree, J.K. & Hommes, C.H. (2000). Heterogeneous Beliefs and the Non-linear Cobweb Model. Journal of Economic Dynamics and Control, 24, 761–798 Hommes, C.H. (2011). The Heterogeneous Expectations Hypothesis: Some Evidence From the Lab. Journal of Economic Dynamics and Control, 35, 1-24.

Rosen, K. & Smith, L.B. (1983). The Price Adjustment Process for Rental Housing and the Natural Vacancy Rate. The American Economic Review, 73(4), 779– 786.

Wheaton, W.C. (1999). Real Estate Cycles: Some Fundamentals. Real Estate Economics, 27(2), 209– 230.

Figure 4. Phase plot (pt, η1t) under rational and naive expectations with construction lag n=2, δ=0.07, a=0.01, β1=0.2, β2=4, V=0, C=0.5, γ=5.

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An application of Market Power Theory in Bilateral Oligopoly Markets to the EU Gas Production and Distribution Industry by: Yukihiko Funaki, Harold Houba and Evgenia Motchenkova

In this note we apply the theory developed in Funaki et al. (2012) for analysis of the EU gas production and distribution industry. We analyze several examples that Â&#x2026;fit the current structure of the European gas production and distribution market and derive important policy implications, which may help improving the EU bargaining power and reduce the market power of existing gas suppliers.

Introduction

Yukihiko Funaki

Markets with a few concentrated suppliers and a few concentrated buyers, who all can exercise market power, are referred to as bilateral oligopolies. The gas production and distribution industry is an example of such a market.

This industry is characterized by the network structure with several big suppliers (also producers) of gas. They are, essentially, Russia, Iran, and Algeria. This industry also has significant costs of building pipelines (links between producers and consumers) and transporting gas through them. In this setting, the increasing market power of big suppliers becomes an important issue. The analysis presented here will shed some light on how the design of network structure can influence the market power of big gas suppliers, such as Russia and Iran. Since oil and gas are supplied by a limited number of countries and the demand side has the US, EU and China making up the largest part of total demand, it is clear that these markets are thin with respect to the number of sellers and buyers.

It is well known that concentration on the supply side increases market power and that it has negative consequences for consumer welfare and aggregate social welfare, see e.g. Tirole (1988) or Motta (2004). These analyses have been extended to bilateral oligopolies in Bloch and Ghosal (1997), Bloch and Ferrer (2001), or Amir and Bloch (2009). Galbraith (1952) is probably the first author who has argued that concentrated buyers can also have countervailing power that can restrain the market power of suppliers. Hence, especially in bilateral oligopolies with high concentration on both sides, the relationship between concentration, market power and efficiency is much more complex, and only a few studies have investigated this relationship both theoretically and empirically. Of those studies, several have tested the countervailing power hypothesis, and there appears to be evidence that buyer concentration negatively affects

is professor at the Faculty of Economics and Political Sciences of the Waseda University in Tokyo. He obtained his Ph.D. from the Tokyo Institute of Technology, in 1985. Funaki is affiliated with Waseda since 1998. His specializations are game theory and its applications to economics.

Harold Houba is associate professor at the Department of Econometrics of the VU University. He obtained his Ph.D. from Tilburg University in 1994. Houba is affiffliated with the VU since 1992. His specialization is bargaining theory and economic theory.

Evgenia Motchenkova is assistant professor at the Department of Economics of the VU University. She obtained her Ph.D. from Tilburg University in 2005. Motchenkova is affiffliated with the VU since 2005.

Her specialization is the economics of antitrust regulation.

the market power of suppliers, see e.g. Scherer and Ross (1990) for a review of this literature that was initiated

by Lustgarten (1975). Also, Schumacher (1991) supports the countervailing power hypothesis in a study based on US manufacturing industries. All studies emphasize that threats to switch orders from one supplier to another strengthen a buyers bargaining position.1 In Funaki et al. (2012), which precedes this note, we quantify the countervailing power hypothesis and use it to analyze market power and efficiency in bilateral oligopoly markets.

1. Another threat by which buyers can strengthen their bargaining position is to start upstream production themselves. In our study we only look at the threat of switching orders.

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The purpose of this note is to provide a number of applications of the theory developed in Funaki et al.

(2012) for the analysis of the EU gas production and distribution industry. In Funaki et al. (2012), we introduce a framework of bilateral oligopolies and explain the main ideas of competition in relation-specific prices and fees on a non-expandable infrastructure. The equilibrium concept is a stability concept that is similar in nature to the Core, but formulated directly in terms of the bilateral oligopoly market. We then perform a general analysis of market power in bilateral oligopoly markets. In short, that study offers three major insights: a theory of market competition and market power in concentrated markets with a non-expandable infrastructure; identification of the non-expandable infrastructure with maximal buyer protection; and emergence of competition in prices and fees instead of oligopolistic competition in prices only.

In our application of this general model, we analyze several examples that the current structure of the European gas production and distribution industry and derive important policy implications, which may help improving the EU bargaining power and reduce the market power of existing gas suppliers. Our analysis implies that the best advise for the EU as a consumer of natural gas, would be to expand its existing infrastructure by building more links to potential producers of oil and gas, such as Norway (UK, Qatar, or Nigeria). This will reduce the market power of existing suppliers, such as Russia, Iran, and Algeria, and increase consumer benefits for the EU. On the other hand, from producersâ&#x20AC;&#x2122; point of view it is best to keep a very restricted network structure.

This would help to enhance both producer surplus and market power.

Another application of this type of analysis could be the postal services market, where contracts between several big delivery firms, like TNT, as service providers and several big consumers of these services, like banks and insurance companies, can be seen as a network of link formation (in terms of signing the contract). In such a market, forming a link by signing a contract is not that costly, but the costs of transportation specified in the contracts should be taken into account. There recently implemented liberalization of postal services in some European countries, e.g. the Netherlands, seems to be a good development based on the conclusions of our model.

Entry of new rivals (service providers) and the potential of establishing new links (contracts) for customers, even if these links are unused, will limit the market power of the strongest provider.

This note is organized as follows. Section 2 provides two examples that illustrate main theoretical results of Funaki et al. (2012). Examples of bilateral oligopoly market on a non-expandable infrastructure with two gas suppliers and two buyers are analyzed in Section 3.

Some concluding remarks and discussion of possible extensions are left for Section 4.

Motivating examples In this section, we discuss competition in both prices and fees in order to stress that it is a natural extension of the standard oligopolistic competition in prices only.

To set ideas, we first consider the smallest market possible on a non-expandable infrastructure, namely the market that consists of a single supplier that is linked to a single buyer, referred to as supplier 1 and buyer 1 (see the left-hand side of Figure 1). Quantity q11 will be traded against price p11 and fee f11. Additionally, we suppose that the constant marginal costs of production

Figure 1: Supplier 1 is the single supplier in Case I, and one of two suppliers in Case II. and transportation are c11 = 1, and buyer 1 has the quasilinear utility function 10â&#x2C6;&#x161;(q11 ) - p11q11 - f11. The maximal joint welfare in this market, which consists of the sum of the producer and consumer surplus, is twenty-five and it can be reached by setting the price p11 equal to marginal costs and trading q11 equal to twenty-five units. Such price implies that the producer surplus equals the fee f11, and the consumer surplus is 25- f11. The fee therefore determines how the joint maximal welfare is divided within each pair.

Given that both the supplier and the buyer can act strategically in this market, negotiations will result in marginal-cost pricing p11 = 1 and a fee f11 [0;25]. In case of a monopoly, the theory in Oi (1971) p r e d i c t s that the supplier will extract the entire consumer surplus by setting the price p11 = 1 and fee f11 = 25. Hence, the monopoly outcome is Pareto efficient, but also very unfavorable for the consumer. This result differs from the standard monopoly where a price above marginal costs is set to extract consumer surplus and fees are absent.

Standard monopoly pricing is Pareto inefficient, but at least the consumer surplus is positive. The monopoly outcome in Oi (1971) can also be seen as the equilibrium outcome of a price-fee-setting game in which the supplier sets a price and fee before the buyer decides how much to buy. By reversing roles in a monopsony, the buyer will set the price p11 = 1 and fee f11 = 0 and it can be supported as the equilibrium outcome of a price-fee-setting game.

To further illustrate our ideas, we expand the previous situation by introducing a second supplier who is less efficient, called supplier 2, who has constant marginal costs of production and transportation c21 = 2. Supplier

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2s price and fee are p21 and f21. The maximal joint welfare supplier 2 and buyer 1 can attain when linked, which again consists of the sum of the producer and consumer surplus, is twelve-and-a-half. It can be reached by setting the price p21 equal to supplier 2s marginal costs and trading q21 equal to six-and-a-quarter units. Such price implies that supplier 2s producer surplus equals his fee f21, and the consumer surplus is 12.5- f21. Again, the fee redistributes the joint maximal welfare. For a non-expandable infrastructure, Figure 1 illustrates two possible cases. In case the non-expandable infrastructure only links supplier 1 and buyer 1, i.e. Case I, the results for the monopoly case still apply.

We therefore consider the case with both suppliers connected to the buyer, which is Case II of Figure 1.

Given that both suppliers and the buyer can act strategically in this market, supplier 1 must take into account the presence of supplier 2 in negotiations on prices and fees.2 Since supplier 2 and buyer 1 can reach a joint welfare of twelve-and-a-half together, supplier 1 cannot extract more welfare from buyer 1 than twentyfive minus twelve-and-a-half, which is also twelve-anda-half. So, negotiations will result in supplier 1s price p11 = c11 and fee f11 [0;12.5], and supplier 2s price p21 = c21 and fee f21 = 0. The theory in Oi (1971) can be easily extended to competition in prices and fees in this duopoly, if one considers the following price-fee-setting game: Simultaneously and independently suppliers set their price and fee combination, and then the buyer decides how much to demand from each supplier. Then, the unique equilibrium outcome supports the above prices and fees with f11 = 12.5, and the buyer purchases twentyfive units from supplier 1 and nothing from supplier 2.3 Hence, this equilibrium outcome is Pareto efficient and more favorable for the buyer than the modified price-feesetting game in the monopoly situation. This result differs from the standard duopoly where supplier 1 sets his price equal to supplier 2’s marginal costs to extract consumer surplus and fees are absent.4 This standard duopoly outcome is Pareto inefficient, supplier 1s producer surplus is six-and-a-quarter, and for this specific numerical example the buyer is equally well off as under competition in prices and fees. Obviously, supplier 1 strictly prefers to set a price and fee instead of only a price without a fee. By doing so, supplier 1 extracts both the consumer surplus and the deadweight loss associated with standard duopoly pricing. So, the price-fee-setting game on a non-expandable infrastructure also explains the phenomenon of setting two-part tariffs in practice. As such, it deserves a more prominent place in standard Microeconomic textbooks. By reversing the roles in a monopsony, the buyer will set p11 = p21 = c11 and f11 = f21

= 0, and supplier 1 will exclusively trade twenty-five units with buyer 1. Note that adding a third supplier, called supplier 3, with marginal costs above 2 will not change the above market outcomes. From here on, we consider three suppliers in our example.

The example makes one point clear: From buyer 1s perspective, the presence of the link between supplier 2 is a safeguard against supplier 1s market power, yet this link will never be utilized for trade. The link with the third-efficient supplier 3 is not needed. This is a fundamental tension between the minimal infrastructure that maximizes social welfare from trade and the minimal infrastructure that minimizes the supply sides market power. In Funaki et al. (2012), we developed a theory that characterizes both such minimal infrastructures and we have shown that the former is included in the latter. The results of the examples and applications presented in the next section are checked for robustness and generalized in the theoretical model developed in Funaki et al. (2012). In addition to analysis of the gas market, they can be applicable to other types of bilateral oligopoly markets as well.

Bilateral

oligopoly

on

non-expendable

infrastructures In this section, we analyze oligopolistic competition in prices and fees on a non-expandable infrastructure with the help of two examples. For more detailed theoretical analysis of the equilibrium concept with deviating (or blocking) coalition in the context of a perfectly divisible

Figure 2: The single supplier infrastructure in Case III is gE, Case IV and V represent duopoly markets, and the complete infrastructure of Case V I coincides with gM.

2. By negotiations, we envision some unmodeled negotiation process that will result in a Core solution. In this case, the two producer surpluses and the consumer surplus sum to twenty- ve and the sum of supplier 2’s producer surplus and buyer 1’s consumer surplus is at least twelve-and-a-half.

3. Since the buyer decides where to buy, existence of an equilibrium follows from Simon and Zame (1990).

4. This equilibrium exists for reasons similar as in the previous footnote.

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good and money on an infrastructure see Funaki et al.

(2012). There we also characterized the set of stable market outcomes and showed that this set has a lattice structure. Further, we analyzed strategic negotiation models that yield each sides most preferred stable market outcome as the unique equilibrium outcome. In essence, Funaki et al. (2012) extends well-known properties of two-sided markets with matching, as surveyed in e.g.

Roth and Sotomayor (1990), to oligopolistic markets with a divisible good and money on an initial non-expandable infrastructure.

Next, we discuss two important examples relevant for analysis of the EU gas market. The first extends the motivating example of Section 2 by having a second buyer.

In this example, both buyers have the same most-efficient supplier. This could be motivated by the situation where there is only one most efficient supplier of gas for any of the EU countries (e.g. Russia) as costs of supplying from Asia or Norway are much higher. In the second example, we consider two geographically differentiated markets, each with a domestic supplier, so that each buyer has a different most-efficient supplier. This model is also a modified version of the spatial competition model in Hotelling (1929). This could be more suitable setting if we would view Russia to be most efficient supplier for e.g. the Northern European Countries and Algeria would be considered to be most efficient (cheaper) supplier for the Southern Europe.

Example 1 Consider a market with two suppliers, supplier 1 being efficient (e.g. Russia) and supplier 2 inefficient (e.g.

Norway or Algeria), and two heterogeneous European buyers, buyer 1 having a higher marginal willingness to

pay than buyer 2. Supplier 1’s constant joint marginal costs of production and transportation are c11 = c12 = 1, and those for supplier 2 are c21 = c22 = 2. Buyer 1 has the quasi-linear utility function 10√(q11 + q21) - p11q11 - f11 - p21q21 - f21, and buyer 2 has 8√(pq12 + q22) - p12q12 - f12 p22 - q22- f22. Then, maximal joint welfare on each link is given by wg (11) = 25, wg (21) = 12.5, wg (12) = 16 and wg (22) = 8. In infrastructure III of Figure 2 both buyers are only connected to their most-efficient suppliers on the complete infrastructure, which is supplier 1. Then, 0 ≤ f11 ≤ wg (11) = 25 and 0 ≤ f12 ≤ wg (12) = 16, and the maximal fees correspond to monopoly market power. In contrast, in infrastructure V I of Figure 2 both buyers are connected to their most-efficient supplier, i.e. 1, and second-mostefficient supplier, i.e. 2, on the complete infrastructure.

Then, under V I the range of fees is smaller 0 ≤ f11 ≤ wg (11) - wg (21) = 12.5 and 0 ≤ f12 ≤ wg (12)- wg (22) = 8, and the maximal fees are limited due to increased competition.

For a graphical illustration of fees and consumer surpluses in relation to non-expandable infrastructures, we can consider all possible infrastructures with two suppliers and two buyers that contain infrastructure III. The most relevant infrastructures are given in Figure 2, the infrastructures of Case III and of Case V I, and both intermediate infrastructures. The graphical representation of the set of stable market outcomes for these nonexpandable infrastructures is given in Figure 3. The largest diamond-shaped area represents the set of stable market outcomes in case of the single supplier infrastructure of case III. The effect of having access to second-efficient suppliers, i.e. infrastructure III augmented with one of the links 21 or 22 or both, are illustrated by the two lines that run through the largest diamond-shape area. The link 21 is associated with the line whose sum is 12.5, and the link 22 with 8. In case both these links are present, we are in infrastructure of Case V I and the smallest diamondshaped area corresponds to the smallest set of stable market outcomes on infrastructures that contain III. Although the links with supplier 2 (Norway or Algeria) will not be utilized, their presence reduces the maximal fee f11 charged to buyer 1 from 25 to 12.5 and the maximal fee f12 charged to buyer 2 from 16 to 8.

Example 2

Figure 3: Different areas represent several sets of stable market outcomes of Example 1, where buyer is consumer surplus is denoted CSi, i = 1,2. The line f21 + CS1 = 12:5 illustrates the effect of the link 21, and f22 + CS2 = 8 the link 22.

As a second example, we consider two geographically differentiated markets, such as Russia supplying to Northern European Regions and Algerian gas being cheaper to ship to Southern European Regions. Supplier 1 (Russia) and buyer 1 (Northern Europe) are situated close to each other, i.e. belong to the same geographical market, while supplier 2 (Algeria) and buyer 2 (Southern Europe) are located in the second market, which is distant from the market 1. For each supplier, the marginal cost of production and transportation for the home market is 1 and for the distant market equal to 2, i.e. c11 = c22 = 1 and

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c21 = c12 = 2. Buyers’ utility functions are the same as in Example 1. In this setting we have wg (11) = 25, wg (21) = 12.5, wg (12) = 8 and wg (22) = 16. In infrastructure V II of Figure 4 both buyers are only connected to their most-efficient suppliers on the complete infrastructure, which is supplier i = j for buyer j = 1,2. In contrast, for infrastructure V I of Figure 4 both buyers are connected to their most-efficient supplier, i.e. i = j, and second-mostefficient supplier, i.e. i ≠ j, on the complete infrastructure.

We might reinterpret this market as a discrete version of the spatial competition model in Hotelling (1929) with two buyers (where buyer 1 lives in the proximity of supplier 1 and buyer 2 lives in the proximity of supplier 2) and the differences in marginal costs, i.e., c21 - c11 and c12 - c22, represent buyers travel costs to visit the supplier outside their proximity.

Each supplier has a home market and may compete on his competitors home market as well. Now, each buyers most-efficient and second-efficient suppliers switch when compared to Example 1. As a consequence, both suppliers are active only in their regional markets and relation-specific marginal-cost pricing with fees prevails.

In particular, in infrastructure V II of Figure 4 both buyers are connected only to their most-efficient suppliers, which are the suppliers on the home market.

Figure 4: For two geographically differentiated markets, the single supplier infrastructure in Case V II is gE, and the complete infrastructure of Case V I coincides with gM. In that case, maximal fees are the highest on all infrastructures containing V II and the ranges of fees are given by 0 ≤ f11 ≤ wg (11) = 25 and 0 ≤ f22 ≤ wg (22) = 16.

On the contrary, in infrastructure V I, where both buyers are connected to their most-efficient and second-efficient supplier, maximal fees are limited to 0 ≤ f11 ≤ wg (11) - wg (21) = 12.5 and 0 ≤ f22 ≤ wg (22) - wg (12) = 8. Again, buyer j’s best protection against excessive fees set by his home (most-efficient) supplier i = j is to have also access to his second-efficient supplier i =6 i, who is situated in a different geographical market. The conclusion of our model is similar to Hotelling (1929), where an increase in travel costs allows local suppliers to charge higher prices and, hence, extract a higher fraction of consumer surplus from local buyers. A similar conclusion holds in our modified price-fee-setting game: a larger difference in marginal costs would imply lower maximal joint welfare wg (12) and wg (21) and, hence, a smaller reduction in

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fees. Finally, not all the links of infrastructure V I are utilized for trade, i.e. links 12 and 21 are not utilized, but their presence prevents suppliers from abuse of market power through setting excessive fees.

Concluding Remarks In this note, we illustrate the implications of the pricefee competition in bilateral oligopoly model introduced in Funaki et al. (2012). More broadly, the results of that study quantify the countervailing power hypothesis that is first articulated in Galbraith (1952): Buyers have countervailing power that can restrain the market power of suppliers. In our study, buyers have a stronger bargaining position if the threat to switch orders from one supplier to another yields a larger maximal-attainable consumer surplus. We quantify this insight for any nonexpandable infrastructure and, generally speaking, the supply sides market power is decreasing in the number of arbitrary links a buyer has. This implies the testable implication that relation-specific fees decrease in the number of such links. We also characterize the minimal infrastructure that protects buyers the most and identify for each buyer two links that are crucial in protecting him from the supply sides market power. Then, the other links become superfluous.

Future research should relax several assumptions made in Funaki et al. (2012). First of all, every supplier can produce any quantity demanded by the buyers that are linked to him and each link can accommodate such demand. We regard a thorough understanding of nonexpandable infrastructures as a first and necessary step towards an analysis of market power on expandable infrastructures under costly investment. Such analysis will be provided in a companion paper Funaki et al.

(2013). Expandable infrastructures are more appropriate in the setting with less costly investment such as contractual relationships, software development for heterogeneous clients, or relation-specific investments in intermediate goods markets to meet heterogeneous buyers’ specifications, as discussed in e.g. Bjornerstedt and Stenneck (2007). Nevertheless, the results for nonexpandable infrastructures are relevant to analyze spotmarkets on infrastructures that cannot be expanded in the short run, such as infrastructure for natural gas and oil, and relation-specific capital investments.

References Amir, R. and F. Bloch (2009). Comparative statics in a simple class of strategic market games. Games and Economic Behavior 65, 7-24.

Bjornerstedt, J. and J. Stenneck (2007). Bilateral oligopoly - the efficiency of intermediate goods markets.

International Journal of Industrial Organization 25, 884-907.

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Bloch, F. and H. Ferrer (2001). Trade Fragmentation and Coordination in Strategic Market Games. Journal of Economic Theory 101, 301-316.

Simon, L. and W. Zame (1990). Discontinuous games and endogenous sharing rules. Econometrica 58, 861872.

A. J. Zaslavski, “Structure of extremals for onedimensional variational problems arising in continuum mechanics“, Journal of mathematical Analysis and Applications 198 (1996), 893-921

Tirole, J. (1988). The theory of industrial organization.

London: MIT Press.

A. J. Zaslavski, “Turnpike properties in the calculus of variations and optimal control”, Springer, New York, 2006 Bloch, F. and S. Ghosal (1997). Stable Trading Structures in Bilateral Oligopolies. Journal of Economic Theory 74, 368-384.

Funaki, Y., H. Houba, and E. Motchenkova (2012).

Market Power in Bilateral Oligopoly Markets with Non-expandable Infrastructures. Tinbergen Institute Discussion Papers 12-139/II, Tinbergen Institute.

Funaki, Y., H. Houba, and E. Motchenkova (2013).

Market power in Bilateral Oligopoly markets with Expandable Infrastructures. Working Paper, VU University Amsterdam, mimeo.

Galbraith, J. (1952). American Capitalism: The concept of countervailing power. New Brunswick, NJ, and London: Classics in Economics Series.

Hotelling, H. (1929). Stability in competition. Economic Journal 39, 41-57.

Lustgarten, S. (1975). The impact of buyer concentration in manufacturing industries. Review of Economic Statistics 57, 125-132.

Motta, M. (2004). Competition Policy: Theory and Practice. Cambridge: Cambridge University Press.

Oi, W. (1971). A Disneyland dilemma: two-part tariffs for a Mickey Mouse monopoly. Quarterly Journal of Economics 85, 77-96.

Roth, A. and M. Sotomayor (1990). Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis.

Cambridge: Cambridge University Press.

Scherer, F. and D. Ross (1990). Industrial market structure and economic performance (3rd edition).

Boston: Houghton Mifflin.

Schumacher, U. (1991). Buyer structure and seller performance in U.S. manufacturing industries. Review of Economic Statistics 73, 277-284.

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Aenorm Survey Readers of Aenorm 77 had the opportunity to submit our survey on the future of the Aenorm. We are happy that so many people took time to complete the survey to help us improve the Aenorm. Currently we are analysing the results and we aim to publish Aenorm 80 (September 2013) in a new format. There will be more attention for VSAE related activities, columns and publications from students. We will provide you with more information on the changes of the Aenorm in the next edition.

For now, we want to thank everybody who completed the survey. The winners of the €50 giftcheque are • Joris Bücker • Joran Houtman They will be contacted soon to receive their price.

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The inventory routing problem A two-phase approach by: Jacob Kooijman The aim of this thesis is to develop a heuristical approach for the inventory routing problem. We will propose a two-phase approach to solve the problem. A novelty of the approach is the use of volume delivery optimization while optimizing the route schedule by means of column generation.

Jacob Kooijman Jacob C. Kooijman finished his master in June 2012 at the Vrije Universiteit Amsterdam with his thesis: â&#x20AC;&#x153;The inventory routing problem, a two-phase approach.â&#x20AC;? He wrote his thesis under the supervision of prof. dr. J.A. dos Santos Gromicho. He is specialized in Operations Research and Business Econometrics, which is also his main area of interest. After his study he started working at ORTEC as a junior software engineer.

Introduction The inventory routing problem arises when a retailer is responsible for the inventory management of his customers and needs to deliver to his customers on time to ensure that they do not run out of stock. An example is an oil company that has multiple gas stations and needs to ensure that each of the gas stations has enough gasoline to serve its customers. A geographical display of a problem instance is shown in Figure 1. We will solve the problem over a planning horizon T. Each customer is assumed to have a usage rate ui , which is the amount of product the customer consumes per time unit. The usage of a customer is thus assumed to be deterministic and constant over time. Secondly, a customer has a starting inventory Ii at the beginning of the planning period and a storage capacity Ci. Customers might have restrictions on visitations times and thus we use time windows to ensure that a delivery takes place within a time window [ai, bi].

The deliverable amount of a customer is the maximum amount that can be delivered at a certain moment in time.

An example of the deliverable amount of a customer in its delivery window is shown in figure 1. To deliver the

customers we have a fleet of M homogeneous vehicles available. The objective is to minimize both short-term and long-term transportation and inventory costs. To apply our solution method we will use the following assumptions: 1. Customer usage rates are constant and deterministic.

2. Only one type of product to deliver.

3. A depot with an infinite amount of the product available.

4. There are no inventory holding cost.

Figure 1: an inventory routing problem instance

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We make these assumptions to limit the problem’s complexity. Some of these assumptions might seem unrealistic, but our approach will take the weaknesses of these assumptions into account. The usage rates in practice are stochastic, but if we would model the usage rates as a stochastic process the model will become even more complex and thereby harder to solve. Instead we will deliver customers earlier than the latest possible time to prevent incorrect forecasts leading to stock outs for the customers. In the next paragraph we will introduce our solution approach.

limited capacity for each vehicle. Some combinations of customers in one route might exceed the available truck capacity and thus result in an infeasible solution. A less obvious relation exists between the decisions what routes to use and when to deliver to a customer. If a customer is visited as the first customer in a route he consumed a small amount of inventory from the start of the day, but if a customer is visited at the end of the route he consumed more of his inventory. This difference can affect the decision when to deliver next. Note that in Figure 2 there is a back arrow from the scheduling phase to the planning phase, because the selection of routes affects the future decisions in the planning phase.

Solution approach The resulting problem is in the class of NP-hard problems and solving it to optimality for even small problems, is a computationally hard task. To solve practical problems we decide to divide the problem into three phases: demand prediction, planning and scheduling. The division in phases is shown in Figure 2. In the first phase the demand is predicted based on historical usage data. In the planning phase, visits to customers are planned, which are called orders. In the scheduling phase the orders are combined into routes to minimize the transportation cost.

Even the scheduling phase is considered to be among the hardest optimization problems. In this thesis we do not consider the prediction of usage rates, but we will focus on the two last phases and assume that the usage rates are given.

Figure 2: the inventory routing problem divided into three phases

A solution of the inventory routing problem (IRP) consists of the following decisions: • • •

When to deliver to a customer?

How much to deliver to a customer?

Which delivery routes to use?

Each of these decisions affects the other decisions. An earlier delivery to a customer results in a smaller maximum delivery to a customer. This is due to the fact that a customer uses less of his inventory when delivering earlier and has a limited storage capacity. Hence, the moment of delivery affects the decision how much to deliver. If the decision how much to deliver is made for each customer this can affect possible routes that can be used due to a

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Solution quality Before we mention our complete algorithm we should have a good measure for solution quality. In routing literature it is common to use the amount of driven kilometers by the vehicles as a cost measure. To reflect shortterm cost this measure is realistic, but for the long-term cost in our problem we should also consider the volume delivered. If we deliver small amounts of volume each time we visit a customer, many visits will be needed to keep the customer from running out of stuck. If we deliver the maximum amount possible to a customer each time we visit the customer less visits are needed, hence decreasing transportation cost in the long-term. To balance between the amount of driven kilometers and the amount of volume delivered we will use the amount of driven kilometers divided by the amount of volume delivered as a measure for solution quality, which is recommended by Song and Savelsbergh (2007). Another important variable is the amount of vehicles required to execute the planning. A solution with a high volume per kilometer value that requires many vehicles might not be the best. In practice the size of the vehicle fleet is generally given, but it might be interesting to analyze the effect of the size of the fleet on the solution quality.

Planning phase The purpose of the planning phase is to plan orders for each customer in such a way that a customer will not run out of stock, while trying to maximize the solution quality. In the planning phase we should use the volume per kilometer measure as a guideline for our design, but another important part is the amount of vehicles required. We will try to minimize the amount of vehicles required, while trying to keep good values for the volume per kilometer

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measure. A very strong assumption is the assumption that we have deterministic usage rates. Delivering at the moment just before a stock-out occurs would maximize the amount of volume that can be delivered in one visit.

If a usage prediction turns out to be incorrect this could lead to high cost, because an emergency visit might need to be scheduled to prevent the stock-out, increasing cost significantly. We introduce the safety stock, which is the amount of stock a customer should always have as inventory to ensure that incorrect demand forecasts will generally not lead to stock-outs. The time window of each generated customer order is adjusted for this to guarantee we deliver before reaching the safety stock.

In the solutions for the planning phase we focused on delivering as late as possible to maximize the delivery volume. If we plan every customer just before he reaches his safety stock we might obtain orders for customers that are very far apart, increasing the amount of driven kilometers. We try to combine customers in routes that have a small geographical distance to one another. The planning is made for a certain period, for example two weeks. Due to the complexity of the scheduling phase we will only solve one day at a time in the scheduling phase.

We create a planning for two weeks, then find routes for the orders on the first day. Afterwards we move on to the next day and make a planning again. We recalculate the planning, because as mentioned earlier routing decisions affect the latest possible delivery time for the next delivery. We could decide to just leave the planning as it was, but the computational effort required to recalculate the planning is small with the current implementation of our algorithms.

Scheduling phase In the scheduling phase we need to find routes which execute all the generated orders in the planning phase.

All these orders are called must-go orders and should be executed within their time window. Besides these orders we also introduce may-go orders, which are orders for customers who do not require a visit in the planning period, because they reach their safety stock outside the planning period. We will use may-go customers to fill up the vehicle capacity in a route, but only if it is beneficial. If adding such a customer to a route improves the volume per kilometer measure it is considered beneficial to add the customer. The routes are constructed using a column generation approach, which is commonly used for routing problems. The idea of column generation is that many possible routes exist, but only a few will be part of the optimal solution. If we would consider every route we will have an immense amount of variables and the problem becomes nearly impossible to solve. Instead we start with a limited amount of routes that result in a feasible solution and try to find routes that can improve the solution. By using theory from linear programming

we can quite rapidly find routes that improve the solution. One novelty of our approach is the fact that we use delivery volume optimization before we check which routes can improve the solution. Delivery volume optimization postpones routes to a later time to improve the deliverable volume. If a customer is visited later he consumed more of his inventory, hence a larger amount of the product can be delivered. Delivery volume optimization is generally applied after selecting the routes, but that does not have to lead to an optimal combination of routes. The effect of delivery volume optimization for some routes might not allow postponing the route to a later moment in time. Postponing a route later in time might also not be beneficial, because the maximum deliverable quantity could have already been reached due to capacity constraints of the vehicle.

Results To evaluate our algorithms we used a dataset provided by the Georgia Tech University. In our research we found out that the research community did not supply any results on the instances, but there were also no results from other instances to compare with using the volume per kilometer measure. Instead we decided to compare different solutions for our own algorithms.

In the scheduling phase we select a set of routes based on an objective function, which is the sum of the cost of the selected routes. In principle any cost function can be used to determine the cost of a route. We investigated two types of cost functions. A weighted cost function that weighs the amount of driven kilometers and the unused volume in the vehicle. The second cost function is the amount of kilometers driven in a route divided by the amount of volume delivered. We try to maximize the volume per kilometer, so we should minimize the opposite. Note that the cost functions are applied per route and not over all selected routes together. We cannot calculate the volume per kilometer over all routes, because the column generation formulation requires a linear objective function. In figure 3 we compared both cost functions for a planning period of 30 days.

Figure 3: comparison between weighted cost function and km/volume cost function with the volume per km on the y-axes and the weight for the amount of unused capacity on the x-axes.

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The km per volume cost function has constant and quite good behavior, but for certain values of the weights the weighted cost function outperforms the km per volume cost function. One interesting comparison is to compare our cost functions with a cost function based on the amount of kilometers driven, which is normally used in routing literature. If the weight of the weighted cost function is zero it only considers the amount of kilometers.

From Figure 3 it follows that the km per volume cost function slightly outperforms the standard cost function for routing problems in our case and a better optimized weight can even improve this further. For other research results we would like to refer the reader to the thesis.

Conclusion We developed a two-phase approach for the inventory routing problem. A very important aspect is the collaboration between the planning and scheduling phase. We focused on maximizing the total amount of volume delivered divided by the total amount of driven kilometers.

As mentioned, delivering every customer at the latest possible time maximizes the delivered volume. When creating routes for these customers the geographical distance between them might be very large, hence increasing the total amount of kilometers driven. It is thus very important to already consider the effects of decisions made in the planning phase, before solving the scheduling phase.

References Campbell, A., L. Clarke, A. Kleywegt and M. Savelsbergh. The inventory routing problem , Fleet Management and Logistics. Kluwer Academic Publishers (1998): 95-113.

Campbell, A. and M. Savelsbergh. “Delivery volume optimization.”, Transportation Science 38.2 (2004): 210-223.

Feillet, D. “A tutorial on column generation and branchand-price for vehicle routing Problems.”, 4OR: A Quarterly Journal of Operations Research 8 (2010): 407-424.

Song, J. and M. Savelsbergh. “Performance measurement for inventory routing.”, Transportation Science 41.1 (2007): 44-54.

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Rust in de financiële markt, dat is keihard werken.

Begin je carrière bij DNB. Ontdek de mogelijkheden op werkenbijdnb.nl

Bij DNB werk je in het zenuwcentrum van onze economie.

Iedere beslissing die we nemen, wordt kritisch besproken door de hele financiële wereld. Een dynamische wereld die we tot rust moeten brengen. Dat vraagt om aanpakken en volhouden. Want iedere dag krijg je te maken met een ander complex vraagstuk en moet je de actualiteit zien voor te blijven. Daarmee lever je een belangrijke bijdrage aan financiële stabiliteit en vertrouwen.

Kun jij die druk aan en zie je het als een uitdaging om onze economie vooruit te helpen? Denk dan eens aan een carrière bij DNB. Kijk voor meer informatie en de mogelijkheden op werkenbijdnb.nl.

Werken aan vertrouwen.

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The Impact of Expectation Feedback Systems on the Reaction of Market Price to Large Unanticipated Shocks by: Te Bao Expectation formation plays a central role in modern economic modeling. Bao et al (2012) study how the expectation feedback system influences the behavior of individual expectations and market price after the fundamental price experiences large unexpected shocks. We find markets with negative expectation feedback quickly converge to the new fundamental, while markets with positive expectation feedback do not converge, but show underreaction in the short run and overreaction in the long run. A heterogeneous agent model explains these differences in aggregate outcomes.

Introduction It is never easy to make “precise” prediction on economic dynamics, because the prediction of the market participants (e.g. investors, producers, traders etc.) determines their individual decisions (e.g. on investment, production, trading quantity etc.), and therefore the market price that they are predicting. People learn from the past market prices and make predictions which, in turn determines the current market behavior and so on. Such process can be characterized by an expectation feedback system. Figure 1 is an illustration of the mechanism of an expectation feedback system.

There are two kinds of expectation feedback systems: positive expectation feedback (and henceforth “positive Figure 1: an illustration of the mechanism of an expectation feedback system

feedback” and negative expectation feedback (and henceforth “negative feedback”). In a positive feedback system the real price is high when the people in the market predict it to be high, usually seen in speculative asset markets. In a negative feedback system the real price is low when the people in the market predict it to be high, usually seen in commodity market with a production delay.

Former study by Heemeijer et al (2009) show that the type of expectation feedback system has a major impact on determining whether a market can learn the rational expectation equilibrium (REE), or the fundamental price. They design a learning to forecast experiment where the subjects make a price forecast, and a computer program solves the optimization problem and make the optimal quantity decision which determines the market price. They find that all the negative feedback markets converge to the REE quickly, while the markets with positive feedbacks fail to converge, and generate a lot of oscillations. A natural question is then how the expectation feedback system influences the behavior of market price after large shocks, such as a financial crisis.

In the experiment by Bao et al (2012), we investigate this question using a new learning to forecast experiment.

Te Bao Te Bao obtained his PhD in Economics from the University of Amsterdam in October 2012. Now he is a postdoc researcher at CeNDEF, University of Amsterdam for the INET (the Institute for New Economic Thinking founded by George Soros) project “Heterogeneous Expectations and Financial Crisis”. His research interest includes experimental macroeconomics, experimental finance and real estate economics.

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Experimental settings There are two treatments, the positive feedback treatment and the negative feedback treatment. In both treatments the price is a function of the average expectations in an experimental market consisting of 6 participants. The two treatments are all the same except the sign before the average expectations in the function. The price determination function is:

in the positive feedback treatment, and

Figure 2: the price dynamics under the REE

in the negative feedback treatment, where at period t.

is the REE

The shifts in the REE represent the large unexpected shocks in period 21 and 44. If a market always stays at the REE, the price dynamics should be the same as the one in Figure 2.

We find big differences in the market prices in the two treatments, as shown in Figure 3. There are 8 markets in each treatment. We see that all markets with negative expectation feedbacks converge to the new REE quickly after each shock, and none of the markets in the positive feedback treatment makes quick convergence. It seems that the price underreacts to the shocks in the short run, and overreacts in the long run.

The Heuristic Switching Model The price dynamics in our experiment is obviously very different from the one defined by the REE. We also tried some homogeneous agent model assuming all agents in the same market use the same simple heuristic, such as naive expectation, adaptive expectation or a trend following rule. We find although some of this kind of models can explain the price behavior in one treatment well, none of them can provide a good description of the price dynamics in both treatments.

Figure 3: market prices in the markets with positive feedbacks (upper panel) and negative feedbacks (lower panel)

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Anufriev and Hommes (2012) provide a heuristic switching model (HSM), an extension of Brock and Hommes (1997). The key idea of the model is that the subjects chose between four simple heuristics depending upon their relative performance. The heuristic that is more accurate in the recent past attracts more followers.

We apply this model to our experiment. The four heuristics in our model are an adaptive expectations rule, a contrarian rule, a trend following rule and an anchoring and adjustment heuristic (A&A), as in Tversky and Kahneman (1974). The simulated market price and shares of users of different heuristics are shown in Figure 4. We can see the HSM provides a very good fit of the data.

Conclusion This paper studies how the expectation feedback system influences the behavior of individual expectations and market price after the fundamental price experiences large unexpected shocks. We find markets with negative expectation feedback quickly converge to the new fundamental, while markets with positive expectation feedback do not converge, but show underreaction in the short run and overreaction in the long run. Our findings under positive feedback are consistent with the empirical observation that stock prices underreact to news in the short run and overreact in the long run (see Barberis et al., 1998), and therefore suggest that the positive feedback feature of speculative asset market alone may be the main force causing this phenomenon. The results from the simulations suggest that rational expectation hypothesis and homogeneous agent models have difficulty in explaining data from learning to forecast experiments. Models with heterogeneous expectations and reinforcement learning, e.g. Brock and Hommes (1997, 1998), and Anufriev and Hommes (2012) fit these experiments quite well.

Figure 4: experimental and simulated prices using HSM in one typical group from the positive (top left, group P8) and negative feedback treatment (bottom left, group N8) respectively; squares are the experimental data, and circles are simulated prices from the HSM. The right panels show the evolution of market heuristics in the positive (top right) and negative feedback treatments (bottom right). The trend following rule dominates in the positive feedback markets, while the contrarian rule dominates in the negative feedback markets.

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References Anufriev, M., and Hommes, C. (2012). Evolutionary selection of individual expectations and aggregate outcomes in asset pricing experiments. American Economic Journal: Microeconomics 4, 35-64.

Bao, T., Hommes, C.H., Sonnemans, J.H., Tuinstra, J., 2012, Individual expectation, limited rationality and aggregate outcomes, Journal of Economic Dynamics and Control 36, 1101–1120.

Barberis,N., Shleifer,A., Vishny,R., 1998. A model of investor sentiment. Journal of Financial Economics 49, 307-343.

Brock, W.A.,Hommes, C.H.,1997. A rational route to randomness. Econometrica 65, 1059–1095.

Brock, W.A., Hommes, C.H.,1998.Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control 22, 1235–1274.

Heemeijer, P., Hommes,C.H.,Sonnemans,J.,Tuinstra,J.,2009.Price stability and volatility in markets with positive and negative expectations feedback: an experimental investigation. Journal of Economic Dynamics and Control 33, 1052– 1072.

Tversky, A., Kahneman,D.,1974. Judgment under uncertainty: heuristics and biases. Science 185, 1124–1130.

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Puzzle On this page youâ&#x20AC;&#x2122;ll find a few challenging puzzles.

Try to solve them and compete for a prize! Submit your solution to Aenorm@vsae.nl.

Answers to puzzles Aenorm 77

New puzzles

Geese counting There are five little geese that swim behind Mother Goose. This way, there are four geese in front, four at the back and three in the middle.

Divide some barrels The three thieves had to divide the amount of 15 completely filled barrels. This can be achieved with two thieves both getting 5 full barrels and 5 empty barrels, and the other thief getting 10 half filled barrels.

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A quadruple of consecutive integers The numbers (160,161,162) constitute a set of three consecutive integers that are divisible, respectively, by 5, 7, and 9. Determine a set of four consecutive positive integers that are divisible, respectively, by 5, 7, 9 and 11.

Puzzle Alternative Sudoku As the usual sudoku, in this figure you have to fill out the numbers 1 to 9 in every highlighted square. In every row and every column all the numbers have to be used.

In addition, some numbers have a circle around it, with an arrow attached. This means that the numbers on the arrow have to add up to the number in the circle attached.

Winner Aenorm 77 Thijs van den Ende

Solutions Solutions to the puzzles above can be submitted up to May 1st 2013. You can hand them in at the VSAE room (E2.02/04), mail them to aenorm@vsae.nl or send them to VSAE, for the attention of Aenorm puzzle 78, Roetersstraat 11, 1018 WB Amsterdam, Holland. Among the correct submissions, one will be the winner. Solutions can be both in English and Dutch.

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Members of the VSAE ended the year in style with the active members diner and the cocktail chic party. 2012 was a good year for our association and we celebrated the end of the year, the party was great! The previous board used the monthly drink in January to say goodbye to all the members.

The new board started their year by travelling to Utrecht for the National Econometricians Day (LED), it was an interesting and succesful day. The Actuarial Congress in February was an informative and inspiring day on the topic of solidarity. In March VSAE celebrated the 50th anniversary of the association with a week full of activitiets and events. It was a fantastic week and an awesome experience.

With spring coming up VSAE is ready to host another edition of the Econometric Game. Universities from all over the world will travel to Amsterdam to take part in our competition of econometrics. Although we can’t reveal the topic of the case yet, we can assure you that it will be interesting and challenging.

After the Econometic Game it’s time for our students to show their skills in risk managment during the Risk Intelligence Competition. After this event we travel to Paris to enjoy spring in France.

Agenda Econometric Game

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•

•

•

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Agenda

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With much pride I can announce that the Ball we had organized, together with three of our brother associations, at the Holland Casino has been marvelous, and also the LED has received great reviews from our members.

But that doesn’t mean there is nothing greats to look forward to!

First we’ll have the Special Monthly Drink to celebrate the end of our exam week at the 28th of March. And of course there is the yearly Games-marathon, which varies from a Poker Tournament to showing your singing skills with Sing Star. One of the main activities is the Study Trip to Istanbul where about 20 of our students accompanied by one of our teachers will visit the National Bank, attending a college at the university and much more.

With a little effort we were able to settle a day to have planned the yearly soccer competition against the VSAE, this time probably transformed to a futsal competition.

We look forward to beating them!

Aside from the Study Trip there is our Queens Day activity. Like last year, Kraket can then be found sailing on the canals of Amsterdam on a boat with loud music and lots to drink!

For now, this will be the last Aenorm Kraket lent a hand with, since we will be focusing more on our own external magazine, the SECTOR. We wish the VSAE and their Aenorm commission all the best!

9 - 11 April

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Monthly Drink / Special

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11 April

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Games Marathon

15 April

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7 & 8 May

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9 - 12 May

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Soccer tournament with Kraket Risk Intelligence Competition Short Trip to Paris

15 May

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Monthly Drink

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6 Days Study Trip to Istanbul

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Queens Day activity: boat trip on the canals of Amsterdam

6 May

Masterclass at DSF

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