Three essays in dynamic economic analysis [Elektronische Ressource] / vorgelegt von Sebastian Scholz

Sebastian.Scholz

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• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2009
• Nombre de lectures: 17
• Langue: English

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Three Essays in Dynamic Economic
Analysis
Inaugural-Dissertation
zur Erlangung des Grades
Doctor oeconomiae publicae (Dr. oec. publ.)
an der Ludwig-Maximilians-Universität München
2009
vorgelegt von
Sebastian Scholz
Referent: Prof. Ray Rees
Korreferentin: Prof. Dr. Monika Schnitzer
Promotionsabschlussberatung: 19. Mai 2010Contents
Preface 1
1 Learning and Technology Adoptions 5
1.1Introduction................................. 5
1.2TheModelwithanexogenousinnovationdate.............. 8
1.2.1 TheSocialPlanner’sProblem................... 8
1.2.2 TheMonopolist’sProblem..................... 13
1.2.3 Apartialcomparativeanalysis 16
1.2.4 A di fferentinnovationcostfunction................ 20
1.3Themodelwithanendogenousinnovationdate............. 20
1.3.1 Analyticalpart........................... 20
1.3.2 Numericalpart........................... 23
1.4 More on welfare e ffects 27
1.5Conclusion.................................. 30
Appendix to Chapter 1 34Contents ii
12 Optimal Fertility Decisions in a Life-Cycle Model 44
2.1Introduction................................. 4
2.2 The Baseline Model............................. 46
2.2.1 Solvingthemodel.......................... 50
2.2.2 Theoptimalityconditionforthetimingofchildbirth...... 54
2.2.3 Theoptimalityconditionforthenumberofchildren....... 56
2.2.4 Results................................ 58
2.3 Extension A: Divorce............................ 61
2.3.1 Step 1: The Optimal Plan before and after Divorce known to
occur at time d............................ 62
2.3.2 Step 2: The optimal plan before an unknown date of divorce . . 65
2.4ExtensionB:Divorce,anumericalsimulation.............. 67
2.5Conclusions................................. 71
1This chapter is a joint work with Ray Rees.Contents iii
3 Derivatives and Default Risk in the Electricity Market 72
3.1Introduction................................. 72
3.2Forwards..... 7
3.2.1 Pre-liberalizationperiod...................... 77
3.2.2 Postliberalizationperiod 80
3.2.3 Results........... 85
3.3Options................................... 90
3.3.1 Pre-liberalizationperiod 92
3.3.2 Postliberalizationperiod...................... 96
3.3.3 Results................................ 98
3.4Conclusion.... 99
Bibliography 101List of Figures
1.1Costatesjumpatthedateofinnovation................. 18
1.2 Benefitsandcostsofdelayinginnovation 2
1.3Acomparativeanalysis,whenalvariablesareendogenous....... 26
1.4 Comparative statics with y( T)beingexogenouslydetermined...... 28
1.5 Welfare e ffectsofgovernmentinterventions................ 31
1.6Exchangingvariables............................ 39
2.1Theperperiodincomeoveralife-cycle................... 49
2.2 The co-states of phase two, when a divorce does not occur and when it
does for a known and an unknown d.................... 67
3.1 The e ffect of s on α, expected welfare and profits............ 87
3.2Whenrenegotiationsormergersarepreferable.............. 89
3.3Welfare:Forwardsvs.Options....................... 98List of Tables
2.1 Functional forms.............................. 58
2.2 How the optimal number of children and the timing is a ffected by the
underlyingparameters............................ 59
2.3 The e ffect of divorce related parameters on the variables of the model . 70
3.1Welfareintheabsenceofbankruptcy................... 96Preface
Still, intuitiveassumptionsaboutbehaviorisonlythestartingpointofsystematicanaly-
2sis, for alone they do not yield many interesting implications.
This dissertation consists of three self-contained chapters that are contributions to
the fields of industrial organization, family economics, and energy economics. Each
chapter has its own introduction and can be read independently of the other two
chapters.Althreechaptershavethecommontheme“dynamicoptimization”ofeither
an individual’s or firm’s objective. The first two chapters apply the tools of optimal
control theory to study di fferent aspects of learning and timing, one in the field of
industrial organization, the other in family economics.
The first model studies the optimal timing for a firm to adopt a new technology.
Infant industries have often rendered positive externalities, which justify subsidies.
Examples can be found in the renewable energy sector; these technologies not only
provide electricity to their owners, but they also reduce the carbon dioxide content in
the atmosphere. Thus, it is in the public’s interest to support this sector, such that it
can reduce its costs to a level where it can compete with conventional, C0 emitting2
technologies. A policy that has been implemented by governments throughout the
worldtoreducethecostlevel, istoeithersubsidizetheresearchofthesetechnologiesor
theirdistribution. Till thisdaythe economic literature lacks a model that canevaluate
these instruments in a suitable way, allowing predictions of their e ffects on consumer
andproducersurplus, andwelfareingeneral. Chapter1demonstrateshowgovernment
interventions can a ffect the optimal timing for adoption of a new technology. The
timing increases positive externalities, as for example in the renewable energy field.
It is not only relevant that renewable energy technologies reach a low cost level in
the future, it is also important to know how many products are distributed before
this future date is reached. In addition, the timing of distribution matters. Imagine
2Gary Becker (Nobel laureate in Economics, 1992)Preface 2
there are two production plans for distributing solar panels, where both reach the
same cost level at a distant date in the future with the same number of solar panels
installed. Then the production plan, according to which distribution is larger in the
beginning, is preferred to one, where distribution takes place later, because the first
more greatly reduces the amount of carbon dioxide being released in the atmosphere.
Furthermore this first chapter makes predictions on how the e ffects change, when the
total quantity that can be produced is fixed; the installations of wind powered energy
plants in Germany exemplify this point. Onshore, there have only been a few new
instalments of wind power plants lately, because of a lack of suitable space. Sales and
research subsidies have a very di fferent e ffect in this case, when the total production
quantity is not endogenous. Depending on whether producer rents, consumer rents or
early implementation are more important to the government, the chapter o ffers the
appropriate tools to attain its objective.
The second model analyzes the optimal timing for a woman to give birth. Malthu-
sianism has become a widely used term, one that stems from the paper ‘Essay on the
Principle of Population’ written by the infamous Thomas Malthus. He is one of the
main founders of population economics; forecasting that population growth would ulti-
matelyoutstriptheworld’sfoodsupplyin1798. WiththeimmigrationtotheAmericas
andIndustrialization,theargumentsofhisessaybecamequicklyneutralized. AsIndus-
trialization advanced on the world, fertility began to stagnate and then to the surprise
of many avid Malthusians, recede.
Startingintherichercountries,fertilityfirstbegantofallinindustrializedcountries.
Withinthelastdecadesithasfinallybecomepossibletoseeadeclineingrowthratesin
thedevelopingworld,astheyslowlyhavebecomericher.Whatisastonishingisnotonly
the rate at which this is happening but the scale of the decline. Developing countries
are changing so rapidly that the demographic transition has become one of the largest
social changes taking place. An example of this is Iran, in 1984 the fertility rate was
still relatively high at 7 children, in 2006 is had dropped to 1.9. With the worldwide
debate over the threats and solutions to climate change larger than ever before, the
Maltusian worries are resurfacing. Fears of a growing, richer, more consumer driven
population have steered economists to take a closer look at population growth. With
fertility rates falling in India, Brazil and Indonesia, the fertility rate has now reached
the replacement rate of 2.1 in half of the world. The trepidation of the environmental
impact due to high fertility can, at least for now, be negated.
A decrease of fertility along with a longer life expectancy, leads to an increasePreface 3
in the proportion of people that are retired compared to those that are working. A
pay-as-you-go (PAYG) social security system is characterized by contributions to their
beneficiaries, financed through the regular payment flows of working individuals, such
that reserves do not need to be created. If a fall in fertility occurs too quickly, then
aPAYGfinanced pension system could collapse. Retired people generally have ac-
cumulated own savings, but these are often insu fficient to cover the entire retirement
phase if the share of the working population is relatively too low. Fewer people being
born means, there is less income during those periods, when they would have been
contributing on the job market. Lower old age pensions mean that the society’s wel-
fare decreases. In most pension systems there is no coherence between fertility and
pensions. Chapter two evaluates government policies that increase the incentive to
have children in order to smooth the digression of fertility.
This chapter is a joint work with Ray Rees, and contains a