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Essays on International Trade, Growth and the Environment

Permanent Link: http://ufdc.ufl.edu/UFE0042360/00001

Material Information

Title: Essays on International Trade, Growth and the Environment
Physical Description: 1 online resource (94 p.)
Language: english
Creator: Levy, Ting
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: development, economic, environment, environmental, firm, international, monopolistic, sustainable, technology, trade
Economics -- Dissertations, Academic -- UF
Genre: Economics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The relationship between environmental degradation and economic growth has been central to the debate over sustainable growth. The first chapter uses utility growth as an index of sustainable growth, which is positively related to economic growth and negatively related to environmental degradation. Skilled and unskilled labor are used in this economy and the population is growing over time generating growth without scale effects. The pollution growth rate is higher in a decentralized economy, whereas the sustainable growth rate is higher in an economy with a social planner. An increased rate of population growth is associated with a higher sustainable growth rate in both economies. A higher share of skilled labor is associated with a higher sustainable growth rate in a decentralized economy. A simple monopolistic competition model is developed to examine the impact of environmental standards upon firms' profitability, pollution and consumers' welfare. There is a continuum of firms and each firm produces a variety with different environmental quality. The second chapter shows that when regulators impose a more stringent environmental standard, there will be fewer firms in the market at the steady-state equilibrium; firms' average profits will be higher as competition will be less intense; and the overall effect on the welfare of consumers will be ambiguous because the effect on pollution generated is unclear. In addition, an optimal standard is calculated under Pareto distribution and the factors which affect the optimal standard are discussed. The third chapter develops a trade model to examine the impact of trade liberalization upon firms' profitability, pollution and consumers' welfare. Firms with high levels of environmental quality export, whereas firms with low levels of environmental quality only serve the domestic market. An increase in the number of trading partners raises the cutoff export environmental quality; a reduction in foreign market entry costs reduces the cutoff export environmental quality; and a reduction in per-unit trade costs reduces the cutoff export environmental quality. A more stringent environmental standard increases successful firms' revenues and profits. Due to trade liberalization, firms that only serve the domestic market make lower revenues and profits; firms that are able to export will increase their sales to foreign countries, compensating for their loss from domestic sales and making overall revenues higher. Trade liberalization ultimately increases aggregate consumption.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ting Levy.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Dinopoulos, Elias.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042360:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042360/00001

Material Information

Title: Essays on International Trade, Growth and the Environment
Physical Description: 1 online resource (94 p.)
Language: english
Creator: Levy, Ting
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: development, economic, environment, environmental, firm, international, monopolistic, sustainable, technology, trade
Economics -- Dissertations, Academic -- UF
Genre: Economics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The relationship between environmental degradation and economic growth has been central to the debate over sustainable growth. The first chapter uses utility growth as an index of sustainable growth, which is positively related to economic growth and negatively related to environmental degradation. Skilled and unskilled labor are used in this economy and the population is growing over time generating growth without scale effects. The pollution growth rate is higher in a decentralized economy, whereas the sustainable growth rate is higher in an economy with a social planner. An increased rate of population growth is associated with a higher sustainable growth rate in both economies. A higher share of skilled labor is associated with a higher sustainable growth rate in a decentralized economy. A simple monopolistic competition model is developed to examine the impact of environmental standards upon firms' profitability, pollution and consumers' welfare. There is a continuum of firms and each firm produces a variety with different environmental quality. The second chapter shows that when regulators impose a more stringent environmental standard, there will be fewer firms in the market at the steady-state equilibrium; firms' average profits will be higher as competition will be less intense; and the overall effect on the welfare of consumers will be ambiguous because the effect on pollution generated is unclear. In addition, an optimal standard is calculated under Pareto distribution and the factors which affect the optimal standard are discussed. The third chapter develops a trade model to examine the impact of trade liberalization upon firms' profitability, pollution and consumers' welfare. Firms with high levels of environmental quality export, whereas firms with low levels of environmental quality only serve the domestic market. An increase in the number of trading partners raises the cutoff export environmental quality; a reduction in foreign market entry costs reduces the cutoff export environmental quality; and a reduction in per-unit trade costs reduces the cutoff export environmental quality. A more stringent environmental standard increases successful firms' revenues and profits. Due to trade liberalization, firms that only serve the domestic market make lower revenues and profits; firms that are able to export will increase their sales to foreign countries, compensating for their loss from domestic sales and making overall revenues higher. Trade liberalization ultimately increases aggregate consumption.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ting Levy.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Dinopoulos, Elias.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042360:00001


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1 ESSAYS ON INTERNATIONAL TRADE, GROWTH AND THE ENVIRONMENT By TING LEVY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Ting Levy

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3 To my family -Without their love and support none of this would have been possible.

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4 ACKNOWLEDGMENTS Many people have contributed to the completion of this dissertation. First and foremost I acknowledge my advisor, Elias Dinopoulos, for his help and guidance with my research. He has always encouraged me and led me in the right direction. He has always been interested in my ideas and available to guide me. I am grateful for his motivation, patience, support and incredible knowledge in this field. Without his help, this dissertation would not be possible. I would like to thank my graduate committee, Chunr ong Ai, David Denslow, James Seale and Douglas Waldo. They have been very helpful with my research and gave me great guidance and advice. I am indebted to my parents Chuan Tu and Peiming Dong They never los t faith in me and always were there to support m e. I would like to thank them for their unconditional love. I also want to thank my inlaws, Andrea and Stanton Knoller and Rosalind Bodow. Last but not least, I would like to thank my husband Eric Levy for his love and support and my son Joshua Levy for b eing the sunshine of my life.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF FIGURES .......................................................................................................... 7 ABSTRACT ..................................................................................................................... 8 CHAPTER 1 IS POPULATION BAD FOR THE ENVIRONMENT ................................................ 10 Introduction ............................................................................................................. 10 The Model ............................................................................................................... 12 Overview .......................................................................................................... 12 Consumers and Workers .................................................................................. 13 Manufacturing ................................................................................................... 15 Total Factor Productivity ................................................................................... 15 Pollut ion Abatement ......................................................................................... 16 Sustainable Growth .......................................................................................... 18 The Decentralized Economy ................................................................................... 19 First Best Solution .................................................................................................. 23 SecondBest Outcomes .......................................................................................... 30 Conclusions ............................................................................................................ 33 Algebraic Details ..................................................................................................... 33 Market Equilibrium Solution .............................................................................. 33 The First Best Solution ..................................................................................... 34 The SecondBest Solution ................................................................................ 35 Compar at ive Statics ......................................................................................... 36 2 HETEROGENEOUS POLLUTERS AND ENVIRONMENTAL STANDARDS ......... 38 Introduction ............................................................................................................. 38 The Model ............................................................................................................... 42 Consumers ....................................................................................................... 42 Firms ................................................................................................................ 45 Entry Decisions ................................................................................................ 48 Aggregation ...................................................................................................... 49 Free Entry and the Value of the Firms .............................................................. 51 Welfare ................................................................................................................... 54 Parameteri zation and the Optimal Standard ........................................................... 56 Conclusions ............................................................................................................ 59 Algebraic Details ..................................................................................................... 60 Proof of Lemma 2 1 .......................................................................................... 60 Proof of ( 2 23) ( 2 24) and ( 2 25) ..................................................................... 61 Proof of Proposition 2 1 .................................................................................... 61

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6 3 TRADE, POLLUTION AND ENVIRONMENTAL STANDARDS .............................. 63 Overview ................................................................................................................. 63 The Model ............................................................................................................... 63 Consumers ....................................................................................................... 63 Firms ................................................................................................................ 66 Entry D ecision s ................................................................................................ 69 Aggregation ...................................................................................................... 72 Free Entry and the Value of the F irms .............................................................. 74 Steady State E quilibrium .................................................................................. 75 Pollution and Welfare .............................................................................................. 78 The Impact of International Trade ........................................................................... 80 Conclusions ............................................................................................................ 81 Algebraic Details ..................................................................................................... 82 Proof of Lemma 3 1 .......................................................................................... 82 Proof of the aggregate vari ables (332), (3 33) and (334) ............................... 84 Proof of (3 42 ) .................................................................................................. 85 Proof of Proposition 3 2 .................................................................................... 86 Proof of Proposi tion 3 3 .................................................................................... 86 LIST OF REFERENCES ............................................................................................... 90 BIOGRAPHICAL SKETCH ............................................................................................ 94

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7 LIST OF FIGURES Figure page 3 1 Effect of an increase in the environmental standard ...................................... 89

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8 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ESSAYS ON INTERNATIONAL TRADE, GROWTH AND THE ENVIRONMENT By Ting Levy December 2010 Chair: Elias Dinopoulos Major: Economics The relationship between environmental degradation and economic growth has been central to the debate over sustainable growth. Th e first chapter uses utility growth as an index of sustainable growth, which is positively related to economic growth and negatively related to environmental degradation. S killed and unskilled labor are used in this economy and the population is growing over time generating growth without scale effect s. The p ollution growth rate is higher in a decentralized economy whereas the sustaina ble growth rate is higher in an economy with a social planner. An increased rate of population growth is associated with a higher sustainable growth rate in both economies A higher share of skilled labor is associated with a higher sustainable growth rate in a decentralized economy. A simple monopolistic competition model is developed to examine the impact of environmental standards upon firms' profitability, pollution and consumers' welfare. There is a continuum of firms and each firm produces a variety with different environmental q uality. The second chapter shows that when regulators impose a more stringent environmental standard, there will be fewer firms in the market at the steady state equilibrium; firms' averag e profits will be higher as competition will be less intense;

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9 and th e overall effect on the welfare of consumers will be ambiguous because the effect on pollution generated is unclear. In addition, an optimal standard is calculated under Pareto distribution and the factors which affect the optimal standard are discussed. T he third chapter develops a trade model to examine the impact of trade liberalization upon firms' profitability, pollution and consumers' welfare. Firms with high level s of environmental quality export, whereas firms with low level s of environmental qualit y only serve the domestic market. An increase in the number of trading partners raise s the cutof f export environmental quality; a reduction in foreign market entry costs reduces the cutoff export environmental quality; and a reduction in per unit trade cos ts reduces the cutoff export environmental quality. A more stringent environmental standard increases successful firms' revenues and profits Due to trade liberalization, firms that only serve the domestic market make lower revenues and profits; firms that are able to export will increase their sales to foreign countries, compensating for their loss f rom domestic sales and making overall revenues higher. Trade liberalization ultimately increases aggregate consumption.

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10 CHAPTER 1 IS POPULATION BAD FO R THE ENVIRONMENT Introduction Can the pursuit of economic growth cause the world to come to an end? Are we paying t oo much attention to productivity, while ignoring the damage to our natural resources? Alternatively, can economic growth be the driving force behind improvements in our environmental quality and standards of living? The relationship between environmental degradation and economic growth has been central to the debate over sustainable growth1. This paper builds upon Byrnes (1997) threesector endogenous growth model where technology is the engine of growth and pollution could be abated. It compares optimal solutions in a decentralized economy (equilibrium) with an economy with a social planner (first best). Using utility growth as an index of sustainable growth, it captures the interaction between economic growth and environmental degradation. Similar to th e outcome demonstrated by Byrne, o ptimal pollution control reduces the pollution growth rate without necessarily lessening economic growth. However, Byrnes paper suffers a scaleeffects problem. The rate of technological progress is assumed to be proport ional to the level of Research and Development ( R&D) inputs. For example, if R&D inputs are doubled, the growth rate of technological progress also will double. This scale related characteristic implies that an economys long run per capi ta growth rate increases in proportion to the population. In the presence of positive population growth, 1 The m ost commonly used definition of sustainable development is given in the Brundtland Report (1987) it defines sustainable development as development that meets the needs of the present without compromising the ability of future generations to meet their own needs.

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11 the scaleeffects characteristic implies that the per capita growth rate increases exponentially over time, becoming infinite in steady state equilibri um.2 The model presented in this paper assumes that labor is the only factor of production in the economy and that population is growing at a positive rate. This paper has important policy implications. By introducing exogenous population growth, it asks whether sustainable growth is possible with a growing population. Further, it shows the need f or the government to put effort into pollution abatement activities and to set limits on economic growth to ensure a sustainable growth rate. Since skilled labor and unskilled labor are distinguished, this paper also sheds some light on the impact of education and skilled labor migration on the sustainable growth path. The impact of population growth on sustainable growth has been debated intens ely. Pessimists bel ieve that a growing population is one of the greatest threats to the environment and the natural resource base. In An essay on the principal of population Malthus (1798) expresses concerns about a possible tendency of human populations to grow more rapi dly than can be accommodated by arable land and other components of the resource base. This tendency would sow the seeds of human self decline. Malthus further suggested that increases in fertility would tend to offset the underlying output increase. Brander (2007) suggests that continued demographic transition to lower fertility is the primary requirement for achieving sustainable growth. High population growth rates can dissipate the surplus that might otherwise support investment in R&D. Optimists, such as Boserup (1981) and Simon (1981) propose the induced innovation hypothesis that population growth itself induces more rapid 2 See Jones (1995a, 1995b) for further discussion of scaleeffects property.

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12 technological pressures. As population increases, more pressure is placed on the existing agricultural system, stimulating inven tion. Kremer (1993) additionally suggested that very long run time series evidence (from 1 Million B.C. to 1990) was consistent with this induced innovation hypothesis. Barbier (1998) develops an endogenous growth model with resource scarcity and populat ion growth to explore balanced gr owth properties. Barbier assumes that resource availability constrains the supply of innovation, and concluded that it is still possible to achieve a long run growth of per capita consumption while avoiding resource exhaust ion. Pender (1998) employs a neoclassical growth model, using capital and natural capital as inputs to production. He found that population growth had a positive impact on investment in renewable resources and other forms of capital and a negative impact o n per capita production and consumption (based on the assumption of constant or decreasing returns to scale production function). This chapter argues that higher population growth could lead to a higher sustainable growth rate under certain conditions. Whe n the population grows at a higher rate, benefits from innovation are greater (creating economic incentives to innovate) and sustainable growth may be achieved. The Model Overview The standard optimal control techniques are used to solve the utility maximization problems of a representative infinitely lived consumer and compare the market equilibrium growth path with the efficient growth path. Labor is the only factor in this econom y which is growing at an exogenous rate n and is partitioned into two distinct

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13 types: skilled labor which is denoted by () Ht and unskilled labor which is denoted by () Lt Labor can be employed in three activities (sectors): manufacturing which uses both skilled and unskilled workers, produces goods for consumption and generates pollution emissions during the production process; R&D which uses only skilled labor is pollution neutral; and pollution abatement which uses both skilled and unskilled labor reduces pollution emissions. Both skilled labor and unskilled labor are assumed to be perfectly and costlessly mobile across sectors. Consumers and Workers I model consumers as dynastic households with infinitely lived members. In this economy, there is a fixed unit length measure of identical households who provide labor services. Each individual member of a household lives forever and is endowed with either one unit of skilled labor or one unit of unskilled labor, which is supplied inelastically to the labor market. The size of each household, measured by the number of its members, grows exponentially at a fixed positive rate n which is the population g rowth rate. Normalizing the initial size of each household to unity assuming each household is endowed with S share of skilled labor and 1 S share of unskilled labor, the number of household members at time t is given by nte Assume H and L are the initial number of skilled and unskilled labor in this economy, let ()ntHtHe denote the supply of skilled

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14 labor at time t, ()ntLtLe denote the supply of unskilled labor and ()()()ntNtNeHtLt denote the aggregate supply of labor3. Therefore, at any time t, both the skilled labor share ( S ) and the unskilled labor share ( 1 S ) are constant in each household and in the whole economy, depending on their initial endowment shares respectively: () ()nt ntHtHeH S NtNeN (1 1) and, () 1 ()nt ntLtLeL S NtNeN (1 2) Denote skilled labor in manufacturing, R&D and pollution abatement as MH, AH and ZH respectively. Further, denote unskilled labor in manufacturing and pollution abatement as ML and ZL. Then the full employment conditions are given as MAZHHHH and MZ LLL Divide both sides of these two equations by the total population () Nt we can get MAZHHH H NNNN and MZLL L NNN Thus, the full employment conditions can be rewritten as: MAZShhh (1 3) and, 1MZSll (1 4) where the lower case h and l denote the per capita skilled and unskilled labor. 3 I have assumed that both skilled and unskilled labors are growing at the same rates as the total population simply because the model does not have steady state equilibri um if the growth rates differ.

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15 Manufacturing Firms in the m anufacturing sector hire skilled labor MH and unskilled labor ML to produce a single final good () Yt A ll output is consumed at each point in time: 1()()()MMYtCtAtHL (1 5) w here () Ct is the instantaneous consumption and () At is the level of technology at time t Per capita consumption expenditure () ct can be expressed as: 1 1() ()() () () ()()()MM MMAtHL CtYt ct Athl NtNtNt ( 1 6) where Mh and Ml are the per capita skilled and unskilled labor respectively. As Byrne (1997) states, this structure has no technological spillovers, and thus, highlights the effect of the pollution externality. Without an environmental externality, the competitive equil ibrium will be optimal growth. Any divergences between the efficient and equilibrium paths are therefore due to the environmental externality. Total Factor Productivity As in equation (15), technology is one of the inputs of production. In the R&D sector only skilled labor can be used to discover new technology and innovate. T here is no depreciation of technology and R&D is pollution neutral, which means, in the innovation process, skilled labor does not generate any pollution. The evolution of total fac tor productivity is governed by the following knowledge production function: () () ()()A AHt At g AtXt ( 1 7) where Ag denotes the growth rate of technology, ()AHt is skilled labor devoted to R& D activities and () Xt is a measure of R&D difficulty. Higher v alue of () Xt implies tha t the

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16 same number of skilled workers generates a lower growth rate of technology4. Assumptions that govern the evolution of () Xt play a crucial role in regulating the scaleeffects property and in conditioning the nature of long run Schumpeterian growth. Following the variety expansion approach5, I assume that aggregate R&D difficulty is directly proportional to the number of varieties and the production of () Xt does not require any economic resources Under the right market structure assumptions (profit maximization and market driven free entry of monopolistically competitive firms) it can be shown that the number of varieties is directly proportional to the level of the economys population6: ()() XtNt ( 1 8) where is an inconsequential parameter. Substituting equation (18) into equation (17) yields : ()() () ()()()AAA AHtHth At g AtXtNt ( 1 9) where Ah is per capita skilled labor devoted to R&D activities. Pollution Abatement The presence or absence of the pollution abatement sector is the key to whether we can lower pollution, support ongoing growth and provide reasonable predictions for 4 Segerstrom (1998) was the first study to introduce variable X(t) in the knowledge production function of a scaleinvariant Schumpeterian growth model based on quality improvements. 5 Peretto (1998) introduc ed the variety expansion approach where vertical product differentiation takes the form of process innovations Young (1998) also introduced the variety expansion approach where vertical product differentiation is modeled as quality improvements. Aghion and Howitt (1998, Chapter 12), D i nopoulos and Thompson (1998) and Howitt (1999) have developed further this approach. 6 This linear relationship between the number of varieties and the level of population can be derived from market based mechanism s with solid micro foundations. See Dinopoulos and Sener (2007) for more details

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17 the costs of pollution control. Following Byrne (1997), I assume that pollution stock () Zt is growing at a rate Zg which takes the following form: 1 12() ()Z MMZZZt ghlhl Zt (1 1 0) According to equation (110), e missions are the byproduct of the manufacturing process and are directly caused by per capita skilled labor Mh and unskilled labor Ml devoted to production. I assume that the growth rate of the pollution stock rise s linearly in per capita skilled and unskilled labor in manufacturing and is not affected by the current level of technology Parameters 1 and 2 measure the dirtiness of the production process in manufacturing and can be thought of as pollution intensities H igher values of parameters 1 and 2 are associated with higher rates of pollution for any given amount of per capita skilled and unskilled labor. In addition, if 1 is greater (lower) than 2 then additional skilled (unskilled) labor is more p olluting The last term of equation (110) represent s the pollution abatement technology. The p resence of an explicit pollution abatement sector allows for greater flexibility in the tradeoffs between production and environmental degradation. Emission abatement activities also depend on per capita skilled labor Zh and unskilled labor Zl with the precise dependence captured by a CobbD ouglas function. Parameter measures the effectiveness of the abatement process and can be thought of as a fixed level of abatement technology.7 7 For future research, an abatement R&D sector can be included to relax this fixed abatement technology

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18 Sustainable Growth The intertemporal utility of a representative household is defined as () 0ln()ntUevtdt ( 1 11) where is the subjective discount rate. T he greater is the less the consumer values future consumption relative to current consumption. n is the population growth rate. n is the effective discount rate, which must be greater than zero. () vt is the instantaneous utilit y function which depends on per capita consumption expenditure () ct and on the pollution stock () Zt at time t: ()()() vtctZt ( 1 12) where parameter represents the relative utility of consumption and pollution8. The sustainable growth rate is defined as the long run rate of growth of per capita instantaneous utility, which takes into account the growt h rates of both consumption and the pollution stock : ()() ()()uvctZt g vctZt ( 1 13) The sustainable growth rate is affected positively by growth in consumption and neg atively by growth in pollution emissions. There is a tradeoff between economic growth and pollution abatement since limited resources have to be allocated between them. 8 Parameter will likely be different among countries and captures different preferences for a clean environment in a society. Developed countries tend to care more about the environment they are living in, i.e., is higher; Developing countries worry more about their econo mic growth, so they will put less emphasis on pollution, i.e., is lower.

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19 The Decentralized Economy Since pollution is modeled as a negative externality, households will take the aggregate pollution stock as given, denoted by () Zt, and h ouseholds have no incentive to put their efforts in to emission reduction activities Thus, in the absence of government interv ention, no pollution abatement is undertaken, 0ZZHL Emissions are unabated; the growth of pollution stock only depends on the per capita skilled labor devoted to the manufacturi ng sector and the aggregate per capita unskilled labor, t hu s the growth rate of pollution emissions is always positive: 12()()Z MMZt ghl Zt ( 1 14) Each household maximizes the following lifetime utility: () 0[ln()ln()]ntUectZtdt ( 1 15) subject to the following constraints: 1()()MMctAthl ( 1 16) ()()/AAtAth ( 1 17) MAShh ( 1 18) and, 1mSl ( 1 19) In this decentralized economy, s killed labor is divided between manufacturing and technology improvement, while unskilled labor is used only in the manufacturing sector.

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20 A t the steady state equilibrium the allocation of per capita skilled labor in the manufacturing sector, 0 Mh and the R&D sector, 0 Ah the growth rate of technology, 0 Ag the growth rate of pollution stock, 0 Zg and the sustainable growth rate of this economy, 0 ug are all constant and given by (derivation shown in Algebraic Details ): 0()Mhn ( 1 20) 0()AhSn ( 1 21) 0()AS gn ( 1 22) 0 12()(1)ZgnS ( 1 23) a nd, 0 12()()(1) u S gnnS ( 1 24) If the share of skilled labor in the population S is less than () n all the skilled labor will be devoted to the manufacturing sector, no technology improvement is undertaken, 00Ah and there is no economic growth in this decentralized economy. Since all individuals take pollution as given and do not abate emissions, the growth rate of pollution emissions is always positive and the sustainable growth rate is always negative. Equation ( 1 2 4) leads to the following proposition which establishes the existence of long run sustainable growth. Proposition 1 1 : In a decentralized economy the long run sustainable growth rate is positive if and only if : 12 2()(1) 1 n S ( 1 25)

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21 Condition ( 1 25) holds for a sufficiently high amount of skilled labor. Therefore, if a decentralized economy has a large skilled labor share S the disutility from the increasing pollution is outweighed by the g ains to technology accumulation. T his allows for a positive sustainable long run growth rate. However if the skilled labor share S is not large enough, there will either be no technology accumulation or the positive utility from technology accumulation will be dominated by the disutility from the increasing pollution. In this case, the sustainable growth rate is negative. Propositi on 1 2: If condition ( 1 25) holds, then a decentralized economy with a higher rate of populat ion growth experiences a higher rate of technological progress, a lower growth rate of pollution and a higher sustainable growth rate. The intuition behind propos ition 1 2 is as follows : i n this decentralized economy, both skilled and unskilled labor are growing at the same rate as population growth, therefore the shares of skilled and unskilled labor must always be constant. If population is growing at a higher rate, all unskilled labor will still work in the manufacturing sector. However, skilled labor will move to the R&D sector from the manufacturing sector, leading to a higher technology growth rate. The growth rate of pollution depends on the shares of skilled and unskilled labor in manufacturing S ince higher population growth reduces the share of skilled labor in manufacturing without affecting the share of unskilled labor in manufacturing, the growth rate of pollution decreases. Higher technology growth and lower pollution growth lead to higher long run s ustainable growth. Thus contrary to popular beliefs, population growth is good for the environment.

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22 Proposition 1 3 : In the decentralized economy, a higher skilled labor share will increase the technology gr owth rate and lower the pollution growth rate, leading to a higher long run sustainable growth rate. Changes in the endowments of skilled and unskilled labor have exactly opposite effect s on sustainable growth. By assumption, for any given endowment of total population, a higher skilled labor endowment leads to a higher share of skilled labor, S Notice that the skilled labor share in the manufacturing sector, 0 Mh is constant ( 0 Mh depends only on the parameters due to the CobbDouglas production function) therefore the additional skilled labor will be absorbed by the R&D sector which leads to a higher technology growth rate Ag At the same time, t he dec line in unskilled labor will lead to a lower pollution growth rate even without any abatement activity These two changes will lead to a higher long run sustainable growth Proposition 1 3 highlights the importance of education and migration. If a country can devote more resources to education or allow more skilled immigrants to increase its skill abundance, it can achieve higher long run sustainable growth. Therefore, both education and immigration of skilled labor are utility growth improving .9 Parameter captures the complexity and difficulty of R&D technology. An increase in this parameter means that it is more difficult to develop new technolog y, using the same amount of per capita skilled labor. This will lead to a lower growth rate of technological progress. Some skilled labor will move from the R&D sector to the manufacturing sector resulting in a lower technology growth rate, a higher pollution growth rate and a lower long run sustainable growth rate. 9 Notice that if the unskilled labor share increases, per capita output and consumption at any point in time will increase, but it is a level effect. The rate of growth of final goods production will decrease over time.

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23 Paramet er captures the productivity of skilled labor in manufacturing. A higher value of implies that skilled labor will move from R&D to manufacturing. This shift will generate a level effect resulting in higher per capita output and co nsumption. However, in the long run, the per capita output growth rate will be lower and the pollution growth rate will be higher. The same effects occur when consumers care more about current relative to future consumption (i.e., have a higher subjective discount rate ) S killed labor will shift from R&D to manufacturing to produce more output for current consumption at the cost of a lower long run sustainable growth rate. Parameters 1 and 2 capture the pollution intensity associated with skilled and unskilled labor employed in manufacturing. Different levels of 1 and 2 will not affect the allocation of labor or the economic growth rate; however, higher levels of 1 and 2 will lead to a higher pollution growth rate, and in turn lower the sustainable growth rate. If 1 and 2 are too high, that can even lead to a zero long run sustainable growth rate. First Best Solution In this section, I explore the bal anced growth properties of the model when all allocation decisions are made by a benevolent social planner. Suppose the social planner takes care of the pollution externality and optimally allocates skilled labor among three activities: manufacturing, technology improvements and pollution abatement. Unskilled labor is divided between the manufacturing s ector and the pollution abatement sector. The first best solution can be obtained by ass um ing that the social planners objective is to maximize the discounted utility of a representative household:

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24 () 0[ln()ln()]ntUectZtdt ( 1 26) subject to, 1()()MMctAthl ( 1 27) ()()/()A Ah AtAtHXtA ( 1 28) 1 12() ()MMZZZthlhlZt ( 1 29) and two full employment conditions MAZShhh ( 1 30) 1MZSll ( 1 31) In this economy, all output from production is consumed at the same time and technology improvement depends on the per capita skilled labor devoted to the R&D sector These conditions are exactly the same as in the decentralized economy. The only difference between the first best and decentralized economy solutions is that the social planner takes into account the environmental externality which in turn affects the pollution and sustainable growth rates. At the first best steady state solution the allocation of per capita skilled and unskilled labor in the manufacturing sector, Mh Ml R&D sector, Ah and the pollution abatement sector, Zh Zl are all constant and given by ( derivation shown in Algebraic Details ): 2 1 1() () 1Mn hn ( 1 32)

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25 1 2()(1) [(1)()]Mn l ( 1 33) 1 1 2 1 1 1 1 1 2() ()(1)() () (1)() 1 [(1)()]An n hSn S ( 1 34) 1 1 1 1 1 2()(1)() (1)() [(1)()]Zn hS ( 1 35) and, 1 2()(1) 1 [(1)()]Zn lS ( 1 36) In the first best solution, skilled and unskilled labor can be allocated to abate pollution. In the manufacturing sector, both skilled and unskilled labor shares are positive and in general are less than or equal to the decentralized economys shares of both types of labor. The first best level of per capita skilled labor in the production of final goods (given by equation ( 1 32)) is less than that of the decentralized economy (given by equation ( 1 20)). The difference between the first best level and the decentralized equilibrium level of per capita skilled labor is captured by the last term in equation ( 1 32) which is related to the environmental externality. As the relative disutility of pollution falls, both per capita skilled and unskilled labor in manufacturing increase towards the equilibrium level. Notice in the trivial case when approaches zero, the first best solution is identical to the equilibrium solu tion. In the R&D sector and the pollution abatement sector, whether the shares are positive or negative depends on the skilled labor share S and the unskilled labor share 1 S Only when

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26 1 2()(1) 1 [(1)()] n S will skilled labor and unskilled labor be alloc ated to the pollution abatement sector So if the initial unskilled labor share 1 S is low, or unskilled labor is not so polluting ( 2 i s low), or the disutility of pollution ( ) is low or some policy restraints are binding, then the social planner may not allocate resources to abate pollution at all This situation where pollution is not abated at all happens un der certain condi tions. For example, when the initial skilled labor share S is large enough, there is no need to abate the pollution in this economy since the output growth will outweigh the negative effect of pollution. Lower prod uctivity of unskilled labor in manufacturing (measured by 1 ), higher productivity of unskilled labor in pollution abatement (measured by 1 ) and more effective abatement activity (higher ) will make abatement activity more likely. Proposition 1 4 : The growth rate of technology Ag in the first best solution cannot be ranked against the decentralized equilibrium growth rate 0 Ag : *0 AAgg The growth rate of pollution in the first best solution is below its decentralizedequilibrium level: *0 ZZgg The sustainable growth rate in the first best solution is unambiguously higher than the decentralizedequilibrium sustainable growth rate: *0 uugg The growth rate of technology in the first best solution is given by: 11 11 1 1 1 2() (1)()()(1)() () 1 [(1)()]An S Sn gn ( 1 37) In both the decentralized and first best solutions, the growth rate of technology is proportional to per capita skilled labor in the R&D sector. In the first best solution, the

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27 technology growth rate may be larger, smaller or equal to the growth rate associated with the decentralized economy, depending on whether the last three terms in equation ( 1 37) are positive, negative or zero, because the first two terms are equal to the decentralized equilibrium technology growth rate. Some of the skilled labor released from the decentralized manufacturing sector goes into the abatement sector, but some may also be allocated by the social planner to nonpolluting technology accumulation. In this case the first best technology growth rate is higher: *0 AAgg However u nder other circumstances pollution abatement incentives may draw skilled labor out of both the manufacturing and R&D sectors, leading to lower economic growth: *0 AAgg Thus, neither per capita skilled labor in the R&D sector, nor the growth rate of technology can be ranked unambiguously against the decentralized solution. We can vary the value of the skilled labor productivity parameter in the abatement sector to rank the equilibrium and first best growth rates of technology as an illustration. It can be shown that the firstbest technology growth rate Ag is a monotonic decreasing function of the param eter Notice that per capita skilled labor in the manufacturing sector Mh is independent of Therefore when the skilled labor productivity parameter is approaching 0, the social planner will allocate a very s mall fraction of skilled labor to the abatement sector an d allocate most skilled labor to the R&D sector, leading to a higher technology growth rate than in the decentralized economy. As increases, the social planner will direct more skilled labor to the abatement sector and less to the R&D sector, causing the technology growth rate to decrease. If is large enough, the technology growth rate wil l be lower than in the decentralized economy. Actually, there is a critical value of which satisfies

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28 11 11 1 1 1 2() ()(1)()(1)() 1 [(1)()] n nS Given all other parameters, denote this critical value as When the technology growth rates in the decentralized economy and in the one with a social plan n er are the same: *0 AAgg The growth rate of pollution in the first best solution is given by: 1 12 1 1 1 2() ()(1)[()] (1)() 1 [(1)()]Znn gS ( 1 38) Zg can be optimally positive, negative or zero depending on the following condition: 1 12 1 1 1 2()()(1)[()] (1)() 1 [(1)()] nn S ( 1 39) If Zg is optima lly negative or zero, it i s obvious ly less than the equilibrium pollution growth rate 0 Zg in the setting without a social planner as in that case the pollution growth rate is always positive (given by equation ( 1 23)). I prove in proposition 1 4 that even when Zg is optimally positive, it is less than 0 Zg The reason is very simple: the social planner allocates skilled labor and unskilled labor to the pollution abatement sector to decrease emissions F urthermore, skilled and unskilled labor that are polluting in the manufacturing sector are less than those in the decentralized economy. The sustainable growth rate in the first best solution is given by:

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29 1 1 1 2 1 2()(1)[(1)()] (1)(1)()() [(1)()]un SS gn (1 4 0) The sustai nable growth rate in the first best solution is unambiguously higher than the equilibrium sustainable growth rate: *0 uugg The social planner can allocate resources to decrease pollution growth. The e conomic growth may be high er or low e r than in the decentralized solution dep ending on the parameter values. H owever, because the negative externality of pollution is internalized, the sustainable growth rate is unambiguously higher. Proposition 1 5 : In the firstbest solution, if the population is growing at a higher rate, the pollution growth rate is lower, leading to a higher sustainable growth rate. H owever, the effect on the technology growth rate is ambiguous. If the population is growing at a higher rate, the social planner wil l allocate less skilled and unskilled labor in the manufacturing sector and more in the pollution abatement sector, causing the pollution growth rate to be lower. Because per capita skilled labor in the R&D sector Ah depends on the total per capita skilled labor S per capita skilled labor in the manufacturing sector Mh and per capita skilled labor in the pollution abatement sector Zh the effect of higher popul ation growth on the technology growth rate is ambiguous. However, as I proved in proposition 1 5, the gain in utility from lower pollution dominates the reduction in the technology growth rate, leading to a higher sustainable growth rate.

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30 Proposition 1 6 : In the firstbest solution, an increase in skill abundance S will increase the technology and the pollution growth rates, leading to an ambiguous effect on the economys sustainable growth rate. U nlike the decentralized economy, increasing the skilled labor endowment will increase the first best pollution growth rate. Higher skilled labor abundance will not affect the per capita skilled and unskilled labor in the manufacturing sector. All the additional skilled labor will be devoted to the R&D sector. Further, because the unskilled labor share is lower in the pollution abatement sector, per capita unskilled labor will be lower as well. This in turn requires less per capita skilled labor due to the CobbDouglas production function. The amount of skilled labor released from the pollution abatement sector will also be devoted to the R&D sector. Therefore, the technology growth rate will be higher. Since both per capita skilled and unskilled labor are lower in the pollution abatement sector, the pollution growth rate will be hi gher as well. Thus, the effect on the sustainable growth rate is ambiguous depending on which force is stronger. SecondBest Outcomes In this section, I explore the optimal solution if there is a prohibition placed on pollution abat ement. As mentioned in section of first best solution, under some circumstances, the social planner may not allocate resources to abate pollution at all. It is likely that in less developed countries, government s will take economic growth as their priority. Suppose the social planner takes the pollution externality into account when she maximizes the representative consumers utility, but she does not allocate any labor to abate the pollution. Now the social planners objective is to maximize the discounted utility of a representative household as following:

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31 () 0[ln()ln()]ntUectZtdt ( 1 41) Subject to, 1()()MMctAthl ( 1 42 ) ()()/()A Ah AtAtHXtA ( 1 43) 12() ()MMZthlZt ( 1 44) and t wo full employment conditions, MAShh ( 1 45) 1M Sl ( 1 46 ) In this economy where pollution abatement is prohibited, at the steady state, the allocation of per capita skilled labor in the manufactur ing sector, SB Mh the R&D sector, SB Ah the growth rate of technology, SB Ag the growth rate of pollution emissions, SB Zg and the sustainable growth rate of this economy, SB Ug are all constant and given by (derivation shown in Algebraic Details ) : 1() 1SB Mn h ( 1 47) 1() 1SB SB AMn hShS ( 1 48) 1 () 1SB SB A Ah Sn g ( 1 49) 1 12 2 1() (1) 1SBSBSB ZMMn ghl S ( 1 50 ) a nd,

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32 1 2 11() () (1) 11SB un Sn gS ( 1 51) Proposition 1 7 : The growth rate of technology SBAg in the secondbest solution is higher than the equilibrium growth rate 0 Ag : 0 SB AAgg The growth rate of pollution in the secondbest solution is reduced below the equilibrium level: 0 SB ZZgg The sustainable growth rate in the secondbest solution is unambiguously higher than the equilibrium sustainable growth rate: 0 SB uugg Proposition 1 8 : The growth rate of technology SB Ag in the secondbest solution is higher than the first bes t growth rate Ag : SB AAgg The growth rate of pollution in the second best solution is also higher than the efficient level: SB ZZgg The sustainable growth rate in the secondbest solution is unambiguously lower than the efficient sustainable growth rate: SB uugg When pollution abatement is prohibited, technological progress i s faster than in either the equilibrium solution or the first best solution. In this specification, the social planner has an in centive to internalize the externality of pollution emissions. However, since no labor can be devoted to the pollution abatement sector, the social planners objective can only be achieved by reducing unskilled labor in the manufacturing sector. All unskilled labor that optimally would have been used in pollution abatement, as well as some additional unskilled labor being released from manufacturing, will move to the R&D sector and therefore increase the economic growth rate.

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33 Conclusions This chapter explores the tradeoff between economic growth and environmental degradation and compares the optimal solutions in a decentralized economy with an economy with a social planner W ithout government intervention, a decentralized economy will have a faster pollution growth rate. H ouseholds do not internalize the relationship between environmental quality and economic productivity, pollution would increase without bound and no investment would be made in abatement technology. An economy with a social planner will have unambiguously a higher sustainable growth rate. However, the rate of technology accumulation cannot be ranked. In addition, this chapter focuse s on the relationship between population growth and sustainability. Unlike other studies which suggest that the demographic transition to lower fertility is essential to sustainable development, this chapter suggests that population growth could boost technolog ical progress and generate faster economic growth which would outweigh the disutility from pollution T herefore a positive sustainable growth rate is achievable. Moreover, in an economy with a social planner, an explicit pollution abatement sector makes it possible to decrease the pollution growth rate below the equilibrium level. Algebraic Details In this section, we include the proofs and algebraic details for Chapter 1. Market E quilibrium S olution: Set up the current value Hamiltonian: 11ln()ln/ln()ln()/MM A MM MHAhlZAhAhlZASh where denotes the shadow price associated with technology accumulation.

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34 The first order conditions are: 0Mh MA H h 1MSh n A The growth rate of technology Ag and its shadow price are constant along the balanced growth path Ta king logarithms and differentiating with respect to time, we have: 0 A A From the above conditions, we can obtain 1 0 n A T ogether with the first order conditions, we can solve for equations ( 1 20) ( 1 24) The F irst B est S olution: S et up current value Hamiltonian: 11 12ln()ln ( )A MM MMZZh HAhlZAZhlhl ( )(1)hMAZlMZShhhSll where and are the shadow prices of technology accumulation and pollution emissions respectively and where h and l are the La g range multipliers associated with the full employment conditions for skilled and unskilled labor respectively. The first order conditions are: 10Mhh MHZ h

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35 0AhhA H 110Zh ZZhHZhl 21 0Mll MHZ l (1)0Zl ZZlHZhl 1Ah n A and, 1 12 MMZZnhlhl Z The growth rates of technology, consumption and pollution emissions are constant along the balanced growth path. Ta king logarithms and di fferentiating with respect to time, we have 0 A A and 0 z z implying that 1 0 n A and 0 n z T ogether with the first order conditions, we can solve for equations ( 1 32) ( 1 36). The SecondB est S olution: Set up the current value Hamiltonian: 1 12ln()ln ()()A MM MMhMAh HAhlZAZhlShh where and are the shadow prices of technology accumulation and pollution emissions respectively and where h is the La g range multiplier associated with the full employment condition for skilled labor.

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36 The first order conditions are: 10Mhh MHZ h 0AhhA H 1Ah n A and, 12 MMnhl Z Using t hese first order conditions we can solve for equations ( 1 47) ( 1 51). Comparative S tatics : (Proof for Proposition 12, 1 3 and 1 6) I have derived the long run growth rate of technology growth, the growth rate of pollution emissions and the sustainable growth rate under three different settings: the equilibrium, the first best and the secondbest The foll owing results can be used to show the effect s on these growth rates when the population growth rate and s killed l abor share change: 00Adg dn *0Adg dn 0SB Adg dn ; 00Zdg dn *0Zdg dn 0SB Zdg dn ; 00Udg dn *0Udg dn 0SB Udg dn ; 00Adg dS *0Adg dS 0SB Adg dS ;

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37 00Zdg dS *0Zdg dS 0SB Zdg dS ; and, 00Udg dS *0Udg dS 0SB Udg dS

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38 CHAPTER 2 HETEROGENEOUS POLLUT ERS AND ENVIRONMENTA L STANDARDS Introduction Do more stringent environmental standards lower an industry's productivity and make firms less competitive? The relationship between environmental protection and economic competitiveness has received increasing attention from both scholars and policy makers in the past several decades. On one hand, the Porter Hypothesis suggests that strict environmental regulations often enhance the competitiveness of the domestic industries against their foreign rivals. Porter and Van der Linde (1995) argue that tough standards trigger tec hnological innovation that may result in inexpensive ways to reduce pollution. The nations with the most rigorous regulations often lead in the exporting of those products. On the other hand, economists have been skeptical of this hypothesis. Palmer et al. (1995) survey firms affected by regulation and find that most firms say that the net cost of regulation is indeed positive. We observe that industries have opposed stricter environmental regulations. The automobile industry has been fighting mandates to i mprove fuel efficiency, even though meeting them could stimulate innovations that make products more competitive. Transportation is a major source of air pollution in the United States. Vehicle emissions contribute to health and environmental problems such as air toxics, urban smog, and global warming. In numerous cities across the country, the personal automobile is the single greatest polluter, as emissions from millions of vehicles on the road add up. Driving a private car is probably a typical citizens most polluting daily activity. The vehicles release over 1.7 billion tons of 2CO into the atmosphere each year contributing to global climate change. On average, each gallon of gasoline burned

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39 generates 20 pounds of 2CO which leads to 6 to 9 tons of 2CO each year for a typical vehicle. For a typical household, vehicle emissions contribute to 51% of 2CO emissions, followed by appliances (26%) and heati ng and cooling (18%). Congress first adopted the fuel economy standards known as CAFE (Corporate Average Fuel Economy) standards in 1975 as a response to the oil embargo of 19731974. CAFE doubled new car fuel mileage to 27.5 mpg by 1985. In May 2009 t he Obama administration announced the greenhouse gas emissions standard for cars. The standard is a joint rule by the Environmental Protection Agency (EPA) and the Department of Transportation (DOT) and will require cars to average 35.5 mpg by 2016, four y ears earlier than under previous fuel economy requirements. The purpose of this chapter is to develop a model to study the effect of more stringent environmental standards on firms profitability, pollution and consumers' welfare while emphasizing the importance and the nature of uncertainty in environmental R&D. Investment in environmental R&D aimed at improving firm s' environmental performance is common in U.S. manufacturing industries. Scott (2003) surveys a group of manufacturing companies and finds that on average, 23.9% of a firms total R&D expenditures are channeled towards environmental projects. Moreover, over onehalf of the firms participating in the survey indicate that their environmental R&D projects are undertaken as a response to specific environmental legislation. For example, Goldberg(1998) finds that CAFE offers incentives for producers to develop environmentally friendlier technologies and vehicles. Environmental R&D is generally modeled as a response to government regulation, aiming at r educing firms' compliance costs. Environmental R&D could reduce the cost of

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40 abatement or reduce the amount of polluting inputs used in the production process. (See Xepapadeas and Zeeuw (1999), and Bovenberg and Smulders (1995)). I offer an alternative appr oach in this chapter : environmental R&D is modeled as a compulsory investment before any production. Without this investment, firms will not be able to discover and produce any products. All firms have to pay the same amount of environmental R&D ef but discover varieties with different environmental quality. The amount of environmental R&D is stochastically related to the level of environmental quality. Different levels of environmental quality are obtained due to the uncertainty of the R&D process and the outcomes of environmental quality are realized by a commonly known distribution. Recent theory has shown that differences in firm specific variables will lead to differences in prices and therefore firms' revenues and profits. For example, in Melitz (2003) and Melitz and Ottaviano (2007), firms are heterogeneous in their productivity. More productive firms have lower marginal costs and are able to charge lower prices to earn higher revenues and profits. A number of recent models have developed firm heterogeneity in their quality.1 For example, Dinopoulos and Unel (2010) introduce entry deterring limit pricing strategies where higher quality firms will be able to charge higher prices and markups to earn higher revenues and profits. In this chapter firm heterogeneity comes from an R&D structure that follows the literature. When firms engage in R&D to discover new products, they face uncertainty with respect to the future level of environmental quality contained in their products. In the automobile industry, there is firm heterogeneity in environmental quality: different brands or models 1 See Baldwin and Harrigan (2007), Johnson (2009), Antoniades (2008) among many others.

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41 often have different levels of environmental quality. F or example, a 2010 Toyota Prius gets 48 MPG (miles per gallon), a 2010 Ferrari 599 GTB Fiorano ge ts 15 MPG and a Mercedes Benz SLK350 get s 25 MPG. Some brands are constrained by the environmental standards and the environmental quality of some brands exceeds the environmental standards. Therefore, when regulators decide to impose stricter standards, firms that no longer meet the standards will have to exit the market. This model is suitable to take into account firm heterogeneity in environmental quality. We have not seen many papers addressing the impact of environmental policy on heterogeneous firms. Yokoo (2009) uses a monopolistically competitive firm setup and studies the effect of an environmental tax on productivity. He finds that an increase in the tax rate will drive up average productivity and lower each firm's revenue and profit. However, his paper did not study the uncertainty of the environmental R&D process and the effect of environmental standards is also not discussed. Following the literature, we assume that firms pay a fixed entry cost t o invest in environmental R&D to be able to draw an environmental quality parameter from a common and known distribution. A new utility function is introduced to account for the facts that : (1) consumers prefer goods with better environmental quality; and (2) pollution emissions reduce utility. The regulator sets an environmental standard and this standard is strictly enforced. Firms with very low environmental quality will not enter the market since they do not meet the standard. We find that firms with low environmental quality will be forced to exit the market when the regulator imposes a stricter standard and firms with high environmental quality stay in the market, produce heterogeneous goods and generate less pollution per unit of output. With a strict er standard, there will

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42 be fewer firms in the market at the steady state equilibrium, and firms' average profits will be higher since the com petition will be less intense. T hey will generate less pollution per unit of output and the overall effect on the w elfare of consumers will be ambiguous. An optimal standard is also calculated using a Pareto distribution. The Model Consumers Assume a country has L consumers with identi cal preferences The preferences for a representative consum er are given by UQZ (2 1) where Q is the aggregate consumption ov er a continuum of products that is indexed by and is defined as a C.E.S function 1/() () q Qd L (2 2) where 01 so that the elasticity of substitution between any two products is 1/(1)1 () q is the aggregate consumption of brand is the set of varieties available to consumers and ()1 denotes the timeinvariant environmental quality of brand Values of environmental quality () depend on firms' R&D ability. Motivated by the automobile industry, we can consider the environmental quality as the fuel efficiency of different models of vehicles, so the model with a higher level of environmental quality has be tter fuel economy, i.e., higher miles per g allon (MPG). If a firm develops an electronic vehicle, () is very large.2 0 is a parameter capturing 2 Electronic vehicles generate other types of pollutions that for simplicity we do not discuss.

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43 the intensity of consumers preference for the differentiated g oods with some degree of environmental quality. According to a 2009 survey by the Consumer Reports National Research Center, the most important considerations for todays new car buyers are fuel economy, quality, safety, price, and value. Many consumers ar e willing to pay higher prices and even submit to a waiting list to purchase the environmentally friendly hybrid vehicles. Higher means that environmental quality counts more in a representative consumer 's preference for the differentiated goods When is approaching zero, it means that consumers do not care about environmental quality contained in a product at all. The consumption of these products generates pollution. Z is defined as the total amount of pollution summed over all varieties consumed in a country: () Zzd (2 3) The amount of pollution generated from consuming brand by all consumers is: ()()() zq (2 4) where 0 is a parameter capturing the pollution intensity. Higher means that for a given environmental quality, consuming the same amount of a brand will generate less pollution. When approaches infinity, there will be no pollution; when approach es zero, the environmental quality does not affect pollution. P ollution from consuming a brand bec omes proportional to the quantity demanded. 0 is a parameter capturing this relationship, indicating that consuming 1 unit of brand generates units of pollution if 0 Given parameters and if a brand has a higher level of environmental quality, consuming one unit of this product will generate less pollution.

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44 Consuming varieties with higher environmental quality increases consumer utility in two ways: first, a representative consumer has preferences for those goods; and second, consuming the same amount of goods with higher environmental quality generates less pollution. The representative consumer assumes that her own behavior does not affect aggregate pollution, so she takes aggregate pollution as given. Maximize her utility ( 2 1) subject to a budget constraint: () () q pdE L (2 5) where E is per capita consumer expenditure summed over all varieties, L is the number of consumers in the market, () p is the corresponding price of brand and () q is the aggregate consumption of brand For a particular brand aggregate consumption () q and aggregate expenditure () r are: 1 (1)()()() qELPp (2 6) 11 (1)()()()()() rpqELPp (2 7) where the price index adjusted for environmental quality (the green price index) is defined as: 1/(1) 1() () p Pd (2 8) When consumers do not have any preference for the environmentally friendly products, 0 the green price index collapses to the standard aggregate price index as shown in Melitz (2003). The aggregate consumption and the optimal expe nditure for

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45 brand both increase in aggregate consumer expenditure EL the green price index P and its level of environmental quality () ; and both decrease in its own price () p Firms Labor is the only factor of production, with each worker supplying one unit of labor, so the labor supply is given by the number of consumers, L There is a continuum of firms and each firm chooses to produce a different variety. Initially, the regulator sets an environmental standard and firms have to invest in environmental R&D before they start producing. In order for any firm to begin producing a variety, it will first invest a fixed entry cost 0ef that is measured in units of labor and is interpreted as the number of R&D researchers required by the entrant to discover a new variety. All firms pay the same entry cost ef but will discover varieties with different environmental quality. Therefore, we interpret this fixed entry cost as environmental R&D. After incurring environmental R&D, firms draw their environmental quali ty parameter, out of a commonly known distribution. This process captures the uncertainty of environmental R&D. For any producing firm, assume that marginal cost is an increasing function of environmental quality: MC where 0 Further, assume that there is no fixed production cost once the variety has been discovered. Therefore, in order to produce q units of output, lq units of labor are required. Because marginal cost and total cost both increase in environmental quality, it will cost more for those firms wi th higher environmental quality levels to produce the same amount of output For the remainder of this chapter p roducts are labeled based on their environmental quality levels since each brand is associated with a unique environmental quality level.

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46 Regardless of the differences in environmental quality, each firm faces a residual demand curve with constant elasticity because of the C.E.S consumption index. The producing firms maximize their profits by taking the number of firms M and the green price index P as given. A firm with environmental quality will set the profit maximizing price as a constant markup over its marginal cost () p (2 9) where we normalize the wage rate to one ( 1 w ). Combine ( 2 4), (2 6), ( 2 7) and ( 2 9), its demand () q revenue () r profit () and pollution () z are given by: 1(1)() qELP (2 10) 1()(1)()()()() rpqELP (2 11) 1()(1)()() () rELP (2 12) and 1(1)() zELP (2 13) The ratios of any two firms' outputs, revenues, profits and pollution generated depend only on the ratio of their environmental quality levels: (1) 11 22() () q q (2 14) ()(1) 111 222()() ()() r r (2 15) and (1) 11 22() () z z (2 16)

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47 When the profit function is increasing in the level of environmental quality. Consumers have strong preference for products with better environmental quality. Therefore, higher demand for environmentally friendly products compensates for the fact that it cost s firms more to produce these products. A firm with a higher environmental quality level earns higher revenue because it is able to charge a higher price and make higher profits. If a firm happens to discover a variety with envir onmental quality equal to the environmental standard, compared to all the producing firms, this firm will make the lowest profit. However, it is not clear whether the consumption of this product causes more or less pollution. If consumers' preference for environmen tally friendly products is strong enough ( ()/(1) ) when a product has a high environmental quality level consumers actually buy more of the product which leads to more pollution. When ()/(1) the pollution will be decreasing in the environmental quality. Furthermore, w hen the consumption of a product with higher will generate less pollution. When the profit func tion is decreasing in the level of environmental quality. Consumers have a preference for those products with better environmental quality, but not strong enough to compensate for the higher costs associated with the production of those goods In this case, firms with higher environmental quality earn less revenue and profits. The firm with environmental quality equal to the standard level will make the highest profit compared to all the producing firms and as approaches infinity profit approaches zero. When profit is not directly affected by its environmental quality level at all.

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48 Entry Decisions The regulator sets an environmental standard This regulated level is strictly enforced so any firm producing a variety with will not be able to sell its products at all in the market. Suppose that there are a large number of prospective ex ante identical entrants. Initial ly, a firm incurs the fixed entry cost, which is the environmental R&D, ef then it draws its environmental quality parameter from a common and known distribution () g with positive s upport over (0,) and with continuous cumulative distribution () G The properties of () g determine the benefits of entry measured by the relevant expected discounted profits. After observing its environmental quality level a firm decides whether to exit the market immediately or start producing. If a firm discovers a product with low environmental quality it does not meet the environmental standard and will immediately exit and not produce. If a firm discovers a product with environmental quality level equal to or greater than the standard it will enter the market and make positive profits. Any producing firm that meets the environmental standard is always earning positive profits without the fixed production cost because of the constant markup over marginal cost due to the C.E.S structure. Each incumbent firm faces a constant probability of death in each period as a result of being hit by a stochastic shock ( 01 ). In the present context, this stochastic shock can be interpreted as changing tastes that eliminate the demand for a particular variety. Sinc e the exit is uncorrelated with the environmental quality, the exit process will not affect the equilibrium environmental quality distribution () As in Melitz (2003), the ex ante probability of drawing an environmental quality level is governed by the density function () g and the ex ante probability of successful entry

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49 1()inpG The equilibrium distribution of environmental quality () is then determined by the initial draw, conditional on successful entry 1()inpG Therefore, () is the conditional distribution of () g on the interval : () () 1() g G (2 17) If the regulator decided to set a higher environmental standard, t hat the equilibrium distribution of environmental quality () would change. It would then be harder for any potential firm to enter the market, the ex ante probability of successful entry would be lower and the equilibr ium distribution would be larger Aggregation At the steady state equilibrium, suppose there are M fir ms with a distribution () of environmental quality levels. The green price index ( 2 8) becomes 1/(1) 1 0() () p PMd (2 18) Using the pricing rule ( 2 9), when ( 2 18) can be written as3: 1/(1) 1/(1) 1/(1) ()(1) 0() MM Pd (2 19) where is defined as 1 ()(1) ()(1)1 () () 1() gd G ( 2 20) is a weighted average of environmental quality of all produced varieties and can be interpreted as the average or expected environmental quality level. The 3 The case when is trivial. Revenues and profits are not affected by environmental quality.

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50 environmental standard and the ex ante distribution () g will determine the average environmental quality in equilibrium. Since any firm that does not meet the environmental standard is not able to enter the market at all, the regulated environmental standard is the minimum env ironmental quality level of all producing firms and it will be lower than the average environmental quality level. Furthermore, an increase of the standard forces firms with low environmental quality levels to exit the market, which in turn increases the average environmental quality level of all produced varieties. The following lemma summarizes these properties. (See Algebraic Details for proof). Lemma 2 1 : The average environmental quality level of all produced varieties in an economy is strictly g reater than and increases in the environmental standard, i. e., and /0 The green price index is decreasing in the number of firms in the market. When there are more firms in the market, compet ition gets more intense. T herefore, the price index will be smaller. When the green price index is increasing in the average environmental quality level. Since the costs of production are high, firms charge higher prices. When the green price index is increasing in the average environmental quality level. High demand for products makes it profitable even if firms charge lower prices. The aggregate revenue and aggregate profit are given by: 0()() RrMd ( 2 21) and

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51 0()() Md (2 22) Also, the aggregate quantity, average revenue and profit per firm can be derived (see Algebraic Details ): 1 1QM (2 23) () R rr M (2 24) () M (2 25) An industry with M firms with a distribution of environmental quality () that yields the same average environmental quality level will have the same aggregate quantity, revenue and profit as an industry with M representative firms that have the same environmental quality Free Entry and the Value of the Firms A firm producing a vari ety with environmental quality level earns a per period profit () Since each firm faces a constant probability of death in each period, the market value of a firm with environmental quality level is given by 0() ()max0,(1)()max0,t tv The second equality follows from the fact that the environmental quality contained in each firm's product remains constant during its lifetime, so every period it earns the same profit. Because the probability of successful entry is 1() G the net benefits of entering the domestic market are equal to the expected value of a firm 1() G where / is the ex ante value of a

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52 prospective entrant and is defined by ( 2 25) Setting the benefits of entry equal to the fixed R&D costs yields the free entry condition: 1()e f G (2 26) The average profit is solely determined by the probability of death the fixed environmental R&D ef and the environmental standard Given the probability of death and the fixed environmental R&D ef if the regulator sets a higher level of environmental standard, then prospective firms are less likely to enter successfully, an entrant would expect there will be fewer firms in the market and its expected value would be higher. At the steady state equilibrium, the aggregate variables must remain constant over time, so the number of firms is constant. Therefore in any single period, the number of successful entrants inepM must be equal to the number of incumbe nt firms who are forced to exit the market due to a bad shock, i.e., inepMM where eM is the number of potential entrants and inepM is the n umber of successful firms. Because the entering and exiting firms have the same distribution of environmental quality levels, at the steady state equilibrium the distribution of environmental quality () is not affected by this simultaneous entry and exit. The labor employed by the prospective entrants for environmental R&D to discover the varieties and the labor employed by the incumbent firms for manufacturing are denoted by eL and mL For the full employment condition to be satisfied, labor demand equals labor supply, i.e., emLLL Total payments to workers in manufacturing are equal to the difference between aggregate revenue and

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53 profit: mLR The labor employed by the prospective entrants for environmental R&D to discover the varieties are given by eeeLMf Using the aggregate stability condition, inepMM and the free entry condition, 1()ef G eL can be written as: 1()eee eM LMffM G (2 27) Thus, the aggregate amount of labor employed by the prospective entrants for environmental R& D equals the level of aggregate profits earned by all producers in the economy. Also, the aggregate revenue mmeRELLLL must also equal the total payments to labor L and is solely determined by the total number of consumers. Per capita expenditure equals unity due to the choice of labor as the numeraire, i.e., 1 Ew and the aggregate revenue RL The number of producing firms in any period can then be determined from the average profit using ( 2 26): 1()eLG ELL M rf (2 28) At the steady state equilibrium, the number of varieties is determined by the size of the economy, the elasticity of substitution between any two products, the stochastic shock, environmental R&D and the environmental standard. If the size of the economy is larger, there is more labor available to discover the varieties and more labor available for manufacturing. Therefore, there are more varieties produced. If the environmental standard is higher or the required amount of environmental R&D is higher, it would be harder for the potential entrant s to enter the market successfully. There will be fewer varieties. With a higher elasticity of substitution and given the average profit the

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54 average revenue will be higher. Since the aggregate revenue R is fixed by the size of the economy, there will be fewer varieties available at the steady state. Welfare Both consumers and producers take the aggregate pollution as given. Using ( 2 13), ( 2 19) and ( 2 28), the pollution generated by consuming a brand wit h environmental quality is given by: ()(1)() ()(1)()() / 1()e f zL M G (2 29) When there are more varieties available in the market, the pollution generated by consuming a speci fic brand is smaller. Substituting ( 2 29) into ( 2 3), the aggregate pollution Z can be expressed as ()(1) (1)() 1() L Z gd G (2 30) Notice that the aggregate pollution is not directly affected by the number of firms. When there are more firms in the market, it will drive down the green price index and demand for every existing brand will be smaller. Consumers are buying more varieties while spending less on each variety and these two effects cancel out exactly. Substitut ing ( 2 28) into ( 2 23) and using ( 2 10), ( 2 19) and ( 2 30), per capita welfare is given by: ()(1) 1/(1) 1/(1) 1/(1) (1)1()() () 1()eL WLGf gd G (2 31) Depending on the parameter values, per capita welfare W can be either positive or negative. A more stringent environmental standard affects per capita wel fare in several ways: first a more stringent environmental standard makes it more difficult for

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55 prospective entrants to enter the market successfully. There will be fewer firms producing at the steady state equilibrium and the competition among all producing f irms will be less intense. A representative consumer becomes worse off because she has to consume fewer varieties. Even though a representative consumer prefers products with better environmental quality, she has to pay a higher price for them, so aggregat e consumption is smaller. Second, the effect of a more stringent environmental standard on aggregate pollution is unclear. When the environmental standard is higher, there are fewer varieties available and the average environmental quality is higher. Howev er, consumers consume more of each variety. The pollution emissions generated from each variety are higher and therefore, a higher standard may increase or decrease aggregate pollution. Overall, the effect of a more stringent environmental standard on per capita welfare is ambiguous. The following proposition summarizes these results (see A lgebraic Details for proof): Proposition 2 1 : A more stringent environmental standard will decrease aggregate consumption and may increase or decrease aggregate p ollution. T herefore, the overall effect of raising the environmental standard on per capita welfare is ambiguous. In the case where a higher standard increases aggregate pollution, per capita welfare is unambiguously decreasing in the standard and the optimal policy for the regulator would be to set the environmental standard as low as possible. However, if a higher standard decreases aggregate pollution, the effect of a higher environmental standard on per capita welfare is ambiguous and an optimal standard may be obtained.

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56 In the next section we use a Pareto distribution to illustrate this possibility and the factors that affect the optimal standard ar e also discussed. Parameterization and the Optimal Standard To have a better understanding of the properties of the model, we assume that environmental quality levels are drawn from a Pareto distribution with scale parameter b and shape parameter k which is a commonly used distribution in the literature (see Helpman et al. (2004), Dinopoulos and Unel (2009)). In particular, we assume ()(1)()(1) k .4 Assuming that environmental quality levels follow a Pareto distribution is not essential in this paper. However, it makes the analysis more tractable. With a Pareto distribution, the cumulative distribution is defined as: for 0 b ()1kb G (2 32) T he probability distribution function is then given by: 1()k kkb g (2 33) Using ( 2 33), the average environmental quality ( 2 20) can be written as: 1/(()(1))()(1) k k (2 34) 4 We ass ume that ()(1) k to ensure the average environmental quality has a solution and is positive and we assume that ()(1) k to ensure the second order condition is satisfied.

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57 It is clear that average environmental quality is an increasing function of the standard a s we have shown in lemma 1. Given the Pareto distribution and parameter values this relationship becomes linear Using equations ( 2 28) and ( 2 32), the number of firms is given by: 1()kk eeLG Lb M ff (2 35) A ggregate consumption is given by: 1 1 /(1)[()(1)]k k eLkb Q fk (2 36) Aggregate consumption is a decreasing function of the environmental standard as shown in proposition 2 1 When the environmental standard is more stringent consumers enjoy fewer varieties, pay a higher average price and consume more of each variety. A ggregate pollution is given by: ()(1) () k ZL k (2 37) which is decreasing in the environmental standard. Per capita welfare is given by: 1 1 /(1)()(1) [()(1)] ()k k eLkb k WQZ L fk k (2 38) Set 0 W the optimal standard is given by

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58 1 1 ()(1) ()(1) *() ()(1) [()(1)]k k k ek Lkb L fk (2 39) Proposition 2 2 : Given the Pareto distribution, there exists an optimal level of environmental standard to maximize welfare, that is given by equation ( 2 39). Given any level of environmental standard, suppose the required environmental R&D increases. In order for any entrant to discover a new variety, firms must hire more R&D researchers. There will be fewer firms producing in the market and each firm's revenue and profit will be higher at the steady state equilibrium. Because more researchers are needed in order to discover a variety fewer entrants will successfully enter the market and keep producing. The competition will be less intense and every firm will make more revenue and profit. Consumers will be worse off because there will be fewer varieties available at the steady state equilibrium. An increase in environmental R&D, however will not affect aggregate pollution. There will be fewer firms producing at the steady state equilibrium, but each firm will be producing more which generates more pollution. O verall, aggregate pollution will not change. An increase in environmental R&D will unambiguously decrease per capita welfare. If the size of the economy is larger aggregate expenditure will be higher and there will be more firms producing in the market. The size of the economy has s everal effects on per capita welfare. E ach consumer becomes better off because she consumes more varieties. But, she becomes worse off because as she spreads her expenditure (equal to her wage) among more varieties, consumption on each good becomes less. T hird, with more firms producing and each firm producing the same amount of output as before each consumer becomes worse off due to higher aggregate pollution. Overall,

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59 the effect of bigger size of the economy on per capita welfare is ambiguous depending o n the value of the elasticity of substitution. If the elasticity of substitution is big enough ( 2 ), the benefit from consuming more varieties will outweigh the negative utility caused by pollution. Per capita welfare will increase in the size of the economy and the optimal standard will be higher. Otherwise, per capita welfare will decrease in the size of the economy and the optimal standard will be lower. The following proposition summarizes these properties: Proposition 2 3 : If th e required environmental R&D i ncreases, it will be harder for potential entrants to enter the market successfully. Aggregate consumption will be lower and aggregate pollution will not be affected. Therefore, it will decrease per capita welfare and increase the optimal standard; With a larger economy, aggregate consumption and aggregate pollution will be higher. Overall effect on per capita welfare is ambiguous. If the elasticity of substitution is big enough, the optimal standard will increase in the size o f the economy. Conclusions This chapter develops a model of heterogeneous firms to study the effect of a stricter environmental standard on firm's profitability, pollution an d consumers' welfare. Firms in this model face C.E.S preferences and charge prices as a constant markup over their marginal costs which are positively related to the firm specific environmental quality levels. We find that with a stricter standard, firms with low levels of environmental quality will exit and the competition will be less intense, successful firms earn higher revenues and profits. McManus and Kleinbaum (2009) find that increasing fuel economy standards 30% to 50% (35 MPG to 40.5 MPG) would increase the Detroit biggest three firms gross profits by roughly $3 billion per year. Although there will be

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60 fewer firms in the market, each consumer consumes more of each variety. The effect of the standard on aggregate pollution is unclear. The overall effect on welfare is ambiguous d epending on the relative importance of consumption and pollution to consumers. Algebraic Details In this section, we include the proofs and algebraic details for Chapter 2. Proof of Lemma 2 1 : Since when ()(1)()(1) Substitute it in to the integral expression of equation ( 2 20) to obtain ()(1) ()(1) ()(1) ()(1)11 () () 1() 1() gd gd GG which yields Similarly, when we can also get Let ()(1)1 () () 1() H gd G differentiating equation ( 2 20) yields : 1/()(1)11 () ()(1) H H where ()(1) ()(1) ()(1)()(1) 2()1() ()() () 1() 1() gG gdg g H G G Since H and will have the same sign. Therefore, 0

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61 Proof of ( 2 23) ( 2 24) and ( 2 25) : Substitute ( 2 15) into aggregate revenue definition 0()() RrMd we can obtain ()(1) ()(1) 0() ()() Rr MdMr A ggregate profit is defined as 0()() Md since ()()/ r 0()()/()/() rMdMrM A ggregate quantity is given by 1/ 0() () q Q Md L using (2 10) and ( 2 14), 1/ (1) 11/ 1/ 1 0() () ()/ M Qq dMqLM L Proof of Proposition 2 1 A ggregate consumption is given by : 1/(1) 1/ 1/(1) 1/(1)()/1()()eQMqLLGf Using the definition of which i s given by (220), we can rewrite aggregate consumption as 1 1/(1) (1) ()(1)()eL Q gd f Differentiati ng this equation yields: 1 1/(1) 1 (1) ()(1) ()(1)1 () ()0 (1)edQL gd g df From (2 30), aggregate pollution can be rewritten as (1) ()(1)() () Lgd Z gd Differentiating this equation yields:

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62 ()(1)(1) (1) ()(1) 2 ()(1)() () () () gd gd Z Lg gd Whether Z is positive or negative depends on the values of parameters and the distribution.

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63 CHAPTER 3 TRADE, POLLUTION AND ENVIRONMENTAL STANDARDS Overview This c hapter extends the previous chapter, developing an international trade model with firm specific environmental quality heterogeneity. The Model We consider a global economy consisting of 1 n identical countries with 1 n Each country has only one industry with heterogeneous firms and labor is the only factor of production. In each country, the aggregate supply of labor, L is fixed and remains constant over time. Consumers Assume we have L consumers with identical preferences within a country. The preferences for a representative consumer are given by UQZ (3 1) where Q is the aggregate consumption over a continuum of products which is indexed by and is defined as a C.E.S function 1/() () q Qd L (3 2) where 01 so that the elasticity of substitution between any two products is 1/(1)1 () q is the aggregate consumption of brand is the set of varieties available to consumers in a typical country and ()1 denotes the timeinvariant environmental quality of brand Values of environmental quality () depend on fi rms' R&D ability. Motivated by the automobile industry, we can consider the

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64 environmental quality as the fuel efficiency of different models of vehicles, so the model with a higher level of environmental quality has better fuel economy, i.e., higher miles per g allon (MPG). If a firm develops an electronic vehicle, () is very large.1 0 is a parameter capturing the intensity of consumer's preference for the differentiated goods with some degree of environmental quality. According to a 2009 survey by the Consumer Reports National Research Center, the most important considerations for todays new car buyers are fuel economy, quality, safety, price, and value. Many consumers are willing to pay higher prices and even submit to a waiting list to purchase environmentally friendly hybrid vehicles. Higher means a representative consumer has a higher preference for the differentiated goods given their environmental quality. When is approaching zero, it means that consumers do not care about environmental quality contained in a product at all. The consumption of these products generates pollution. Z is defined as the total amount of pollution summed over all varieties consumed in a country: () Zzd ( 3 3) The amount of pollution generated from consuming brand by all consumers is: ()()() zq (3 4) where 0 is a parameter capturing the pollution intensity. Higher means that given an environmental quality, consuming the same amount of one brand will generate less pollution. When approaches infinity, there will be no pollution; when approaches zero, the environmental quality does not affect pollution anymore. P ollution from 1 Electronic vehicles generate other types of pollution that for simplicity we do not discuss

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65 consuming a brand becomes proportional to the quantity demanded. 0 is a parameter capturing this relationship, indicating that consuming 1 unit of brand generates units of pollution if 0 Given parameters and if a brand has a higher level of environmental quality, consuming one unit of this product will generate less pollution. Consuming varieties with higher environmental quality increas es consumer utility in two ways: first, a representative consumer has preferences for those goods; and second, consuming the same amount of goods with higher environmental quality generates less pollution. The representative consumer assumes that her own behavior does not affect aggregate pollution, so she takes aggregate pollution as given. Maximize her utility ( 3 1) subject to a budget constraint: () () q pdE L (3 5) where E is per capita consumer expenditure summed over all varieties, L is the number of consumers in a typical (home or foreign) market, () p is the corresponding price of brand and () q is the aggregate consumption for brand T he aggregate consumption () q and the aggregate expenditure () r for a particular brand ar e: 1 (1)()()() qELPp (3 6) 11 (1)()()()()() rpqELPp (3 7) where the price index adjusted for environmental quality (the green price index) is defined as:

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66 1/(1) 1() () p Pd (3 8) When consumers do not have any preference for the environmentally friendly products, 0 the green price index collapses to the standard aggregate price index as shown in Melitz (2003). The aggregate consumption and the optimal expenditure for brand both increase in aggregate consumer expenditure EL the green price index P and its level of environmental quality () ; both decrease in its own price () p Firms Labor is the only factor of production, with each worker supplying one unit of labor, so the labor supply is given by the number of consumers, L There is a continuum of firms and each firm chooses to produce a different variety. Initially, in a typical market, the regulator sets an environmental standard and firms have to invest in environmental R&D before they start producing. In order for any firm to begin producing a variety, it will first invest a fixed entry cost 0ef that is measured in units of labor and is interpreted as the number of R&D researchers required by the entrant to discover a new variety. All firms pay the same entry cost ef but will discover varieties with different env ironmental quality. We interpret this fixed entry cost as environmental R&D. After incurring environmental R&D, firms draw their environmental quality parameter, out of a commonly known distribution. This process captures the un certainty of environmental R&D. For any producing firm, assume the marginal cost is an increasing function of environmental quality: MC Further, assume that there is no fixed production cost once the variety has been discovered. Therefore, in order to produce q

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67 units of output, lq units of labor are required. Because marginal cost increases in environmental quality, it will cost more for those firms with higher environmental qualities For the remainder of this chapter products are labeled based on their environmental quality levels because each brand is associated with a unique environmental quality level. Firms ha ve the choice whether to incur fixed trade cost s 0x f and Iceberg per unit trade costs 1 in order to export N either of these costs depend on a firms environmental quality level Iceberg trade costs are modeled as 1 units of output mu st be produced at home in order for one unit to arrive at a foreign country. Firms make the export decision after they learn their environmental quality levels. Regardless of the differences in environmental quality, each firm faces a residual demand curv e with constant elasticity because of the C.E.S consumption index. The producing firms maximize their profits by taking the number of varieties and the green price index P as given. A firm with environmental quality will set its domestic profit maximizing price as a constant markup over its marginal cost () p (3 9) where we normalize the wage rate to one ( 1 w ) and () dp is the consumer price prevailing in the domestic market. An exporting firm will set a higher price in the foreign market due to the Iceberg trade cost and the consumer price prevailing in the foreign market ()xp is given by ()xp (3 10)

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68 A firm with environmental quality will sell ()dq amount in the domestic market and if it decides to export, it will sell () xq amount in each of n foreign markets: 1(1)()dqELP (3 11) and, 1(1)()xqELP (3 12) Therefore, the combine d production of a firm, () q depends on its export status: If the firm does not export, ()()dqq (3 13) If the firm exports to all n foreign countries 1(1)()()()(1)()(1)dx dqqnqnqnELP ( 3 14) Respectively, t he revenues earned from domestic sales ()dr and sales in each of n export markets ()xr are given by 1()(1)()()drELP (3 15 ) and 1 1 1()(1)()()()xdrrELP (3 16) Therefore, the combine d revenue, () r also depends on its export status: If the firm does not export, 1()(1)()()()drrELP (3 17) If the firm exports to all n foreign countries, 1 1 1()(1)()()()(1)()(1)()dx drrnrnrnELP (3 18)

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69 Similarly, the profits of any exporting firms in each period can be decomposed into two parts: profits earned from domestic sales ()d and profits earned from sales in each of n export markets ()x () ()d dr (3 19 ) and () ()x xxr f (3 20) A firm with environmental quality that produces for its domestic market exports to all n countries if ()0x No firm will ever export and not produce for its domestic market since the domestic profit, ()d is always positive as long as it meets the current environmental standard. Therefore, a firm with environmental quality earns a combined per period profit () that is given by: ()()max0,()dxn (3 21 ) The total pollution generated from a firm with an environmental quality () z depends on its export status: If the firm does not export, 1(1)() zELP (3 22) If the firm exports to all n foreign countries, 1(1)()()()(1)()(1)dx dzznznznELP (3 23) Entry D ecision s Every country sets an environmental standard ( 1 ). This regulated level is strictly enforced so any firm producing a variety with will not be able to sell its

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70 products at all in ei ther domestic or foreign markets. Suppose that in each country, there are a large number of prospective ex ante identical entrants. Initially, a firm incurs the fixed entry cost, the environmental R&D, ef then it draws its environmental quality parameter from a common and known distribution () g with positive support over (0,) and with continuous cumulative distribution () G The properties of () g determine the benefits of entry measured by the relevant expected discounted profits. After observing its environmental quality level a firm decides whether to exit the market immediately or start producing. If a firm discovers a product with low environmental quality it does not meet the current environmental standard and will immediately exit and not produce. If a firm discovers a product with environmental quality equal to or greater than the standard it will enter the market and make positive profits. Any producing firm which meets the current environmental standard is always e arning positive profits in the domestic market without the fixed production cost because of the constant markup over marginal cost due to the C.E.S structure. Also, after observing its environmental quality level a firm decides whether to incur the fixed export cost xf to sell its products to foreign markets. A firm with environmental quality produces for its domestic market exports to all n foreign count ries, only if ()0x Assume that consumers have a strong preference for products with better environmental quality, In this case, higher demand for environmentally friendly products compensates for the fact that it costs firms more to produce these products. A firm with a higher environmental quality level earns higher revenue because it is able to charge a higher price and make higher profits. ()x increases monotonically in

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71 Denote x as the cutoff environmental quality level for exporting firms, where ()()/0xxxxxrf (3 24) Proposition 3 1 : As long as the fixed export cost xf is greater than 1()(1)() LP there will be some firms that will export while some firms will only serve the domestic market. The fixed export cost xf has to be greater than 1()(1)() LP to ensure t hat the cutoff environmental quality meets the standard. In the absence of the fixed export cost (0x f ), all firms who survive in the domestic market will export to foreign markets as well. Each incumbent firm faces a constant probabi lity of death in each period as a result of being hit by a stochastic shock ( 01 ). In the present context, this stochastic shock can be interpreted as changing tastes that eliminate the demand for a particular variety. Since the exit is uncorrelated with the environmental quality, the exit process will not affect the equilibrium envir onmental quality distribution () As in Melitz (2003), the ex ante probability of drawing an environmental quality level is governed by the density function () g and the ex ante probability of successful entry 1()inpG The equilibrium distribution of environmental quality () is then determined by initial draw, conditional on successful entry 1()inpG Therefore, () is the conditional distribution of () g on the interval : () () 1() g G (3 25)

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72 Suppose the regulator decided to set a higher environmental standard, it would change the equilibrium distribution of environmental quality () It would be harder for any potential firm to enter the market, the ex ante probability o f successful entry would be smaller and the equilibrium distribution would be bigger. The ex ante probability that an incumbent firm will export is given by 1() 1()x xG pG (3 26 ) This probability is also the ex post fraction of firm s that export. Aggregation Let pM denote the number of varieties produced in any country and xM be the number of varieties that each country exports. xM is given by: xxpMpM (3 27) Then, the total number of varieties available for consumption in any country is given by : (1)cpxxpMMnMnpM (3 2 8 ) Let p denote the weighted average of the environmental quality levels of all domestically produced goods: 1 ()(1) ()(1)1 () () 1()pgd G (3 29) p is a weighted average of the environmental quality levels of all domestic firms and can be interpreted as the expected environmental quality level. The environmental standard and the ex ante distribution () g will determine the average environmental quality p in equilibrium.

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7 3 Let x denote the weighted average environmental quality level of exporting firms: 1 ()(1) ()(1)1 () () 1()xxx xgd G (3 30) The combined average environmental quality of all goods, c is given by : 1 ()(1) ()(1) 1 1()p x cp x ccM nM MM (3 31) c is the weighted average environmental quality level of all varieties from bot h domestic and foreign firms competing in one country. Because any firm that does not meet the environmental standard is not able to enter the market at all, the standard level is the minimum environmental quality level of all producing firms and it will b e lower than the average environmental quality level of all firms. Furthermore, an increase of the standard forces firms with low environmental quality levels to exit the market, that in turn increases the average environmental quality level of all produced varieties. Similarly, the export environmental quality cutoff level is the minimum environmental quality level of all exporting firms and it will be lower than the average environmental quality level of all exporting firms. An increase of the cutoff leve l forces firms with low environmental quality levels to only serve the domestic market. T herefore, the average environmental quality level of all exporting firms also increases. The following lemma summarizes these properties. (See A lgebraic Details for proof). Lemma 3 1 : T he average environmental quality level of all produced varieties in an economy is strictly greater and increases in the environmental standard, i. e., p

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74 and /0p The average environmental quality level of all exporting firms is strictly greater and increases in the export cutoff environmental quality level, i. e., xx and /0xx The green price index P expenditure level R and aggregate quantity Q in any country can then be written as functions of only the average level of environmental quality c and the number of varieties consumed cM (See A lgebraic Details ) 1/(1)/ccPM (3 32) ()cdcRMr (3 33) 1/(1) ccQM (3 34) The aggregate equilibrium in any country is identical to one with cM representative firms that have the same environmental quality c The overall average revenue, r and profit, from both domestic and foreign mar kets are given by: ()()dpxxxrrpnr (3 3 5 ) and ()()dpxxxpn (3 36 ) Free E ntry and the Value of the Firms A firm producing a variety with environmental quality level earns a per period profit () Because each firm faces a constant probability of death in each period, the market value of a firm with an environmental quality level is given by:

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75 0() ()max0,(1)()max0,t tv (3 3 7 ) where the second equality follows from the fact that the environmental quality contained in each firm's product remains constant during its lifetime, so that every period it earns the same profit. Because the probability of successful entry is 1() G the net benefits of entering the domestic market are equal to the expected value of a firm 1() G where / is the ex ante value of a prospective entrant and is defined by ()()dxxxpn Setting the benefits of entry equal to the fixed R&D costs yields the free entry condition: 1()e f G (3 38) The average profit is solely determined by the probability of death the fixed environmental R&D ef and the environmental standard Given the probability of death and the fixed environmental R&D ef if r egulators set higher standards prospective firms are less likely to enter successfully, an entrant would expect there will be less firms in the markets and its expected value would be higher. Steady State E quilibrium At the steady state equilibrium, the zero cutoff profit condition will determine the relationship between the average profit per firm and the export cutoff environmental quality level x Combine (315) and (3 19), we have ()(1)()() ()()dpdpp dxdxxr r (3 39)

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76 From (3 16), we have ()(1)() ()xxx xxxr r (3 40) Using (3 20), (3 24) (3 39) and (340), the overall average profit from both domestic and foreign markets (336) becomes ()(1) ()(1) 11p x x xx xx f pnf (3 41) where xp and x are both functions of x Therefore, equation (341) identifies the new zero cutoff profit condition for the open economy. At the steady state equilibrium, given environmental standard from the free entry condition (338), the overall average profit can be identified. Together with the new zero cutoff profit condition, a unique cutoff environmental quality level x can be identified. This equilibrium cutoff environmental quality level x and the standard determine the average environmental quality level of exporting firms x the average environmental quality level of all domestically produced goods p and the combined average of all goods c The ex ante successful entry and export probabilities inp and xp are determined as well. The average revenue (3 35) is then determined by the zero cutoff profit condition (3 41) and the free entry condition (338) : (See A lgebraic Details ) ()xx rpnf (3 42) At the steady state equilibrium, the aggregate variables must remain constant over time, so the number of firms is constant. Therefore in any single peri od, the number of

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77 successful entrants inepM must be equal to the number of incumbent firms who are forced to exit the market due to a bad shock, i.e., ineppMM where eM is the number of potenti al entrants and inepM is the number of firms who successfully enter the market. Since the entering and exiting firms have the same distribution of env ironmental quality levels, at the steady state equilibrium, the distribution of envi ronmental quality () is not affected by this simultaneous entry and exit. The labor employed by the prospective entrants for environmental R& D to discover the varieties and the labor employed by the incumbent firms for manufacturing are denoted by eL and mL For the full employment condition to be satisfied, labor demand equals labor supply, i.e., emLLL Total payments to workers in manufacturing are equal to the difference between aggregate revenue and profit: mLR The labor employed by the prospective entrants for environmental R&D to discover the varieties is given by eeeLMf Using the aggregate stability condition, ineppMM and the free entry condition, 1()ef G eL can be written as: 1()p eee epM LMffM G ( 3 43) Thus, the aggregate amount of labor employed by the prospective entrants for environmental R&D equals the level of aggregate profits earned by all producers in a typical market. Also, the aggregate revenue mmeRELLLL must also equal th e total payments to labor L and is solely determined by the total number of consumers. Per capita expenditure equals unity due to the choice of labor as the numeraire, i.e., 1 Ew and the aggregate revenue RL Using (3 38) and (342), t he

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78 number of producing firms in any period can then be determined from the average profit: 1() () 1()p xx e xxLG ELL M rpnf fGnf (3 44 ) At the steady state equilibrium, the number of varieties produced domestically is determined by the size of the economy, the elasticity of substitution between any two products, the stochastic shock, environmental R&D and the environmental standard. Substituting ( 3 44) into ( 3 28) yields the total number of vari eties that are available for consumption: 1()1() (1) 1()x cxp e xxLGnG MnpM fGnf (3 45 ) Notice that in the absence of trade ( 0 n ), the number of varieties produced equals the number of varieties consumed, i.e., pcMM Pollution and Welfare Both consumers and producers take aggregate pollution as given. A ggregate pollution Z can be expressed as (1) (1) ()(1)() ()xp x cc cM M Ln Zdd MM (3 38) Per capita welfare is given by: (1) (1) 1/(1) ()(1)() ()xp x cc x x cM M n Ldd MM L W f (3 39) Depending on the parameter values, per capita welfare W can be either positive or negative. A more stringent environmental standard affects per capita welfare in

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79 several ways: F irst, a more stringent environmental standard m akes it more difficult for prospective entrants to enter the market successfully and firms that cannot meet the new standard will have to exit the market There will be fewer domestic firms producing at the steady state equilibrium and consumers will enjoy mo re varieties of imported goods. However, the total number of varieties that are available for consumption is not clear depending on the trade costs. For example, if the fixed trade cost is small ( 1()e xf f G ), there are more foreign firms that are able to export their products and domestic consumers will have more varieties to consume. However, w hen there are more varieties available in a typical market, the green price index is driven down and there is lower demand for every brand. Consum ers are buying more varieties while spending less on each variety and these two effects cancel out exactly. Similar logic applies when there are fewer variet ies. Therefore, the number o f varieties does not affect aggregate consumption directly. A stricter environmental standard drives down the cutoff environmental quality level for exporting firms and the average environmental quality level is lower. Because consumers prefer products with better environmental quality, aggregate consumption is smaller. Secon d, the effect of a more stringent environmental standard on aggregate pollution is unclear. When the environmental standard is higher, if there are fewer varieties available, the average environmental quality is higher and consumers consume more of each va riety. The pollution emission generated from each variety is higher and, therefore, a higher standard may increase or decrease aggregate pollution. Overall, the effect of a more stringent environmental standard on per capita welfare is ambiguous. The following proposition summarizes these results:

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80 Proposition 3 2 : A more stringent environmental standard will decrease the export cutoff environmental quality level x decrease aggregate consumption and may increase or decrease aggregate pollution. T herefore, the overall effect of raising the environmental standard on the per capita welfare is ambiguous. (See Figure 31.) The Impact of International Tr ade Trade liberalization is measured by an increase in the number of trading partners n a reduction in foreign entry cost xf or a reduction in per unit trade costs The effects of trade liberalization are transmitted through changes in the export cutoff environmental quality level x as described in Lemma 32. ( See A lgebraic Details for proof.) Lemma 3 2 : An increase in the number of trading partners ( n ) increases the export cutoff environmental quality level x ; whereas a reduction in for eign entry cost ( xf ) or a reduction in per unit trade costs ( ) decreases x (i.e., /0 xddn, /0xxddf and /0xdd ). For any given environmental standard the export cutoff environmental quality level x the total number of varieties available for consumption cM and the ex ante expected profit are fixed. Any form of trade liberalization does not change the ex ante profits (given by equation (338)). An increase in the number of trading partners ( n ) increases the number of available varieties cM Because there are more firms competing in the market, it reduces the profits of the marg inal exporter, and the cutoff environmental quality level x has to increase to restore profits back to the equilibrium level.

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81 A reduction in foreign entry cost ( xf ) or a reduction in per unit trade costs ( ) has two effects: First, i t makes firms more likely to export to foreign markets because it increases profits from exports and the cutoff environmental quality level x has to decrease to restore profits ba ck to the equilibrium level. Second, the increased competition tends to reduce profits and requires an increase in the cutoff environmental quality level x The first effect dominates, therefore, lower trade costs generate lower cu toff environmental quality level x The following proposition discusses the effect s of trade liberalization on aggregate consumption, pollution and the per capita welfare. ( See A lgebraic Details for proof.) Proposition 3 3 : Tra de liberalization increases aggregate consumption (i.e., /0 dQdn /0xdQdf and /0 dQd ) and may increase or decrease aggregate pollution. T herefore, the overall effect of trade liberalization on the per capita welfare is ambiguous. Conclusions This chapter builds a simple monopolistic competition model of firm heterogeneity and international trade. Firms in this model face C.E.S preferences and charge prices as a constant markup over their marginal costs that are positively related to the firm specific environmental quality levels. It studies the effect of a stricter environmental standard on firms profitability, pollution and consumers' welfare when countries are allowed to trade. I find that with a stricter standard, firms with low levels of environmental quality will exit the market. However, in order to restore the steady state equilibrium condition, more firms are able to export to foreign markets. Firms are making higher revenues and profits t han before, despite their exporting status. The

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82 effect of the standard on aggregate pollution is unclear. The overall effect on welfare is ambiguous depending on the relative importance of consumption and pollution to consumers. T he impact s of trade liberalization are also studies Trade liberalization changes the cutoff environmental quality. Firms who only serve the domestic market make lower revenues and profits ; firms who are able to export now increase their sales to foreign countries, make up their loss of domestic sales and overall revenues are higher. Trade liberalization ultimately increases the aggregate consumption. Unfortunately, it is hard to tell whether trade liberalization increases or decreases the aggregate pollution. Algeb raic Details In this section, we include the proofs and algebraic details for Chapter 3. Proof of Lemma 3 1: Since every producing firm has to meet the environmental standard, we have ()(1)()(1) Substitute in to the definition of p, which is given by equation (329), to obtain ()(1) ()(1) ()(1) ()(1)11 () () 1() 1()pgd gd GG which yields p Let ()(1)1 () () 1() H gd G differentiation of equation ( 3 29 ) yields : 1/()(1)11 () ()(1) H H

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83 where ()(1) ()(1) ()(1)()(1) 2()1() ()() () 1() 1()pgG gdg g H G G Since p 0 H Therefore, 0p x is the weighted average environmental quality level of all exporting firms and is given by equation (330). x is the cutoff environmental quality level, so for every exporting firm, its environmental quality level has to be higher x We have ()(1)()(1) x Substitute into equation (330) to obtain ()(1) ()(1) ()(1) ()(1)11 () () 1() 1()xxx xx xxgd gd GG which yields xx Let ()(1)1 () () 1()xx xJ gd G differentiation of equation ( 3 30 ) yields : 1/()(1)11 () ()(1)x xx J J where ()(1) ()(1) ()(1)()(1) 2()1() ()() () 1() 1()xxxx x xxx xx xgG gdg g J G G Since xx 0xJ Therefore, 0x x

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84 Proof of the aggregate variables (332), (3 33) and (334): Using (3 9) and (310), the green price index P (given by equation (38)) can be written as: 1/(1) ()(1) 1()(1) 11() ()xpxP Mdn Md 1/(1) 1/(1) ()(1) 1()(1)() ()xp cx ccM MMdn d MM 1/(1) 1/(1) ()(1) ()(1) 1 p cx px ccM MM n MM 1/(1)/ccM In open economy, aggregate revenue definition 0()() RrMd can be expressed as ()()()()xdp xxRrMdnrMd Using (3 15) and (317), we have ()(1) ()(1) 1 ()(1) ()(1)() () () ()xdc p dc x cc n RrMdrMd ()(1) ()(1) 1 ()(1)() () ()xp dc x c cc cM rM n Mdd MM ()cdcMr A ggregate quantity (3 2) can be expressed as 1/ 1() 1()()()( )()xpxQPMdnPMd 1/ ()(1) (1) ()(1) 1() ()xpxP MdnMd

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85 1/ (1)()(1) ccMP /(1)(1)() ccMP 1/(1) ccM A ggregate pollution is calculated as 1(1) 1(1)() ()xpxZL PMd nL PMd (1) (1) ()(1)() ()xp x cc cM M Ln dd MM (1) (1) ()(1) 1 1 (1) (1) ()(1) 1 1() () () () () ()x xp x cc p x px cc px pp xxM M n Ldd MM M nM MM n LM dM d M nM Proof of (3 42): 1 ()(1) ()(1) 1 ()(1) ()(1) 1 ()(1) ()(1) 1()() () ()xxxx x xx xxx xx x x xx xx x x xx xxrrpnr r pnr f pnf f pnf ()(1) ()(1) 11 ()x x xx xx xx xxf pnf pnf pnf

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86 Proof of Proposition 3 2 : From the zero profit condition ()()/0xxxxxrf we have 11()(1)()xxELP f Us ing 1/(1)/ccPM we can get ()(1) ()(1)1 x xccL fM Further, us ing the definition of c we have ()(1) 1()(1) ()(1) x pp xx xL M nM f Using the definitions of p, x and the solution of pM xM we have the steady state equilibrium condition: ()(1) 1()(1) ()(1)1() () ()xe xx xf Gn gdngd f T otal different iat i ng the steady state equilibrium condition with respect to : ()(1)1 1()(1)1()()(1) ()ex xx xfd Gn g fd Therefore, 1()(1) ()(1)1() 0 1()()(1)x e xx xd g d f Gn f Total differentiating the steady state equilibrium condition with respect to : 2()(1) ()(1)1(1) () 0 1()()(1)x e xx xgd d d f Gn f Total differentiating the steady state equilibrium condition with respect to xf :

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87 20 1()()(1)x ex x ex xxdf df ffnGf Total differentiating the steady state equilibrium condition with respect to n : ()(1)()(1) ()(1)11() 0 1()()(1)xxx x e xx xG d dn f Gn f Proof of Proposition 3 3 : A ggregate consumption is given by (334): 1/(1) ccQM From (3 15), we have ()(1) 1() ()dcc dxx cxr L r Mf so ()(1) ()(1) 1 x c cxL Mf Then, we can get 1/(1) x c cxL Mf A ggregate consumption becomes: 1/(1) x xL Q f Differentiating aggregate consumption with respect to yields: 1/(1) 1()0x x xd dQL df d Differentiating aggregate consumption with respect to n yields: 1/(1) 1()0x x xd dQL dnf dn Differentiating aggregate consumption with respect to yields: 1/(1) 2()1xx xxd dQL dfd

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88 where 1()(1) ()(1)() () 1()x x e xx xgd d d f Gn f Using the steady state equilibrium condition, this expression becomes 1()(1) 1()(1) ()(1)() () () ()xx xgd d d gdngd ()(1) 1 ()(1)1 () 1 ()xgd n gd 1 Therefore, 0 dQ d Differentiating aggregate consumption with respect to xf yields: 1/(1) 1/(1)11 ()(1)1 (1)xx xx x xxdf dQ L f df df where ()(1) 1 1()xx e xxe xxdff dffnGf Therefore, 0xdQ df

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89 Figure 31. Effect of an increase in the environmental standard ZCP x FE FE' ( )

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90 LIST OF REFERENCES Aghion, P., and P.Howitt. (1998). Endogenous Growth Theory Cambridge, MA: MIT University Press. Antoniades, A. (2008). Heterogeneous Firms, Quality and Trade ." Working paper. Baldwin, R. E., and J. Harrigan. (2007). "Zeros, Quality and Space: Trade Theory and Trade Evidence." NBER Working paper No13214. Barbier, E. (1999). "E ndogenous Growth and Natural Resource Scarcity." Environmental and Resource Economics 14, 5174. Boserup, E. (1981). Populati on and Technological Change: A S tudy of Longterm Trend. Chicago : University of Chicago Press Brander, J. (2007). "Viewpoint: Sustainability: Malthus Revisited?" Canadian Journal of Economics 40, 138 Byrne, M. (1997) "Is Growth a Dirty Word? Pollution, Abatement and Endogenous Growth." Journal of Development Economics 54, 261284. Bovenberg, L., and S. Smulders. (1995). "Environmental Quality and PollutionAugmenting Technological Change in a TwoSector Endogenous Growth Model." Journal of Public Economics 57, 369391. Bovenberg, L., and S. Smulders. (1996). "Transitional Impacts of Environmental Policy in an Endogenous Growth Model." International Economic Review 37, 861 893. Brock, W., and M. T arlor (2004). Economic Growth and the Environment: a Review of Theory and Empirics The Handbook of Economic Growth. Brundtland, G. (1987). Our Common F uture. Oxford University Press. Dinopoulos, E., and F. Sener. (2007) New Directions in Schumpeterian Growth Theory. Edgar Companion to NeoSchumpeterian Economics Cheltenham. Dinopoulos, E., a nd P. Thompson. (1998). "Schumpeterian Growth Without Scale Effects", Journal of Economic Growth 3, 313 335. Dinopoulos, E., a nd P. Thompson. (1999). "Scale Effects in Schumpeterian Models of Economic Growth, Journal of Evolutionary Economics 9, 157185. Dinopoulos, E., and B. Unel. (2010). "A Simple Model o f Quality Heterogeneity and International Trade." Working paper.

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94 BIOGRAPHICAL SKETCH Ting Levy was born in 1981 in China. She graduated from Xiangfan High School in Xiangfan, Hubei Pr ovince, China in 1998. She recei ved her Bachelor of Science in e conomics in June 2002 from Huazhong University of Science and Technology, Wuhan, Hubei, China. In 2003, she began her graduate studies at Carleton University, Ottawa, Ontario, Canada and received her master's degree in economics in August 2005. She then moved to Gainesville, Florida and began her doctoral studies at the Univer sity of Florida. She specializes in international trade, environmental economics, economic growth and development. She received her Ph.D. in economics from the University of Florida in the fall of 2010. She currently resides in Boca Raton, Florida with her husband Eric Levy and 16 month old son Joshua.