AAEC 6524: Environmental Theory and Policy Analysis. Outline. Theory of Externalities and Public Goods. Klaus Moeltner Spring 2019.

Transcription

1 AAEC 6524: Theory and Policy Analysis Theory of Externalities and Public Goods Klaus Moeltner Spring 2019 January 21, 2019 Outline

2 Overarching and Related Fields and Microeconomics (consumer, firm, s) Applied Field (draws on microeconomics and all main fields) and Resource : failure, externalities, policy design; often static Resource : Production and use of natural resources; often dynamic Divisions blurred; Both included in traditional grad sequence FREC 5984 Special Studies: Advanced Natural Resource Related Fields, cont d and Ecological Ecol Econ grown out of systems ecology multi-disciplinary (not a sub-field of economics) usually inter-temporal models, long time horizon different take on value of nature lines have become blurred (journal Ecological )

3 Link to Welfare Main focus of : humans nature effect on other humans If impacts are ignored or remain uncompensated (or unpaid): externality Externalities have implications on human welfare welfare economics Link to environmental and policy sciences Env. Econ deals with humans nature Thus, linked to environmental sciences Also deals with humans environmental policy Thus, linked to public policy sciences

4 normative criterion to judge desirability of of different economic outcomes Economic outcome such that a reallocation of resources cannot make at least one person better off without making another worse off. Does not address issues of equity and fairness. Pure focus on efficiency Impossible to implement in practice. Politically unsustainable. Welfare theorems First welfare theorem Complete and perfectly competitive s will lead to -optimal allocation of resources. Second welfare theorem In complete and perfectly competitive s: Any -optimal allocation can be supported by a price system arising from a corresponding redistribution of income via lump-sum taxes and transfers.

5 Point of departure Conditions for welfare theorems usually not met: s are incomplete (fail to address externalities, free-riding, etc), and - at best - impurely competitive (monopolies, oligopolies, etc). Think of these fundamental concepts as points of departure. Objective of Env. Econ.: 1. Understand when and why free s fail to deliver efficient outcomes. 2. Find ways to mitigate these Externalities When the utility or production function of an economic agent depends on real variables generated via consumption or production by another economic agent, and no consideration is given to the resulting change in the first agent s wellbeing. Real variables: noise, pollution, visual impediments, etc So interactions that only result in price changes don t count (i.e. restaurant suffers because new one opens across the street).

6 Example Public goods Goods that are (purely or at least partially) non-rival and non-exclusive. Similar implications on welfare as externalities: s alone will not accomplish efficient allocation. Many environmental problems (and solutions) share PG characteristics. Thus, study of PG-type problems is also topic of Env.Econ.

7 In a nutshell... Externalities, PG s failure of Fundamental Welfare Theorems These analytical starting point for Coordination At the most general level, we could also define Env. as the study of the failure of coordination: missing / incomplete / impure s incomplete / poorly enforced property rights inability of affected individuals to make collective decisions How to promote coordination: Subject of Policy (Part II of this course)

8 Utility U i = U i (x i, z i, E), i = 1, 2 U (.) > 0 x U (.) > 0 z U (.) E < 0 x i : dirty good z i : clean good E: emission (exogenous to consumers) (1) Production x = f (l x, E) l x > 0 E > 0 (2) z = g (l z ) (3) l = l x + l z (4) l, l x, l z : labor

9 highlights So here emissions = input. Reduction in pollution reduces output of x. Could also let x,e be joint products (more notational clutter) First task: find conditions for Optimization problem max L = x 1,x 2,z 1,z 2,l x,l z,e U 1 (x 1, z 1, E) + λ u (U 2 (x 2, z 2, E) ū 2 ) + λ x (f (l x, E) x 1 x 2 ) + λ z (g (l z ) z 1 z 2 ) + λ l (l l x l z ) (5) key: Must hold agent 2 at a pre-specified utility level (her current level, for example)

10 FOCs: Consumption U 1 (.) = λ x x 1 U 1 (.) = λ z z 1 U 2 (.) λ u = λ x x 2 U 2 (.) λ u = λ z z 2 (6) Efficiency in Consumption U 1 (.) / x 1 U 1 (.) / z 1 = U 2 (.) / x 2 U 2 (.) / z 2 = λ x λ z (7) MRS between goods equal for both individuals.

11 Efficiency in Production λ x l x g (.) λ z l z = λ l = λ l Shadow value of MPL for each good = shadow price of labor for each good. (8) Efficiency in Exchange U i (.) / x i U i (.) / z i = g (.) / l z / l x = λ x λ z, i = 1, 2 (9) Slope of Production Possibility curve = slope of each person s indifference curve (IC)

12 FOCs: Emission U 1 (.) E + λ u U 2 (.) E rewrite: divide by λ x, substitute (6): ( U1 (.) / E + U ) 2 (.) / E = U 1 (.) / x 1 U 2 (.) / x 2 + λ x E = 0 (10) E (11) Interpretation more E lowers utility directly, but increases it indirectly via increased production and consumption of x left hand fractions = marginal willingness to give up x for a reduction in E (or marginal benefits of reducing E, as measured in x ) RHS: cost in reduced production of x from reducing E Reduction in E benefits both, so marginal cost in foregone production needs to be compared to sum of marginal benefits. In equilibrium, sum of marginal benefits must equal marginal cost of reducing emissions.

13 Symmetry to Public Goods case Some externalities (or reduction thereof) are like PGs Here: Reduction in E has PG characteristics Benefits enjoyed by one agent from less E do not interfere with benefits for the other Neither can be prevented from enjoying reduction So in this light, equ. (11) is also the Lindahl-Samuelson condition for the efficient allocation of a PG Symmetry to Public Goods case Note: Current solution {x 1, x 2, z 1, z 2, l x, l z, E } is just one of many -efficient outcomes. Setting a different utility for individual 2 (ū 2 ) would yield a different solution and optimal level of pollution.

14 Symmetry to Public Goods case Can free, competitive produce P.O. outcome? 2 Consumers, 2 firms economy. Individuals maximize utility, firms maximize profits. Given: prices p x, p z, wage w, income y i, i = 1, 2 Consumer problem and FOCs max x i,z i L = U i (x i, z i, E) + λ i (y i p x x i p z z i ), i = 1, 2 (12) U 1 (.) / x 1 U 1 (.) / z 1 = U 2 (.) / x 2 U 2 (.) / z 2 = p x p z (13) Marginal rate of substitution (MRS) equals price ratio for all consumers: efficiency in consumption

15 Firm z s problem and FOCs max l z π z = p z g (l z ) wl z (14) p z g (.) l z = w (15) Value of marginal product of labor (MPL) equals wage rate efficiency in production Firm x s problem and FOCs Firm x must select both labor and emission inputs to max. profits, treating emission as a free factor max l x,e π x = p x f (l x, E) wl x (16) p x l x = w p x E = 0 (17)

16 Discussion Efficiency in exchange is met, since from (13),(15), and (23): U i (.) / x i U i (.) / z i = / l x g (.) / l z = p x p z, i = 1, 2 (18) Slope of IC equals slope of production function for both consumers. Discussion, cont d Condition for E is different Before: Now: ( U1 (.) / E + U ) 2 (.) / E = U 1 (.) / x 1 U 2 (.) / x 2 E (19) p x E = 0 (20)

17 Discussion, cont d Firm emits pollution up to level where the value of the marginal product of pollution = 0 (any further pollution input won t help production) E s impact on consumers is not considered in deriving its optimal quantity. with externality (essentially a missing input ) fails to produce a -efficient outcome. Env. econ. deals with design of policies to correct failure. Example: Impose Pigouvian tax (Pigou, 1920) for each unit of E used in production of x: ( τ U1 (.) / E = p x + U ) 2 (.) / E U 1 (.) / x 1 U 2 (.) / x 2 (21)

18 Revised Firm x s problem and FOCs Emission input now has price of τ : p x l x p x E Pigouvian Tax = w max l x,e π x = p x f (l x, E) wl x τ E (22) = τ = p x ( U1 (.) / E + U ) (23) 2 (.) / E U 1 (.) / x 1 U 2 (.) / x 2 Graphical Analysis: Emission 18 Figure 1.1: Efficient Pollution Level and Pigouvian Tax $ U E U E 1 2 px U1 x1 U 2 x2 U p 2 x U2 x2 E MUC2 U1 E px MUC1 E U x 1 1 MUC E E E * f px VMPE E E c E Panel A $

19 Graphical Analysis: Abatement E * E c f px VMPE E E Panel A $ * 2 f - px MC A A U1 A U 2 A px MUBA U1 x1 U 2 x2 * 1 A * =E c E * p U2 px U A U1 E x U1 x1 AE MUB2 x 2 2 MUB1 A A A Panel B Typos fixed 8 July 2011