Diderik Lund

• Graham A Davis and Diderik Lund, "Taxation and investment decisions in petroleum," The Energy Journal, vol. 39, no. 6, 2018, pp. 189-208
• Diderik Lund, "How taxes on firms reduce the risk of after-tax cash flows," Finanzarchiv, vol. 70, 2014, pp 567-598
• Diderik Lund, "Neutrality of the Resource Super Profits Tax," Australian Economic Review, vol. 44, 2011, pp. 233-238
• Diderik Lund, "Rent taxation for nonrenewable resources," Annual Review of Resource Economics, vol. 1, 2009, pp. 287-308
• Diderik Lund, "Neutral company taxation under uncertainty, with some experiences from the petroleum sectors of Norway and Denmark," R. Påhlsson (ed.), Yearbook for Nordic Tax Research 2006, Universitetsforlaget, Oslo, Norway, 2006, pp. 116–123
• Diderik Lund, "How to analyze the investment–uncertainty relationship in real option models?", Review of Financial Economics, vol. 14, 2005, pp. 311–322
• Diderik Lund and Tore Nilssen, "Cream skimming, dregs skimming, and pooling: On the dynamics of competitive screening," Geneva Papers on Risk and Insurance Theory, vol. 29, 2004, pp. 23–41
• Diderik Lund, "Petroleum tax reform proposals in Norway and Denmark," Energy Journal, vol 23, no. 4, 2002, pp. 37–56
• Diderik Lund, "Taxation, uncertainty, and the cost of equity," International Tax and Public Finance, vol. 9, no. 4, 2002, pp. 483-503
• Diderik Lund, "Rent taxation when cost monitoring is imperfect," Resource and Energy Economics, vol. 24, no. 3, June 2002, pp. 211–228
• Erik Fjærli and Diderik Lund, "The choice between owner's wages and dividends under the dual income tax," Finnish Economic Papers, vol. 14, no. 2, Autumn 2001, pp. 104 – 119
• Diderik Lund, "Petroleumsskatt — flere uavklarte spørsmål," (Petroleum taxation — further undecided issues), Økonomisk Forum, vol. 55, no. 9, 2001, pp. 34 – 40.

• Asheim, Geir Bjarne; Fæhn, Taran; Nyborg, Karine; Greaker, Mads; Hagem, Cathrine; Harstad, Bård Gjul; Hoel, Michael; Lund, Diderik & Rosendahl, Knut Einar (2019). The case for a supply-side climate treaty. Science.  ISSN 0036-8075.  365(6451), s 325- 327 . doi: 10.1126/science.aax5011 Vis sammendrag

  During decades of international climate policy negotiations, aiming to limit demand for fossil fuels, the stock of carbon dioxide in the atmosphere has increased considerably, and even the flow of emissions to the atmosphere continues to grow (1). To reach the Paris Agreement's goal of keeping global warming well below 2°C, substantial parts of the world's fossil fuels simply cannot be combusted and must be left in the ground (1, 2). Recent work thus suggests redirecting climate policies toward fossil fuel producers directly (3–5) by capping the flows of extraction and restricting the stocks of resources available for exploration. We synthesize key economic mechanisms that support this approach, arguing that an international treaty among fossil fuel–producing countries could (i) enhance the impact of the Paris Agreement in the presence of free riders; (ii) stimulate investment in low-carbon technology research and development (R&D); (iii) provide insurance against a failed Paris Agreement; and (iv) make carbon policies more acceptable to fossil fuel producers, thus increasing their support. None of these effects depend on universal producer participation. Moreover, such a treaty need not be costly and could in fact help reduce the costs of the required transition to a low-carbon economy.

• Davis, Graham A & Lund, Diderik (2018). Taxation and Investment Decisions in Petroleum. Energy Journal.  ISSN 0195-6574.  39(6), s 189- 208 . doi: 10.5547/01956574.39.6.gdav Fulltekst i vitenarkiv. Vis sammendrag

  When governments apply high tax rates targeted at natural resource rent, there must be generous deductions in order to avoid investment disincentives. How generous is disputed. Based on standard finance theory and recommendations from the OECD and the IMF, the value that firms attach to future deductions depends on the risks of these, and the companies' after-tax weighted-average cost of capital cannot be applied directly. As an example, a simple model quantifies the difference between pre-tax and post-tax systematic risk when tax deductions are less risky than pre-tax cash flows. Osmundsen et al. (2015) suggest that the difference must be ignored by oil companies, since they cannot find the separate market values of tax deductions. But companies operating in different jurisdictions cannot then appreciate differences in tax systems, not even approximately, which will lead to suboptimal decisions. Tax designers may instead assume that companies have gradually adopted more sophisticated methods of investment decision making.

• Fæhn, Taran; Asheim, Geir Bjarne; Greaker, Mads; Hagem, Cathrine; Harstad, Bård Gjul; hoel, michael; Lund, Diderik; Nyborg, Karine; Rosendahl, Knut Einar & Storrøsten, Halvor Briseid (2018). Parisavtalen og oljeeksporten. Samfunnsøkonomen.  ISSN 1890-5250.  3, s 39- 50 Fulltekst i vitenarkiv.
• Lund, Diderik & Nymoen, Ragnar (2018). Comparative statics for real options on oil: What stylized facts?. The Engineering Economist.  ISSN 0013-791X.  63(1), s 54- 65 . doi: 10.1080/0013791X.2017.1283001 Fulltekst i vitenarkiv. Vis sammendrag

  An important application in the real options literature has been to investments in the oil sector. Two commonly applied "stylized facts" in such applications are tested here. One is that the correlation of the returns on oil and the stock market is positive, the other that it is invariant to changes in oil price volatility. Both are rejected in data for 1993-2008 for crude oil and the S&P 500 stock market index. Based on real options theory, consequences are pointed out. A widespread idea, that higher volatility leads to increased value and postponed investment, is not necessarily valid.

• Nesje, Frikk & Lund, Diderik (2018). Risikojustering av kalkulasjonsrenta i samfunnsøkonomiske analysar. Samfunnsøkonomen.  ISSN 1890-5250.  2018(4), s 34- 42 Fulltekst i vitenarkiv.
• Lund, Diderik (2014). How taxes on firms reduce the risk of after-tax cash flows. FinanzArchiv / Public Finance Analysis (FA).  ISSN 0015-2218.  70(4), s 567- 598 . doi: 10.1628/001522114X685492 Vis sammendrag

  Most firms use one discount rate applied to expected net after-tax cash flows. The need to adjust for differences in risk, other than leverage, is commonly neglected. There can be substantial effects of taxation on after-tax risk when there are depreciation deductions. Among the few studies of these effects, even fewer identify all effects correctly. When marginal investment is taxed together with inframarginal, the marginal beta for the Capital Asset Pricing Model differs from the average. The problems identified here imply that currently suggested tax reforms may fail. Tax neutrality results rely on firms correctly discounting for risk, in particular the risk of tax deductions.

• Lund, Diderik (2014). State participation and taxation in Norwegian petroleum: Lessons for others?. Energy Strategy Reviews.  ISSN 2211-467X.  3(C), s 49- 54 . doi: 10.1016/j.esr.2014.02.001 Vis sammendrag

  Starting around 1970, Norway’s system of state participation and taxation in petroleum had important asymmetries, known as distortionary in tax theory. Moreover, tax rates were tailored to oil price changes. From 1986 onwards this has been reformed gradually into a stable and symmetric system, recognized as close to neutral, inducing companies to maximize pre-tax values. But the system is costly and risky for the state. If countries are unable or unwilling to bear costs and risks, they cannot implement the neutral system. Neither did Norway from the beginning. In that case a country faces important trade-offs between risk and the maximization of pre-tax value or state revenue. This may be partly circumvented by slowing the pace of licensing.

• Lund, Diderik (2014). Tvilsom markedsføring av finansielle spareprodukter. Samfunnsøkonomen.  ISSN 1890-5250.  128(7), s 4- 14 Vis sammendrag

  Salg av nye, kompliserte finansielle produkter til kunder som ikke forsto dem, bidro til finanskrisen. I flere rettssaker hevdet kundene at de var feilinformert om risikoen knyttet til produktene. Av tre slike saker i Høyesterett i 2012 endte bare den ene med at kunden, Røeggen, fikk medhold. I Fokussaken hadde 80 kunder tapt 87 prosent av investert beløp, men ingen fikk erstatning. Gjennomgangen viser flere grovt misvisende trekk ved informasjon fra banken. Flere bankansatte hadde mangelfull forståelse av produktet de solgte. Noen forslag til endret regulering blir drøftet. Krav til standardisering av informasjon kan føre til overforenkling.

• Lund, Diderik (2013). Kalkulasjonsrente og skatt i petroleumsvirksomhet. Samfunnsøkonomen.  ISSN 1890-5250.  127(6), s 12- 23 Vis sammendrag

  En artikkel i Samfunnsøkonomen nr. 5/2013 retter kritikk i kraftige ordelag mot forslag fra Finansdepartementet til endringer i petroleumsskatten. Blant annet beskyldes departementet for å regne feil, og for å bruke teori som er ukjent for oljeselskapene. Formålet med artikkelen min er å vise at det snarere er kritikerne som regner feil, og at teorien er kjent og anbefalt av mange fagfolk i verdsetting, i hvert fall utenfor oljeselskapene. Etter hvert vil også oljeselskapene lære nye og mer presise verdsettingsmetoder. Tar dette lang tid, kan imidlertid noen prosjekter bli skrinlagt på feilaktig grunnlag i mellomtida. Til en viss grad kan prosjekter bli overtatt av andre selskaper med andre verdsettingsmetoder.

• Lund, Diderik (2013). Taxation of nonrenewable resources, In Jason Shogren (ed.),  Encyclopedia of Energy, Natural Resource, and Environmental Economics.  Elsevier.  ISBN 9780123750679.  Chapter 57.  s 224 - 231 Vis sammendrag

  Early in the article there is a discussion of different justifications for resource rent taxation, and the implications of these. Three main types of resource taxes are distinguished, royalties, income taxes, and rent taxes. Their effects on companies' decisions are outlined. The relevance of Hotelling-type theory is discussed. Neutral taxation is defined. This must rely on some theory of the behavior of companies. A simple theory is presented, in which a proportional tax on non-financial cash flows, with full and immediate loss offset, is neutral. This is known as a Brown Tax. It is pointed out that the neutrality result holds under very general assumptions. Consequences of two different modifications of the Brown Tax are considered. Next, there is a discussion of the asymmetry often found in all business taxes, known as imperfect loss offset. High uncertainty and the long time lag from exploration to extraction exacerbate this problem. Financial option theory is useful to quantify these tax effects. Arguments for and against a progressive tax system are given. The problems of transfer pricing and income shifting are presented, and various methods for tax analysis are mentioned. Finally, there is a section on tax reform and political risk.

• Lund, Diderik (2012). Er petroleumsvirksomheten subsidiert? :. Samfunnsøkonomen.  ISSN 1890-5250.  126(4), s 22- 31 Vis sammendrag

  Global Subsidies Initiative criticizes subsidies of fossil fuels in many countries. In the report on Norway, the conclusion is that production of petroleum is subsidized. For 2009 the amount is 25.5 billion NOK. But the report has many weaknesses. It is necessary to see the petroleum tax system as a whole. With the discount rates used in the report, the system gives a negative investment incentive, compared with ordinary company taxation. Exploration activity has a certain positive incentive, but much weaker than calculated in the report. The method used in the article does not require choice of discount rate for the operating income of the companies, only for the tax deductions. Thus a controversial topic in earlier discussions on petroleum taxation is avoided.

• Lund, Diderik (2011). Neutrality of the Resource Super Profits Tax. Australian Economic Review.  ISSN 0004-9018.  44(3), s 233- 238 . doi: 10.1111/j.1467-8462.2011.00645.x
• Lund, Diderik (2009). Rent Taxation for Nonrenewable Resources. Annual Review of Resource Economics.  ISSN 1941-1340.  1, s 287- 307 . doi: 10.1146/annurev.resource.050708.144216 Vis sammendrag

  The literature on taxation of rents from nonrenewable resources uses different theoretical assumptions and methods and a variety of empirical observations to arrive at widely diverging conclusions. Many studies use models and methods that disregard uncertainty, investigating distortionary effects of different taxes on whether, when, and how to explore for, develop, and operate resource deposits. Introducing uncertainty into the analysis opens a range of challenges and leads to results that cast doubt on the relevance of studies that neglect uncertainty. There are, however, several ways to analyze uncertainty regarding companies' behavior, resource price processes, and diversification opportunities, all with different implications for taxation. Methods developed in financial economics since the 1980s, though promising, are still not in widespread use. Additional topics covered in this review are optimal risk sharing between companies and governments, time consistency and fiscal stability, the relationship between taxes and discount rates, tax competition, and transfer pricing.

• Lund, Diderik (2006). Neutral company taxation under uncertainty, with some experiences from the petroleum sectors of Norway and Denmark, In Robert Påhlsson (ed.),  Yearbook for Nordic Tax Research 2006.  Universitetsforlaget.  ISBN 9788215010533.  Del 1.10.  s 116 - 123
• Lund, Diderik (2005). How to analyze the investment-uncertainty relationship in real option models?. Review of Financial Economics.  ISSN 1058-3300.  14(3-4), s 311- 322 Vis sammendrag

  The real options tradition originally predicted a decreasing relationship between uncertainty and investment, through the positive effect of higher uncertainty on the trigger level for revenue relative to costs. An opposing effect on the probability of reaching the level has been identified, yielding a total effect with ambiguous sign. This paper makes three points. The "opposing" effect is not always opposing. Systematic risk cannot generally be assumed to be increasing with volatility. A probability is not the best measure of investment. The sign of the total effect is again ambiguous. This ambiguity is illustrated, depending on specification of model and parameters.

• Lund, Diderik & Nilssen, Tore (2004). Cream skimming, dregs skimming, and pooling: On the dynamics of competitive screening. The Geneva Papers on Risk and Insurance Theory.  ISSN 0926-4957.  29, s 23- 41 . doi: 10.1023/B:GEPA.0000032564.19797.21
• Lund, Diderik (2002). Petroleum tax reform proposals in Norway and Denmark. Energy Journal.  ISSN 0195-6574.  23(4), s 37- 56 Vis sammendrag

  During the past two years similar petroleum tax reforms have been proposed in Norway and Denmark. Both were based on results on neutral taxation derived by Boadway and Bruce (1984) and Fane (1987). Main features of the proposals are presented, and important problems of implementation are highlighted. Topics for further research are pointed out. While the risk characteristics of tax deductions caused major disagreements between experts and oil companies, the after-tax cost of capital for risk free cash flows is a less clearly resolved question within the economics literature. Another topic for disagreement is value additivity, disputed by the companies.

• Lund, Diderik (2002). Rent taxation when cost monitoring is imperfect. Resource and Energy Economics.  ISSN 0928-7655.  24(3), s 211- 228 . doi: 10.1016/S0928-7655(01)00053-7 Vis sammendrag

  While rent taxation in some theories is neutral, and the tax rate could be set to one hundred percent to minimize the need for distortionary taxes, this does not occur in practice. An important reason for this is the transfer incentives that would result. When cost transfers can only be imperfectly monitored, it is optimal under some conditions to combine a tax on gross revenue with a rent tax. This contributes to explaining the frequent occurrence of gross revenue taxation in actual rent tax systems, and the frequently observed tailoring of rent tax systems in response to output price changes.

• Lund, Diderik (2002). Taxation, uncertainty, and the cost of equity. International Tax and Public Finance.  ISSN 0927-5940.  9(4), s 483- 503 Vis sammendrag

  Traditionally the pre-tax cost of capital is a function of the interest rate and the tax system. However, uncertainty implies that the market's required return is no single interest rate, but depends on risk. Different tax systems split risk differently between firm and government. Thus the required expected return after corporate taxes depends on the tax system. Expressions for this are derived, based on a CAPM-type model. The weighted average cost of capital is decreasing in the tax rate, even for fully equity financed projects. This effect can be substantial, but is neglected in much of the literature.

• Fjærli, Erik & Lund, Diderik (2001). The choice between owner's wages and dividends under the dual income tax. Finnish economic papers.  ISSN 0784-5197.  14(2), s 104- 119 Vis sammendrag

  Tax-motivated shifting of income between different tax bases erodes tax revenues, confuses income statistics, and makes the effects of tax reforms unpredictable. Few studies have been able to use micro data to investigate this phenomenon. Using a rather unique data set, this study shows that the choice of type of payout from corporations to owners is strongly, but not uniquely, motivated by taxes. There are indications that the personal tax system is more clearly perceived by the owners than is the system of corporate taxes and regulations, and that own wage payments are motivated by rights to social security benefits.

• Lund, Diderik (2001). Petroleumsskatt - flere uavklarte spørsmål. Økonomisk forum.  ISSN 1502-6108.  55(9), s 34- 40 Vis sammendrag

  Forslagene om reformer i skatt på petroleumsutvinning, NOU (2000:18), tok sikte på at skattesystemet skulle være nøytralt etter standard teori. Oljeselskapene møtte forslagene med mange motforestillinger. Noen drøftes her. Innvendingen om at selskapene bruker andre metoder for investeringsanalyser enn de som forslagene bygger på, reiser spørsmålet om hvorfor selskapene ikke tilegner seg nyere teori. Forutsetningen om verdiadditivitet står sterkt i teorien. Eventuelle avvik fra denne må begrunnes nøye. Når det gjelder selskapenes vilje til å investere i Norge, når de også har muligheter i andre land, forutsetter kritikken uten forklaring at de ikke kan gjøre begge deler.

• Lund, Diderik (2001). Under different international agreements: Can a small nation gain from introducing a carbon tax early?, In Alistair Ulph (ed.),  Environmental Policy, International Agreements, and International Trade.  Oxford University Press, Oxford, United Kingdom.  ISBN 0-19-829329-1.  s 209 - 230 Vis sammendrag

  Some authors and authorities have proposed that a small nation could gain from introducing a carbon tax domestically, given that a binding international agreement would come into effect at a later stage. This gain would not be due to the environmental impact, which is tiny and can be disregarded. Instead it is thought that the domestic private sector would redirect its research and development efforts, thus preparing for the future binding agreement. The idea is investigated in a theoretical model, distinguished by R&D going in two different directions, one environment friendly and one non-friendly. R&D has positive externalities. Compared with Lund (1994), the model is now expanded to consider different international agreements. One conclusion is that the agreement should demand payment to an international institution, at least for the marginal emission. If not, the national government would want to counteract the agreement before it becomes effective.

• Lund, Diderik (2000). Nøytralitet i petroleumsskattleggingen, I: Nina Bjerkedal (red.),  Skattlegging av petroleumsvirksomhet, NOU 2000:18.  Statens forvaltningstjeneste, Oslo.  ISBN 82-583-0530-1.  s 185 - 226 Vis sammendrag

  Dette er vedlegg 1 i utredningen fra et offentlig utvalg nedsatt i oktober 1999. Vedlegget tar for seg prinsippene for optimal skatt på petroleumsvirksomhet. Det blir lagt spesiell vekt på begrepet nøytralitet, som blir nærmere definert og drøftet. Et viktig særtrekk i petroleumssektoren er den store usikkerheten, spesielt sett på bakgrunn av prosjektenes lange planleggingshorisont. Dette krever særskilt analyse. Avsnittsoverskrifter bl.a.: Begrunnelse for nøytralitet. Effektivitetsfremmende skatter og vridende skatter. Betydning av nøytralitet. Effektiv utnytting av samlet investering. Nøytralitet og stabilitet. Nøytralitet ikke alltid ønskelig. Eksterne virkninger. Dårlig diversifiserte eiere, eller risikoavers ledelse. Skattegrunnlag avviker fra beslutningsgrunnlag. Maksimering av skatteproveny. Metode under full sikkerhet. Nåverdi etter skatt. Marginale skattesatser. Marginale avkastningskrav. Nøytral skatt på grunnrente. Kontantstrømskatt. Alternativ til skatt: Statsdeltakelse, forhåndsbetaling. Ikke-nøytrale skatteystem, uten usikkerhet. Norsk skatt på kapitalinntekt, hhv. petroleumsinntekt, etter 1992. Ressursrenteskatt. Overskuddsbasert grunnrenteskatt. Sammenlikning av systemene ved egenfinansiering. Vanlig selskapsskatt kombinert med grunnrenteskatt. Nøytralitet i forhold til finansiering. Åpen økonomi. Usikkerhet. Selskapenes beslutninger under usikkerhet. Beslutningsregler slik selskapene beskriver dem. Teori for aksjeselskapers beslutninger. Vurdering av skattesystemene under usikkerhet. Modifikasjoner i forhold til standard teori. CO2-avgift. Skattegrunnlag avviker fra beslutningsgrunnlag. Overføringsproblemet. Kostnadsbevissthet. Finansielt volum, materialitet. Politisk risiko. Appendiks: En modell for avkastningskrav under ufullstendig tapsfradrag.

• Lund, Diderik (1999). Taxation and regulation of an exhaustible natural resource: The case of the Norwegian petroleum, In Eugenio Figueroa (ed.),  Economic Rents and Environmental Management in Mining and Natural Resource Sectors.  University of Chile, Santiago, and University of Alberta, Edmonton.  ISBN 956-19-0307-5.  s 189 - 244
• Bjerksund, Petter; Lund, Diderik & Øksendal, Bernt (1991). The Cost of a Promise to Develop an Oil Field within a Fixed Future Date, In  Stochastic Models and Option Values.  Elsevier Science Publishers B.V. (North-Holland).  faglig_bok_institusjon.  s 103 - 128

Se alle arbeider i Cristin

• Asheim, Geir Bjarne; Fæhn, Taran; Nyborg, Karine; Greaker, Mads; Hagem, Cathrine; Harstad, Bård Gjul; Hoel, Michael; Lund, Diderik & Rosendahl, Knut Einar (2019). En ny, internasjonal klimaavtale bør på plass. Aftenposten (morgenutg. : trykt utg.).  ISSN 0804-3116.
• Lund, Diderik (2019). Kalkulasjonsrente og usikkerhet.
• Lund, Diderik & Nyborg, Karine (2019). Hvordan begrenses oljeutvinningen best?. Aftenposten (morgenutg. : trykt utg.).  ISSN 0804-3116.
• Davis, Graham A & Lund, Diderik (2018). Taxation and Investment Decisions in Petroleum. Vis sammendrag

  When governments apply high tax rates targeted at natural resource rent, there must be generous deductions in order to avoid investment disincentives. How generous is disputed. Based on standard finance theory and recommendations from the OECD and the IMF, the value of future deductions depends on the risks of these, and the companies’ after-tax weighted-average cost of capital cannot be applied directly. As an example, a simple model quantifies the difference between pre-tax and post-tax systematic risk when tax deductions are less risky than pre-tax cash flows. Osmundsen et al. (2015) suggest that the difference must be ignored by oil companies, since they cannot find the separate market values of tax deductions. But companies operating in different jurisdictions cannot then appreciate differences in tax systems, not even approximately, which will lead to suboptimal decisions. Tax designers may instead assume that companies gradually adopt more adequate methods of investment decision making.

• Lund, Diderik (2018). Increasing resource rent taxation when the corporate income tax is reduced?. Vis sammendrag

  Under international tax competition, corporate income tax rates are predicted to decrease, and the tax burden will shift onto immobile factors. This case study considers tax changes that illustrate the predictions for Norway 2012–2018. Petroleum rent was taxed at high rates in 2012, and while corporate income tax rates were reduced in four steps, the marginal tax on rent was kept constant. The four steps are analyzed in light of the tax burden shift predicted by theory, and possible intentions of the government. The tax on petroleum rent has not been increased. Government intentions seem to have been shifting.

• Lund, Diderik (2017). Current issues in taxation of non-renewable natural resources.
• Lund, Diderik & Nyborg, Karine (2017). Behold petroleumsskatten!. Klassekampen.  ISSN 0805-3839.
• Lund, Diderik (2016). Er fradrag for investeringer for gode?.
• Lund, Diderik (2016). Optimal resource rent taxation when nations are credit constrained. Vis sammendrag

  The Resource Rent Tax suggested by Garnaut and Clunies Ross (1975) has been influential in resource rich countries and in academic literature. Several authors show that it distorts investments through asymmetric treatment of profits and losses. Neutrality can only be achieved if authorities commit to treating these symmetrically, guaranteeing loss offset through payouts if necessary. Risks are substantial, both in output (technology, geology) and (output and factor) prices. Many nations will be unable or unwilling to take risks involved in such guarantees. We analyze optimal rent taxation in this situation, maximizing tax revenue subject to a constraint of no loss offset.

• Jortveit, Anne Karin & Lund, Diderik (2015, 30. desember). Oljenæring i særstilling. Dybdeintervju.. [Fagblad].  Rapport fra Norsk Klimastiftelse. Vis sammendrag

  • Oljeselskapenes mulighet til å trekke fra renteutgifter ved beregningen av særskatt, er det mest uheldig ved det norske petroleumsskattesystemet. • Mener det samme nå som i 2013, at friinntekten er for generøs. • Ingen god begrunnelse for ny skattefordel. • Oljenæringen er i en særstilling på grunn av høy skatt og lang ledetid. • Vanskelig å sammenlikne oljenæringen med fornybarnæringen. • For klima og miljø er det viktigere å utlyse færre lisenser enn å endre oljeskattesystemet.

• Lund, Diderik (2015). Optimal resource rent taxation when nations are credit constrained. Vis sammendrag

  The Resource Rent Tax suggested by Garnaut and Clunies Ross (1975) has been influential in resource rich countries and in academic literature. Several authors show that it distorts investments through asymmetric treatment of profits and losses. Neutrality can only be achieved if authorities commit to treating these symmetrically, guaranteeing loss offset through payouts if necessary. Risks are substantial, both in output (technology, geology) and (output and factor) prices. Many nations will be unable or unwilling to take risks involved in such guarantees. We analyze optimal rent taxation in this situation, maximizing tax revenue subject to a constraint of no loss offset.

• Lund, Diderik & Nymoen, Ragnar (2015). Comparative statics for real options on oil: What stylized facts to use?. Vis sammendrag

  An important application in the real options literature has been to investments in the oil sector. Two commonly applied “stylized facts” in such applications are tested here. One is that the correlation of the returns on oil and the stock market is positive, the other that it is invariant to changes in oil price volatility. Both are rejected in data for 1993–2008 for crude oil and the S&P 500 stock market index. Based on real options theory, consequences are pointed out. Higher volatility need not imply increased value and postponed investment.

• Lund, Diderik (2014). Avkastningskrav og skatt.
• Lund, Diderik (2014). Rente i aksjonærmodellen og ACE-modellen.
• Lund, Diderik & Nymoen, Ragnar (2014). Comparative statics for real options on oil: What stylized facts to use?.
• Lund, Diderik (2013). An economist's view.
• Lund, Diderik (2013). Bedre omtrent riktig enn nøyaktig galt :. Samfunnsøkonomen.  ISSN 1890-5250.  127(9), s 14- 18 Vis sammendrag

  I Samfunnsøkonomen nr. 8/2013 svarer Osmundsen, Johnsen og Emhjellen (OJE) (2013) på Lund (2013a), som i sin tur var et svar på Osmundsen og Johnsen (2013). Jeg skal her først diskutere hvilke holdepunkter vi har for å finne de relevante kalkulasjonsrentene. Deretter skal jeg drøfte hvordan staten bør forholde seg til oljeselskapenes påstander om at friinntekten må være rausere fordi de har høyere avkastningskrav enn det staten har lagt til grunn.

• Lund, Diderik (2013). How taxes on firms reduce the risk of after-tax cash flows. Vis sammendrag

  Most firms use one discount rate applied to expected net after-tax cash flows. The need to adjust for differences in risk, other than leverage, is commonly neglected. There can be substantial effects of taxation on after-tax risk when there are depreciation deductions. Among the few studies of these effects, even fewer identify all effects correctly. When marginal investment is taxed together with inframarginal, marginal CAPM beta differs from average. The problems identified here imply that currently suggested tax reforms may fail. Tax neutrality results rely on firms correctly discounting for risk, in particular the risk of tax deductions.

• Lund, Diderik (2013). How taxes on firms reduce the risk of after-tax cash flows.
• Lund, Diderik (2013). How taxes on firms reduce the risk of after-tax cash flows. Vis sammendrag

  Most firms make decisions based on one discount rate applied to expected net after tax cash flows. The need to adjust for differences in risk, other than leverage, is most often neglected. One source of risk differences is the tax system. Even for fully equity-financed firms there can be substantial effects of taxation on after-tax risk when there are depreciation deductions. Among the few studies of these effects, even fewer identify all effects correctly. Some claim to characterize the cost of capital, but fail to identify the marginal investment. When this is taxed together with inframarginal investment, marginal beta differs from average. To find asset betas, observed equity betas should not only be unlevered, but also “unaveraged” and “untaxed.” The problems identified here imply that currently suggested tax reforms may fail. Tax neutrality results rely on firms correctly discounting for risk, in particular the risk of tax deductions.

• Lund, Diderik (2013). Kalkulasjonsrente og skatt i petroleumsvirksomhet.
• Lund, Diderik (2013). Sammenlikning av skattesystemer i petroleumsvirksomhet.
• Lund, Diderik & Nymoen, Ragnar (2013). A theoretical and empirical analysis of invariance assumptions in comparative statics for real options on oil.
• Lund, Diderik (2012). Erfaringer med rammevilkår for petroleumsproduksjon i Norge.
• Lund, Diderik (2012). Sammensatte finansielle produkter - uforståelige eller nyttige?. Vis sammendrag

  Etter finanskrisen i 2008 har investorer opplevd store tap på finansielle produkter de trolig ikke forsto. Domstolene tar stilling til om investorene selv eller de som har solgt produktene, er ansvarlige for manglende forståelse og påfølgende tap. Vi skal se på hvordan produktene er sammensatt, hvilken risiko de innebærer, og om de kan være nyttige for noe eller noen. Vi skal også se på den informasjonen som har vært gitt.

• Lund, Diderik (2011). Marginal vesus average beta of equity, and the risk of depreciation tax shields.
• Lund, Diderik (2011). Neutrality of a Resource Super Profits Tax.
• Lund, Diderik (2010). Marginal versus average beta of equity, and the risk of depreciation tax shields.
• Lund, Diderik (2010). Samfunnsøkonomiske betraktninger rundt regulering av petroleumsvirksomheten.
• Lund, Diderik (2009). Rent taxation for non-renewable resources.
• Lund, Diderik (2009). Rent taxation for non-renewable resources.
• Lund, Diderik (2008). An analytical model of required returns to equity under taxation with imperfect loss offset.
• Lund, Diderik (2008). Rent taxation for nonrenewable resources. Vis sammendrag

  The literature on taxation of rents from nonrenewable resources uses different theoretical assumptions and methods and a variety of empirical observations to arrive at widely diverging conclusions. Many studies use models and methods which disregard uncertainty, investigating distortionary effects of different taxes on whether, when, and how to explore for, develop and operate resource deposits. Introducing uncertainty into the analysis opens a range of challenges, and leads to results which cast doubt upon the relevance of studies which neglect uncertainty. There are, however, several ways to analyze uncertainty, regarding companies' behavior, resource price processes, and diversification opportunities, all with different implications for taxation. Methods developed in financial economics since the 1980's are promising, but still not in widespread use. Some more specific topics covered in this review are optimal risk sharing between companies and governments, time consistency and fiscal stability, the relationship between taxes and discount rates, and transfer pricing.

• Lund, Diderik (2004). An Analytical Model of Required Returns to Equity under Taxation with Imperfect Loss Offset.
• Lund, Diderik (2004). Depreciation, taxes and the cost of capital.
• Lund, Diderik (2003). How to analyze the investment-uncertainty relationship in real option models. Working Papers from Economic Policy Research Unit, University of Copenhagen. 17. Vis sammendrag

  The real options tradition originally predicted a decreasing relationship between uncertainty and investment, through the positive effect of higher uncertainty on the trigger level for revenue relative to costs. An opposing effect on the probability of reaching the level has been identified, yielding a total effect with ambiguous sign. This paper makes three points. The �opposing� effect is not always opposing. Systematic risk cannot generally be assumed to increase with volatility. A probability is not the best measure of investment. The sign of the total effect is again ambiguous. This ambiguity is illustrated, depending on specification of model and parameters.

• Lund, Diderik (2003). Taxation and systematic risk under decreasing returns to scale. Working Papers. 2. Vis sammendrag

  Lund (2002a) showed in a CAPM-type model how tax depreciation schedules affect required expected returns after taxes. Even without leverage higher tax rates implied lower betas when tax deductions were risk free. Here they are risky, and marginal investment is taxed together with inframarginal in an analytical model of decreasing returns. With imperfect loss offset tax claims are analogous to call options. The beta of equity is still decreasing in the tax rate, but increasing in the underlying volatility. The results are important if market data are used to infer required expected returns, and in discussions of tax design.

• Lund, Diderik (2003). Taxation and systematic risk under decreasing returns to scale.
• Lund, Diderik (2003). Valuation, leverage and the cost of capital in the case of depreciable assets: Revisited. Working Paper. 3. Vis sammendrag

  Levy and Arditti (1973) introduced depreciable assets into the Modigliani and Miller (1958) model, and analyzed the implications for the cost of capital. Assuming that the firm reinvests indefinitely to maintain a constant expected cash flow, they found that depreciation increases the cost of capital before and after tax. Most of their assumptions are maintained. However, commitment to perpetual reinvestment is in most cases not a reasonable assumption. Without it, depreciation decreases the cost of capital before and after tax. The effect of depreciation is less in absolute value than in Levy and Arditti, but not insignificant.

• Lund, Diderik (2003). Valuation, leverage and the cost of capital in the case of depreciabel assets: Revisited. Vis sammendrag

  Levy and Arditti (1973) introduced depreciable assets into the Modigliani and Miller (1958) model, and analyzed the implications for the cost of capital. Assuming that the firm reinvests indefinitely to maintain a constant expected cash flow, they found that depreciation increases the cost of capital before and after tax. Most of their assumptions are maintained. However, commitment to perpetual reinvestment is in most cases not a reasonable assumption. Without it, depreciation decreases the cost of capital before and after tax. The effect of depreciation is less in absolute value than in Levy and Arditti, but not insignificant.

• Lund, Diderik (2002). Petroleum tax reform in Scandinavia. Vis sammendrag

  During the past two years similar petroleum tax reforms were proposed in Norway and Denmark. Both were based on results on neutral taxation derived by Boadway and Bruce (1984) and Fane (1987). Main features of the proposals are presented, and important problems of implementation are highlighted. Topics for further research are pointed out. While the risk characteristics of tax deductions caused major disagreements between experts and oil companies, the after-tax cost of capital for risk free cash flows is a less clearly resolved question within the economics literature. Another topic for disagreement is value additivity, disputed by the companies.

• Lund, Diderik (2002). Petroleum tax reform in Scandinavia. Vis sammendrag

  During the past two years similar petroleum tax reforms were proposed in Norway and Denmark. Both were based on results on neutral taxation derived by Boadway and Bruce (1984) and Fane (1987). Main features of the proposals are presented, and important problems of implementation are highlighted. Topics for further research are pointed out. While the risk characteristics of tax deductions caused major disagreements between experts and oil companies, the after-tax cost of capital for risk free cash flows is a less clearly resolved question within the economics literature. Another topic for disagreement is value additivity, disputed by the companies.

• Lund, Diderik (2002). Rent taxation when cost monitoring is imperfect. Vis sammendrag

  While rent taxation in some theories is neutral, and the tax rate could be set to one hundred percent to minimize the need for distortionary taxes, this does not occur in practice. An important reason for this is the transfer incentives that would result. When cost transfers can only be imperfectly monitored, it is optimal under some conditions to combine a tax on gross revenue with a rent tax. This contributes to explaining the frequent occurrence of gross revenue taxation in actual rent tax systems, and the frequently observed tailoring of rent tax systems in response to output price changes.

• Lund, Diderik (2001). Petroleum tax reform in Scandinavia. Vis sammendrag

  During the past two years similar petroleum tax reforms were proposed in Norway and Denmark. Both were based on results on neutral taxation derived by Boadway and Bruce (1984) and Fane (1987). Main features of the proposals are presented, and important problems of implementation are highlighted. Topics for further research are pointed out. While the risk characteristics of tax deductions caused major disagreements between experts and oil companies, the after-tax cost of capital for risk free cash flows is a less clearly resolved question within the economics literature. Another topic for disagreement is value additivity, disputed by the companies.

• Lund, Diderik (2001). Taxation, uncertainty and the cost of equity for a multinational firm. Vis sammendrag

  From a CAPM-type model the cost of equity is derived for a firm operating under various foreign tax systems. The firm´s shares are traded in a market which is unaffected by these systems. The cost of capital depends on the foreign tax system, even for fully equity financed projects. This is neglected in much of the literature. For a corporate income tax the main factor which reduces the cost of equity is the depreciation deductions. Compared to a neutral cash flow tax, this reduces the cost of equity because it acts as a loan from the firm to the government.

• Lund, Diderik (2001). Taxation, uncertainty, and the cost of equity for a multinational firm. Vis sammendrag

  From a CAPM-type model the cost of equity is derived for a firm operating under various corporate tax systems, e.g., abroad or in particular sectors of an economy. The firm's shares are traded in a market which is unaffected by these systems. The cost of capital depends on the tax systems in question, even for fully equity financed projects. This is neglected in much of the literature and practice based on the weighted average cost of capital. For a corporate income tax the main factor which reduces the cost of equity is the depreciation deductions. Compared with a neutral cash flow tax, these reduce the cost of equity because they act risk-wise as a loan from the firm to the government. For a given depreciation schedule the cost of equity is a decreasing function of the corporate tax rate. Under some realistic circumstances the result is stronger: The beta of equity is proportional to one minus the tax rate. The results carry over from two-period to multi-period models. They are modified, but not removed, if the tax value of depreciation deductions is risky. This can be modelled using option valuation techniques. The results are relevant for capital budgeting in firms which face widely different depreciation schedules or corporate tax rates. They are also relevant for discussions of tax reform, and numerically if one wants to apply capital market data in capital budgeting. Compared with previous studies, the method is improved by solving for the after-tax marginal project. Compared with Levy and Arditti (1973) it is argued that their assumption of a perpetual commitment to reinvestment is unrealistic.

• Lund, Diderik (2001). Taxation, uncertainty, and the cost of equity for a multinational firm. Vis sammendrag

  From a CAPM-type model the cost of equity is derived for a firm operating under various corporate tax systems, e.g., abroad or in particular sectors of an economy. The firm's shares are traded in a market which is unaffected by these systems. The cost of capital depends on the tax systems in question, even for fully equity financed projects. This is neglected in much of the literature and practice based on the weighted average cost of capital. For a corporate income tax the main factor which reduces the cost of equity is the depreciation deductions. Compared with a neutral cash flow tax, these reduce the cost of equity because they act risk-wise as a loan from the firm to the government. For a given depreciation schedule the cost of equity is a decreasing function of the corporate tax rate. Under some realistic circumstances the result is stronger: The beta of equity is proportional to one minus the tax rate. The results carry over from two-period to multi-period models. They are modified, but not removed, if the tax value of depreciation deductions is risky. This can be modelled using option valuation techniques. The results are relevant for capital budgeting in firms which face widely different depreciation schedules or corporate tax rates. They are also relevant for discussions of tax reform, and numerically if one wants to apply capital market data in capital budgeting. Compared with previous studies, the method is improved by solving for the after-tax marginal project. Compared with Levy and Arditti (1973) it is argued that their assumption of a perpetual commitment to reinvestment is unrealistic.

• Lund, Diderik (2001). Taxation, uncertainty, and the cost of equity for a multinational firm. Vis sammendrag

  From a CAPM-type model the cost of equity is derived for a firm operating under various corporate tax systems, e.g., abroad or in particular sectors of an economy. The firm's shares are traded in a market which is unaffected by these systems. The cost of capital depends on the tax systems in question, even for fully equity financed projects. This is neglected in much of the literature and practice based on the weighted average cost of capital. For a corporate income tax the main factor which reduces the cost of equity is the depreciation deductions. Compared with a neutral cash flow tax, these reduce the cost of equity because they act risk-wise as a loan from the firm to the government. For a given depreciation schedule the cost of equity is a decreasing function of the corporate tax rate. Under some realistic circumstances the result is stronger: The beta of equity is proportional to one minus the tax rate. The results carry over from two-period to multi-period models. They are modified, but not removed, if the tax value of depreciation deductions is risky. This can be modelled using option valuation techniques. The results are relevant for capital budgeting in firms which face widely different depreciation schedules or corporate tax rates. They are also relevant for discussions of tax reform, and numerically if one wants to apply capital market data in capital budgeting. Compared with previous studies, the method is improved by solving for the after-tax marginal project. Compared with Levy and Arditti (1973) it is argued that their assumption of a perpetual commitment to reinvestment is unrealistic.

• Lund, Diderik (2001). Taxation, uncertainty, and the cost of equity for a multinational firm. Vis sammendrag

  From a CAPM-type model the cost of equity is derived for a firm operating under various foreign tax systems. The firm´s shares are traded in a market which is unaffected by these systems. The cost of capital depends on the foreign tax system, even for fully equity financed projects. This is neglected in much of the literature. For a corporate income tax the main factor which reduces the cost of equity is the depreciation deductions. Compared to a neutral cash flow tax, this reduces the cost of equity because it acts as a loan from the firm to the government.

• Lund, Diderik (2001). Taxation, uncertainty, and the cost of equity for a multinational firm. Vis sammendrag

  From a CAPM-type model the cost of equity is derived for a firm operating under various foreign tax systems. The firm´s shares are traded in a market which is unaffected by these systems. The cost of capital depends on the foreign tax system, even for fully equity financed projects. This is neglected in much of the literature. For a corporate income tax the main factor which reduces the cost of equity is the depreciation deductions. Compared to a neutral cash flow tax, this reduces the cost of equity because it acts as a loan from the firm to the government.

• Lund, Diderik (2001). Taxation, uncertainty, and the cost of equity for a multinational firm. Vis sammendrag

  From a CAPM-type model the cost of equity is derived for a firm operating under various foreign tax systems. The firm´s shares are traded in a market which is unaffected by these systems. The cost of capital depends on the foreign tax system, even for fully equity financed projects. This is neglected in much of the literature. For a corporate income tax the main factor which reduces the cost of equity is the depreciation deductions. Compared to a neutral cash flow tax, this reduces the cost of equity because it acts as a loan from the firm to the government.

• Lund, Diderik (2000). Imperfect loss offset and the after-tax expected rate of return to equity, with an application to rent taxation. Memorandum fra Sosialøkonomisk institutt. 21. Vis sammendrag

  Non-neutral taxation, and in particular imperfect loss offset, is shown to have a strong effect not only on investment decisions, but also on required expected after-tax rates of return to equity. Systematic risk is valued according to the CAPM, while non-linear taxes are valued by option valuation methods.

• Lund, Diderik (2000). Imperfect loss offset and the after-tax expected rate of return to equity, with an application to rent taxation. Vis sammendrag

  Non-neutral taxation, and in particular imperfect loss offset, is shown to have a strong effect not only on investment decisions, but also on required expected after-tax rates of return to equity. Systematic risk is valued according to the CAPM, while non-linear taxes are valued by option valuation methods.

• Lund, Diderik & Nilssen, Tore (2000). Cream skimming, dregs skimming, and pooling: On the dynamics of competitive screening. Vis sammendrag

  We discuss the prevalence of pooling equilibria in a two-period model of an insurance market with asymmetric information. We solve the model numerically. In addition to reporting cases where a pooling equilibrium exists, we pay attention to why, in the case of non-existence of a pooling equilibrium, this is so. In addition to the phenomenon of cream skimming emphasized in earlier literature, we here point to the importance of the opposite: dregs skimming, whereby high-risk consumers are profitably detracted from the candidate pooling contract.

• Lund, Diderik & Nyborg, Karine (2000). Petroleumsskatt - hva nå?. Dagens næringsliv.  ISSN 0803-9372.  s 3- 3 Vis sammendrag

  Petroleumsskatteutvalget la fram sin innstilling i juni (NOU 2000:18), og nå foreligger høringsuttalelsene. Som medlemmer av utvalget ønsker vi å kommentere noen punkter i uttalelsen fra Oljeindustriens Landsforening, OLF. Utvalget har pekt på at skjermingen i dag er for gunstig for de selskapene som er i skatteposisjon. I dagens særskatt gis det både fradrag for netto renteutgifter og for en "friinntekt," som er uavhengig av finansieringsform. Resultatet er at samlede fradrag overstiger det som skal til for å skjerme normal avkastning. Utvalget foreslår et kapitalavkastningsfradrag til erstatning for rentefradraget og friinntekten. OLF hevder at kapitalavkastningsfradraget er for lavt til å oppnå den ønskede skjermingen. De skriver at det må gis fradrag for en normalavkastning med et ikke ubetydelig risikotillegg. OLF mener tydeligvis at risikotillegget bør være uavhengig av hvilken risiko som faktisk er knyttet til kontantstrømmen. Dette gir liten mening. Det fradraget utvalget foreslår, er tilstrekkelig når en tar i betraktning at selskapene vil nyte godt av fradraget med svært stor grad av sikkerhet. Et viktig problem med fradraget for faktiske renteutgifter er at selskapene kan utnytte rentefradraget mot 78 prosent skatt til rimelig finansiering av aktivitet andre steder enn i norsk petroleumssektor. Vi finner en slik subsidiering helt urimelig.

• Lund, Diderik; Nyborg, Karine & Wærness, Eirik (2000). Petroleumsskatten bør endres. Dagens næringsliv.  ISSN 0803-9372.  s 3- 3 Vis sammendrag

  Petroleumsskatteutvalget, oppnevnt 22. oktober 1999, la fram sin utredning om behovet for endringer i petroleumsskattesystemet 20. juni 2000. Utvalget har foreslått endringer i skattesystemet som vil bidra til at selskapene på sokkelen i større grad stimuleres til å handle i tråd med samfunnsøkonomisk lønnsomhet. Siktemålet med utvalgets forslag er å sikre at normalavkastning i virksomheten skal skattlegges tilsvarende som i andre næringer. og at hele den ekstraordinære avkastningen, men bare denne, skattlegges høyere. Artikkelen går gjennom begrunnelsene for å skattlegge petroleumsvirksomheten med en særskilt høy skatt. De viktigste svakhetene ved det eksisterende systemet blir listet opp, og til slutt blir de viktigste endringsforslagene nevnt. Utvalgets forslag er, i motsetning til i det gjeldende systemet, nøytralt, uavhengig av nivået på skattesatsen. Det bør derfor være mulig å diskutere selve systemet utvalget foreslår, separat fra spørsmålet om hvor stor del av inntjeningen staten bør inndra. En reduksjon av særskattesatsen vil trolig ha liten effekt på selskapenes evne og vilje til å gjennomføre små, marginale prosjekter. En reduksjon av særskattesatsen vil imidlertid bedre selskapenes lønnsomhet på allerede lønnsomme prosjekter. Det vil dermed særlig tilgodese etablerte selskaper som har de mest lønnsomme feltene, og i særdeleshet de som har eksisterende felt i produksjon.

• Halvorsen, Hilde E. & Lund, Diderik (1998). Rent taxation when cost transfers are possible, but costly. Memorandum fra Sosialøkonomisk institutt. 20. Vis sammendrag

  While rent taxation in some theories is neutral, and the tax rate could be set to one hundred percent to minimize the need for distortionary taxes, this does not occur in practice. An important reason for this is the transfer incentives that would result. Monitoring to prevent transfer pricing is difficult, in particular on the cost side. For corporations, monitoring implies that both transfer pricing and real transfers will be costly. Assuming a convex cost function for cost transfers, it is shown that the optimal tax system combines a cash flow tax with a royalty, i.e., a tax on gross revenues. It is also shown that the optimal tax rates depend on the output price. This contributes to explaining the frequently observed tailoring of rent tax systems in response to output price changes, in particular in the petroleum sector. These results hold when the corporations are heterogeneous and the government only knows a probability distribution for the two cost parameters. An analogy to the problem analyzed in the present paper, is the problem of a minority shareholder in preventing a majority shareholder to withdraw profits through, e.g., transfer pricing.

• Lund, Diderik (1998). Kontantstøtte - en økonomisk analyse. Dagens næringsliv.  ISSN 0803-9372.
• Fjærli, Erik & Lund, Diderik (1997). The choice between owner's wages and dividends under the dual income tax. Vis sammendrag

  Tax-motivated shifting of income between different tax bases erodes tax revenues, confuses income statistics, and makes the effects of tax reforms unpredictable. Few studies have been able to use micro data to investigate the mechanisms behind this phenomenon. Using a rather unique data set for Norway, 1991, this study shows that the choice of type of payout from corporations to owners is strongly, but not uniquely, motivated by taxes. There are indications that the personal tax system is more clearly perceived by the owners than is the system of corporate taxes and regulations. A higher number of employees encourages wage payments to the owners as opposed to dividends, most likely for some sociological or institutional reasons. Wage payments to the owners may be motivated by the fact that rights to future security benefits are linked to wage income. It has been difficult to distinguish this from other effects empirically.

• Hoel, Michael Olaf; Kverndokk, Snorre & Lund, Diderik (1997). Vi vinner på å vente. Dagens næringsliv.  ISSN 0803-9372.  108(114)
• Lund, Diderik (1997). Usikre investeringer ved ulike grader av diversifisering. Vis sammendrag

  Notatet drøfter hvordan enkelt-aktører vil vurdere usikre investeringer når de maksimerer forventet nytte og kjenner sannsynlighetsfordelinger for de usikre variablene. Det utledes et investeringskriterium, først for det generelle tilfellet der bare deler av aktørenes framtidige usikre inntekter kommer fra en fritt sammensatt portefølje. En aggregert sammenheng for hele økonomien beskriver forventet avkastning på investeringer. Et spesialtilfelle framkommer når alle aktører bare har usikre inntekter fra fritt sammensatte porteføljer. Dette er Kapitalverdimodellen, kjent fra Sharpes, Lintners og Mossins arbeid på 60-tallet. Notatet er en bearbeidet versjon av en artikkel i tidsskriftet Beta, årg. 7, hefte 2.

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