Environmental Economics - 4910 Professor: Bård Harstad University of Oslo January 14, 2019 Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 1 / 24
Environmental Problems Overusing/exploiting renewable and exhaustible resources Land use changes (e.g. tropical deforestation) Waste (e.g. hazardous, or plastic) Water (over-usage, or contamination) Air (particles, NO x , acid rain; ozone layer) Greenhouse gases (e.g., CO 2 ) Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 2 / 24
Classifications National vs. international Political vs. marked-based Number of sources and number of affected parties Tangible vs. nonverifiable pollutants Affecting producers vs consumers Flow pollutants vs. accumulated stocks Contemporary vs. long-term effects Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 3 / 24
Outline Welfare theorems and market failures (micro) 1 Policy instruments (Pigou, Coase, Weitzman) (public ec.) 2 Trade and the environment (int. trade) 3 Self-enforcing vs. binding agreements (game theory) 4 Architectures for agreements (economic systems) 5 Free-riding and participation (contract theory) 6 Supply-side environmental policy (resource ec.) 7 Deforestation and REDD contracts (development ec.) 8 The value of the Future: Discounting (behavioral ec.) 9 10 Integrated Assessment Models (Traeger) (macro) Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 4 / 24
Consumption and Production: "ECON 101" Consumers i ’s utility and good j ’s production function: j ≤ f j � � u i � � and ∑ x i 1 , ..., x i x i y 1 j , ..., y K , j J i ...where i ∈ { 1 , ..., I } consumes x i j of good j ∈ { 1 , ..., J } , and y k j is the quantity of input k ∈ { 1 , ..., K } used in the production of good j . Pareto optimality (PO) requires that u 1 � � x 1 1 , ..., x 1 max s.t. J { x i j } , { y k j } u i � � x i 1 , ..., x i u i , ∀ i ≥ ( shadow value: λ i ) , J f j � � x i y 1 j , ..., y K ∑ ≤ ∀ j (shadow value: µ j ), j j i y k y k ∑ ≤ ∀ k (shadow value: η k ). j j for some default levels ( u i ’s) and input quantities ( y k ’s) . Do we need to include labor/leisure in the model? Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 5 / 24
Consumption and Production: Pareto Optimality Lagrange (/Kuhn-Tucker) problem with foc for x i j and y k j (if λ 1 ≡ 1): λ i u i = µ j , j µ j f j = η k . k The shadow values depend on the default levels; the u i ’s. For PO, it is sufficient that the foc’s hold for some shadow values. When the foc’s are combined: u i µ j � = u i � µ j � i , i � � � j , j � � j k = ∀ , (efficiency in consumption), u i � u i j � l η k � = f j � f j � k , k � � � j , j � � η k k k = ∀ , (efficiency in production), f j f j � k � k � f j � u i � j , j � � j k = ∀ , i , k (efficiency in exchange). u i f j j � k Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 6 / 24
Consumption and Production: Market Equilibrium Consumers’ choice, given endowment E i (with shadow-value ν i ): u i � � j ≤ E i ( ν i ) ⇒ u i s.t. ∑ x i 1 , ..., x i p j x i j = ν i p j . max J { x i j } j j Producers: max p j f j � � − ∑ j ⇒ p j f j y 1 j , ..., y K w k y k k = w k . j k Combined: u i � u i µ j j j = µ j � = if just µ j = p j , u i u i � j � j � η k � = f j � f j η k k k if just η k = w k , = f j f j � k � k � f j � u i � j , j � � = p j j k = p j � ∀ , i , k . u i f j j � k Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 7 / 24
Consumption and Production: Welfare Theorems Theorem Every market equilibrium ⇒ Pareto optimal. 1 Every Pareto optimal outcome ⇒ market equilibrium — given some 2 allocation of endowments. Where is the environment? Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 8 / 24
Consumption and Production: With Externalities Externalities from inputs/productions to consumers: � � j ≤ f j � � and ∑ u i x i 1 , ..., x i x i y 1 j , ..., y K J , ∑ g j j , g j . j i Pareto Optimality is given by the same conditions as above, plus: − u i − u i � − u i � ⇒ u 1 g = ∑ g = ∑ g = ∑ g g µ j f j j f j u 1 ⇒ f j λ i . g j u i u i i i j i j Equilibrium with no regulation: j emits until f j g = 0 . With regulation or tax t j g on j ’s emission: p j f j g = t j g This coincides with the PO outcome if g = t j − u i − u i − u i g = ∑ g = ∑ g g = ∑ g f j ⇒ t j p 1 . u i p j u i u i p j 1 / p 1 1 i j i i So, the emission tax should be the same for all firms , no matter how valuable/dirty they are. Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 9 / 24
Consumption and Production: With Externalities (cont.) 1 = 1 = p 1 ), then t j If good 1 is a numeraire good (i.e., if u i g = ∑ i u i g . Alternatively, the regulator may decide on the g j ’s directly. For each such policy, there will be equilibrium prices and quantities such that payoffs are functions u i ( g ) and profits π j ( g ) . Larger g j ’s is likely to benefit producer j ( B j ( g j ) ) but be costly for consumers ( C i ( g j ) ). Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 10 / 24
Externalities and Public Goods Let g i be emission by agent i ∈ N ≡ { 1 , ..., n } , and g = { g 1 , ..., g n } . Externalities: u i ( g ) , if ∂ u i / ∂ g j � = 0 for some j � = i . Public good/bad: u i ( g ) = u i ( g i , G ) = B i ( g i ) − C i ( G ) , where G = ∑ g j . j ∈ N To get a unique solution, assume u i is concave in g i For example: Every B i is concave while C i is convex. Business as usual (interior) equilibrium: B � i ( g i ) = C � i ( G ) . Suppose transfers enter linearly and additively in u i . The first-best (FB; the unique PO outcome with transfers): i ) = ∑ B � i ( g ∗ C � j ( G ∗ ) . j ∈ N Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 11 / 24
Pigou Taxes (The "Incorrect Prices" Approach) Suppose i pays t i g i and receives T i ( g ) . Then, in equilibrium: ∂ B i ( g i ) i ( G ) + t i − ∂ T i ( g ) = C � . ∂ g i ∂ g i Equivalent: A subsidy T i ( g ) − t i g i , f.ex. t i · ( g i − g i ) . This coincides with the first-best if e.g.: j ( G ) and ∂ T i ( g ) t i = ∑ C � = 0. ∂ g i j ∈ N \ i In principle, it is (almost) irrelevant how tax revenues are spent. For example: T i ( g ) = ∑ j ∈ N \ i t j g j / ( n − 1 ) . If C � i ≈ 0 for each emitter, the linear tax is the same for all: t = ∑ i ( g i ) = ∑ C � j ( G ∗ ) ⇒ B � C � j ( G ∗ ) . j ∈ N j ∈ N Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 12 / 24
Pigou Taxes - Uncertainty Facing the same tax, we get: B � i ( g i , ǫ i ) = t = B � j ( g j , ǫ j ) ∀ ( i , j ) ∈ N 2 even if individual shocks ( ǫ i ) are private information. Then, define ǫ = ( ǫ 1 , ..., ǫ n ) and � � B ( t , ǫ ) ≡ ∑ B �− 1 ( t , ǫ i ) , ǫ i B i . i i ∈ N The optimal tax is given by: � � �� ∑ B �− 1 max E B ( t , ǫ ) − C ( t , ǫ i ) . i t i ∈ N Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 13 / 24
Pigou Taxes - Uncertainty - Example Q Consider the quadratic approximation ( Y =exp. "bliss" point): B ( G , ǫ ) = − b 2 ( Y − G − ǫ ) 2 and C ( G ) = c 2 G 2 , where the aggregate shock is ǫ ∈ R , E ǫ = 0, and variance E ǫ 2 = σ 2 ǫ . The equilibrium, given t : − b 2 ( Y − G − ǫ ) 2 − tG ⇒ b ( Y − G − ǫ ) = t . max G The tax pins down B � and B , leaving the uncertainty to G and C ( G ) . The optimal t : − t 2 2 b − E c 2 ( Y − ǫ − t / b ) 2 ⇒ t ∗ = c ( Y − t ∗ / b ) = cbY max b + c . t The uncertainty does not influence the optimal level of t . (Why?) Welfare loss relative to no uncertainty increases in c : t = c σ 2 ǫ L ǫ 2 . Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 14 / 24
Pigou Taxes and Tax Revenues Tax revenues (at the above optimal t ∗ ): � � = cb 2 Y 2 E tG = E cbY cY Y − ǫ − b + c . b + c b + c Tax revenues (at general t ): t ( Y − ǫ − t / b ) Normally, revenues necessitate distortionary taxes. With the social value λ , the optimal t is thus: − t 2 2 b − E c 2 ( Y − ǫ − t / b ) 2 + E λ t ( Y − ǫ − t / b ) ⇒ max t cb + λ b 2 t = c ( Y − t / b ) + λ b ( Y − 2 t / b ) = b + c + 2 λ bY . which can be increasing or decreasing in λ ... RQ: (When) is there a "double dividend"? Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 15 / 24
Pigou Taxes and ’Double Dividend’ Proposition Weak form: The regulation with Pigou tax revenues raises social 1 efficiency relatively to regulation without tax revenues. Holds trivially Strong form: The optimal tax is larger than the Pigovian level. 2 The strong form may or may not hold. Harstad (University of Oslo) Lecture Notes 1 January 14, 2019 16 / 24
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