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D e p a r t m e n t o f E c o n o m i c s E ssays on Resource E xploitation under Fixed Costs Eero Sillasto D O C T O R A L D I S S E R T A T I O N S

Aalto University publication series D OCTORAL DISSERTATIONS 127/ 2019 Essays on Resource Exploitation under Fixed Costs Eero Sillasto Aalto University School of Business Department of Economics

Supervising professor Professor Matti Liski, Aalto University, Finland Thesis advisors Professor Marko Terviö, Aalto University, Finland Associate Professor Pauli Murto, Aalto University, Finland Preliminary examiners Professor Katheline Schubert, University Paris 1 Panthéon-Sorbonne, France Professor Knut Einar Rosendahl, Norwegian University of Life Sciences, Norway Opponent D.Sc. (Tech.) Mitri Kitti, University of Turku, Finland Aalto University publication series D OCTORAL DISSERTATIONS 127/ 2019 2019 Eero Sillasto ISBN 978-952-60-8633-0 (printed) ISBN 978-952-60-8634-7 (pdf) ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) h ttp://urn.fi/urn:isbn: 978-952-60-8634-7 Unigrafia Oy H elsinki 2019 Finland NORDIC SWAN ECOLABEL Printed matter 4041-0619

A alto University, P.O. Box 11000, FI-00076 Aalto Abstract www.aalto.fi Author Eero Sillasto Name of the doctoral dissertation Essays on Resource Exploitation under P ublisher U nit Series F ield D ate School of Business Department of Economics Language Fixed Costs A alto University publication series D OCTORAL DISSERTATIONS 127/ 2019 of research Economics of the defence English Monograph 14 August 2019 A rticle dissertation Essay dissertation Abstract This dissertation consists of three essays on resource economics. In these essays I analyze the i mplementation of fixed costs for activities with a finite amount of production. I assume that the fi xed costs are a characteristic of an activity and the continuous costs must be incurred for not l osing the activity permanently. I show that, if the economic activity is finite in its duration, fixed c osts induce minimal scales and also discrete effects on market outcomes. I show further how such d iscrete effects influence, for instance, the exploitation paces, the exploitation order and the price path. T he first essay concentrates on the efficient solution of exploiting exhaustible deposits of a c ommodity under fixed costs. In contrast to the previous literature, the efficient solution is well d efined. I derive the characteristics of an efficient solution, and show that it cannot be decentralized a s a competitive allocation, because the price-taking agents would act strategically. The efficient o rder of exploiting the deposits, which is a classical resource economics question, depends both on the deposits' stock allocations and on their cost structures. The second essay describes strategic interactions for private deposit owners under fixed costs. I show that there are equilibria in open-loop strategies, in which deposits are exploited c oncurrently, and others, in which they are exploited sequentially. I show further that agents do not exit simultaneously and that there are no symmetric equilibria. T he third essay introduces the entry. I limit my attention to economic activity where the projects h ave each a fixed production time, and also a given and discrete impact on other projects executed c oncurrently with them. I describe an entry game where the entrants influence other entrants' entry decisions by pre-empting. I show that the entry order and the level of industry concentration are distorted when compared to the efficient solution. K eywords I SBN (printed) I SSN (printed) L ocation resource exploitation, finite production, fixed costs, game, open-loop strategy, entry 978-952-60-8633-0 1799-4934 of publisher H elsinki L ocation I SBN (pdf) I SSN (pdf) of printing 978-952-60-8634-7 1799-4942 H elsinki Y ear 2019 Pages 104 u rn h ttp://urn.fi/urn:isbn: 978-952-60-8634-7

A alto-yliopisto, PL 11000, 00076 Aalto Tiivistelmä www.aalto.fi Tekijä Eero Sillasto Väitöskirjan nimi Esseitä resurssien käytöstä J ulkaisija Y ksikkö Sarja Kauppakorkeakoulu Taloustieteen laitos A alto University publication series D OCTORAL DISSERTATIONS 127/ 2019 T utkimusala Taloustiede Väitöspäivä 14.08.2019 K ieli Englanti Monografia Artikkeliväitöskirja Esseeväitöskirja Tiivistelmä T ämä väitöskirja koostuu kolmesta esseestä, jotka kuuluvat resurssitaloustieteen tutkimusalaan. Tutkin niissä kuinka kiinteät kustannukset vaikuttavat tuotantoon, kun tuotannon kokonaismäärä o n äärellinen ja kun kiinteiden kustannusten jatkuva maksaminen on edellytys tulevalle t uotannolle. Kiinteiden kustannusten takia tuotannolla on minimiskaala, ja siksi tuotannon päättyessä hinta ja tuotannon taso muuttuvat diskreetisti. E nsimmäisessä esseessä keskityn tehokkaaseen ratkaisuun ja kuvaan sen ominaisuuksia. S osiaalisen suunnittelijan ongelma on hyvin määritelty toisin kuin aiemmassa kirjallisuudessa, jossa kiinteät kustannukset riippuvat tuotannosta. Osoitan myös, että kilpailullista allokaatiota ei o le olemassa, koska hinnan ottavat kilpailijat käyttäytyisivät strategisesti. Resurssin varantojen t ehohas hyödyntämisjärjestys riippuu sekä resurssien varantojakaumasta että niiden käytön kustannusrakenteesta. T oisessa esseessä tutkin äärellisiä varantoja, jotka ovat yksityisessä omistuksessa. Oletan, että r esurssien omistajat toimivat strategisesti ja pelaavat open-loop strategioita. Osoitan, että on o lemassa tasapainoja, joissa resurssin eri varantoja käytetään yhtäaikaa, ja toisaalta tasapainoja, j oissa varannot käytetään peräkkäin. Osoitan myös, että omistajat eivät tasapainossa lopeta tuotantoaan samanaikaisesti ja ettei symmetrisiä ratkaisuja ole olemassa. Kolmannessa esseessä tutkin tuotannon aloitusta. Rajoitun tuotantoprojekteihin, joissa tuotannon p ituus on etukäteen tiedossa, ja joiden vaikutukset muihin projekteihin on tunnetut. Kuvaan t uotannon aloituksen pelinä, jossa pelaajat vaikuttavat muiden pelaajien tuotannon aloitukseen o malla tuotannon aloituksellaan. Osoitan, että pelissä tuotannon aloitusjärjestys, aloituksen a jankohdat ja tuotannon taso voivat poiketa tehokkaasta. Kolmen projektin tapauksessa pisin p rojekti aloittaa tasapainossa tuotannon ensin, ja kaksi lyhyempää pisimmän projektin jälkeen kummassa tahansa järjestyksessä. Avainsanat r esurssin käyttö, äärellinen tuotanto, kiinteät kustannukset, peli, open-loop strategia, tuotannon aloitus I SBN (painettu) I SSN (painettu) J ulkaisupaikka 978-952-60-8633-0 1799-4934 H elsinki P ainopaikka I SBN (pdf) I SSN (pdf) H elsinki 978-952-60-8634-7 1799-4942 Vuosi 2019 Sivumäärä 104 u rn h ttp://urn.fi/urn:isbn: 978-952-60-8634-7

Acknowledgements First of all, I want to thank my supervisor Professor Matti Liski. His undisputed knowledge in the field of resource economics and the fact that he shared that knowledge with me was the solid ground that I could base my research on. It was his lectures and work in general that originally inspired me to pick resource economics as my field. Learnings from his persistent attitude to continuously improve the research was probably the greatest take away I got from these studies. I want also thank the other members of my supervision committee, Professor Marko Terviö and Associate Professor Pauli Murto, for their guidance. In addition, I am very grateful for the time and effort that my pre-examiners Professor Katheline Schubert and Professor Knut Einar Rosendahl put into reading and commenting on my dissertation. Finally, I am thankful to DSc Antti Iho for the support and the comments in the final steps. Thank you all for the knowledge and for the guidance. During the studies I had the privilege to share the office and thoughts with inspiring fellow students. I want to mention Annaliina, Laura, Krista, Timo and Sinikka. Time shared with you was, and still is, well spent and also well invested. Thank you all for the journey. I did not achieve this without support from my friends and relations. Some of you inspired me into this. Some of you kept me with it. And, some of you helped me forget it when it came to that. Thank you all for the smile. I am grateful for the financial support that I received from OP-Pohjola Group Research Foundation, Finish Foundation for Technology Promotion (Tekniikan Edistämissäätiö), Emil Aaltonen Foundation, Aalto University and HSE Support Foundation (Helsingin Kauppakorkeakoulun tukisäätiö). I am also thankful to Natural Resources Institute Finland (Luonnonvarakeskus) where I was able to finalize the dissertation. Thank you all for the opportunity. Dear Ilona and Hilda, on purpose have I kept you slightly away from this. The reason is that you serve for the greater good. I wrote a dissertation, but you are writing a different story that is more colorful and important. I am the most pleased of all that I have a role in it. Thank you for being there. Eero Sillasto Helsinki, June 2019

Contents List of Essays Introduction Bibliography i iii vii Essay 1. Exploiting Deposits with Fixed Costs 1 1. Introduction 2 2. Problem Description 5 3. Efficient Solution 8 4. Competitive Allocation 12 5. Extension: Effects of Stock Distribution On Efficient Solution 18 6. Concluding Remarks 20 Appendices 21 A. Efficient Solution 21 B. Competitive Allocation 24 C. Non-Existence of Decentralized Solutions. 25 Bibliography 29 Essay 2. Oligopolistic Resource Exploitation under Fixed Costs 31 1. Introduction 32 2. Problem 34 3. Nash Equilibrium in Open-Loop Strategies 36 4. Simultaneous Exploitation Solutions 41 5. Sequential Exploitation Solutions 45 6. Concluding Remarks 49 Appendices 50 A. Existence of Best Response. 50 B. Conditions for Nash Equilibrium. 52

CONTENTS C. Exploitation Shares 55 Bibliography 57 Essay 3. A Game of Entry and Exit Fixed Length Projects 59 1. Introduction 60 2. Social Planner 62 3. Entry Game 65 4. Concluding Remarks 73 Appendices 74 A. Efficient Solution 74 B. Theorem 76 Bibliography 85

List of Essays This thesis consists of an introduction and the following essays. (1) Exploiting Deposits with Fixed Costs Unpublished manuscript. (2) Oligopolistic Resource Exploitation under Fixed Costs Unpublished manuscript. (3) A Game of Entry and Exit Fixed Length Projects Unpublished manuscript. i

Introduction A fixed cost is a basic concept in economics. The story typically goes that assuming a given entry level, only the variable costs affect the economic activity level. The fixed costs, accordingly, affect only the revenue from this activity. This is valid when the activity is, for instance, reproducible. In my essays I analyze the implementation of fixed costs for activities with a finite amount of production. I assume that the fixed costs are a characteristic of an activity and the continuous payments of them are a requirement for not losing the activity permanently. As an example, consider an offshore rig operating an oil deposit in the seabed. The oil rig has high fixed costs, for instance, due to the rent of having the rig on the spot. To be profitable and to cover both the fixed and the variable costs, the deposit owner must hold a strictly positive exploitation pace. Oil deposits are, however, finite. Each of them one day exhausts and exits from production and such an exit with a positive exploitation scale creates a discrete price effect. Hence, if the economic activity is finite in its duration, fixed costs induce minimal scales and also discrete effects at the exits. In these essays I show how such discrete effects influence, for instance, the exploitation paces, the exploitation order and the price path. In the first two essays I concentrate on the problem of exploiting exhaustible deposits of a commodity under fixed costs. Problems with such temporal economical activities are simple to handle, because all deposits contain the same commodity and, consequently, there is a single price at all times. In the literature on resource exploitation the handling of fixed costs has shown cause problems which my approach avoids. The fixed cost structure typically applied was introduced by Smith (1961). He describes avoidable fixed costs that are altogether avoided over a time interval by choosing not to exploit the resource during that interval. Eswaran et al. (1983) show that such cost structures cause technical difficulties, as there are solutions in which the activity changes at a high frequency between phases of exploitation and no exploitation in order to reduce the average fixed costs level. However, such models are not properly specified according to the critique of Romer (1986), since they lack adjustment costs that would smooth iii

iv INTRODUCTION out the frequent discontinuities in activity. Recently, Bommier et al. (2017) motivate their analysis by a cost structure similar to what I use here, but, in the end, it is not used in their analysis. In my essays the continuation of paying the fixed costs is a requirement for the continuation of the exploitation. This removes the frequent discontinuations in the exploitation activity of which the previous studies suffered. Moreover, in the limit where the firms are atomistic, the existence of the equilibrium is restored while the fixed costs continue to have an impact on the equilibrium path. Outside the limit, I show that with such fixed cost structures the competition is strategic. The strategic interaction literature misses issues the fixed costs introduce. For instance, Lewis and Schmalensee (1980) and Loury (1986) describe exploiting deposits of a resource that have pure linear costs. I extend their work by including also the fixed costs. Finally, throughout the discussions in these essays, there is an analogy to the occupational choice, which Makowski and Ostroy (1995) describe. The choice to continue paying the fixed costs can be seen as an occupation, and stopping these payments is like retiring from that. Hence, if the choices affect the others discretely, a finite occupational choice is always strategic, and distorted to an efficient solution. This dissertation is a collection of three essays. In the first essay, titled Exploiting Deposits with Fixed Costs, I derive conditions for an efficient solution for exploiting deposits with fixed costs, and show that there is no competitive allocation for price-taking agents owning the deposits. To overcome the lack of a competitive allocation, in the second essay titled Oligopolistic Resource Exploitation Under Fixed Costs, I describe the agents strategic interaction in a differential game, in which they apply open-loop strategies, and show that the exploitation share ratios of the concurrently exploited deposits equal to their mark-up ratios. Finally, in the third essay titled A Game of Entry and Exit Fixed Length Projects, I describe the entries of the projects that could be, for instance, projects to exploit deposits of a resource, each of which has a limited lifetime and a given impact on other projects profits. Essay 1: Exploiting Deposits with Fixed Costs. In this first essay I concentrate on the efficient solution, and show that it cannot be decentralized as a competitive allocation when the deposits are characterized by unavoidable fixed costs. I begin by describing the difference between the unavoidable and avoidable fixed cost structures. I show that, when applying the concept of unavoidable fixed costs, there are no technical or economical issues in the efficient solutions,

INTRODUCTION v for instance, relating to the frequently changing activity levels, which appear in the solutions of Eswaran et al. (1983) with the avoidable fixed cost structure. I derive the characteristics of an efficient solution, and show that, if the deposits are exploited concurrently, their marginal costs, which include both the out of the pocket marginal costs and the opportunity costs, are equal. The order of exploiting the deposits, which is a classical resource economics question, depends both on the deposits stock allocations and on their cost structures. I show further, that there is no competitive allocation, because the price-taking agents would act strategically at the exit of a deposit with a strictly positive scale as the exit induces a price jump. However, at the limit, when the stocks of the deposits are minuscule, and if the unavoidable costs are low enough, a competitive allocation exists. Essay 2: The Oligopolistic Resource Exploitation Under Fixed Costs. In the first essay I showed that there is no competitive allocation for exploiting deposits with fixed costs. To recover a competitive solution, in the second essay I introduce strategic interactions for private deposit owners under fixed costs, subsequently characterizing the outcome in the game. There are equilibria in open-loop strategies, in which deposits are exploited concurrently, and others, in which they are exploited sequentially. I extend the results of Lewis and Schmalensee (1980) and Loury (1986) including both the fixed costs and a more general variable costs structure. I show that the deposits exploitation shares ratio equals to the ratio of their mark-ups, where the marginal costs include both the out of the pocket costs and the opportunity costs. This is a deviation from the efficient solution. I show also that agents do not exit simultaneously and that there are no symmetric equilibria. An equilibrium with a sequential exploitation order may be, however, a Pareto improvement to the simultaneous exploitation equilibrium. Essay 3: A Game of Entry and Exit Fixed Length Projects. In the first two essays there are no entries. In the third essay I introduce the entry. I limit my attention to economic activity where the projects have each a fixed length, and also a given and discrete impact on other projects executed concurrently with them. These projects may be, for example, deposits of a resource that are exploited at a fixed exploitation pace. Anderson et al. (2014) describe Texan oil wells and show that the oil pressure in the well defines their exploitation pace. If the oil pressure could be kept constant, the oil wells would produce at a constant pace over time, and they would be suitable as projects for this essay. I describe an entry game for

vi INTRODUCTION fixed length projects where the entrants influence other entrants entry decisions by pre-empting. I show that the entry order and the level of industry concentration are distorted.

Bibliography Soren T. Anderson, Ryan Kellogg, and Stephen W. Salant. Hotelling under Pressure. NBER Working Paper No. 20280, July 2014. Antoine Bommier, Lucas Bretschger, and Fronçois Le Grand. Existence of Equilibria in Exhaustible Resource Markets with Economies of Scale and Inventories. Econ Theory, 63(3):687 721, 2017. Muhesh Eswaran, Tracy R. Lewis, and Terry Heaps. On the Nonexistence of Market Equilibria in Exhaustible Resource Markets with Decreasing Costs. Journal of Political Economy, 91:154 167, 1983. Tracy R. Lewis and Richard Schmalensee. On Oligopolistic Markets for Nonrenewable Natural Resources. The Quarterly Journal of Economics, pages 475 491, November 1980. Glenn C. Loury. A Theory of Oil igopoly: Cournot Equilibrium in Exhaustible Resource Markets with Fixed Supplies. International Economic Review, 27(2): 285 301, June 1986. Louis Makowski and Joseph M. Ostroy. Appropriation and Efficeincy: A Revision of the First Theorem of Welfare Economics. The American Economic Review, 85 (4):808 827, 1995. Paul Romer. Cake Eating, Chattering, and Jumps: Existence Results for Variational Problems. Econometrica, 54(4):897 907, July 1986. Vernon L. Smith. Investment and Production. Harvard University Press, Cambridge, Massachusetts, 1961. ISBN 9780674465008. vii

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