Tutorial #5 Undesirable Outcomes and Production Theory

Transcription

1 Tutorial #5 Undesirable Outcomes and Production Theory Finn R. Førsund University of Oslo * lides prepared for the 14 th International DEA Conference Jianhang University, Wuhan, China ay 23-26, 2016 Desirable and undesirable outputs 1

2 Environmental economics From externalities to environmental pollution Regional/local air/water/land pollution and public health issues Global pollution: climate change The conncection between economic activity and physical emissions of residuals The materials balance principle Environmental consequences of emission of harmful residuals Ecological information in a wide sense Desirable and undesirable outputs 2

3 Preferences for the environment Calculation of damages in monetary terms D D D( z1,.., z k ), 0, s 1,..., k z s Willingness to pay for preventing environmental degradation, for restoration of environmental qualities Pollution is generically a problem with joint outputs Desirable and undesirable outputs 3

4 Joint outputs imultaneous production of multiple outputs Assorted production: Inputs can be applied alternatively to produce different products; agricultural land used for different crops, wood cutting machine for different objects Technical jointness: by-products; mutton and wool, wheat and straw, coke and gas from coal Extreme jointness: fixed proportions; distillates of crude oil Desirable and undesirable outputs 4

5 Engineering foundations A neoclassical production model is an approximate summary of the engineering features of the underlying technology How to establish in an operational form "the range of techniques implied by a given stock of knowledge"? (alter 1960) The production function is defined as a function where output is maximised for given inputs Desirable and undesirable outputs 5

6 Economists approach to production functions is to consider technology as the family of feasible engineering arrangements The conventional division between economics and engineering which has been assumed by economists is purely arbitrary separation. (Chenery, 1953 p. 507) Chenery advocates establishing engineering production functions by building on three elements: i) a source of energy ii) a means of transforming energy iii) a means of control The factors of production are classified as raw materials and process inputs. The latter are capital and labour. Desirable and undesirable outputs 6

7 Formulating production relations A choice has to be made as to the most relevant production function concept for the problem at hand The data must match this choice Use of a production function at an aggregated level Technical substitution and scale properties only exist on a real engineering level. There is a fallacy of misplaced concreteness Desirable and undesirable outputs 7

8 The production possibility set T = {( y,x ): y 0 can be produced by x 0} y Output-input y2 Output-output Constant x Frontier Output set Production possiblity set x x2 Input-input y1 Input set Constant y x1 Desirable and undesirable outputs 8

9 The boundary of the production possibility set is the standard textbook transformation F( y,x) F( y,x) m n F( y,x ) 0, y R+, x R+, 0, 0, yi x j i = 1,..,m, j = 1,..,n aximal flexibility; a given input x can be used to produce any combination of y1 and y2 y2. A P dy dy 2 1 F y y 1 F 2 B y1 Desirable and undesirable outputs 9

10 Introducing bads, z (Baumol & Oates, 1975): F( y,z, x ) 0( F 0, F 0, F 0) The material balance for raw materials ax by cz Input x is constant: a change along the curve at P is only possible if residuals decrease causing y to increase and z to decrease, but this is impossible because efficiency is assumed in constructing the transformation function y z x 0 A y Desirable and undesirable outputs 10. P dy dz F z F B y? z

11 Bads as inputs (Baumol&Oates, 1975) Bads z cannot be input together with real inputs x arginal productivity of bads as input: dy dz F z F y But y and z cannot increase for constant x; against the material balance Assuming that inputs can be moved from abatement to production thus increasing output y is not compatible with given resources x Desirable and undesirable outputs 11

12 The strong conclusions from multi-output production theory and materials balance There is no transformation possible between the good and the bad for constant inputs Output can only increase (decrease) when resources are given if residuals decrease (increase), but this is not possible on the frontier Residuals z cannot act as inputs because production of y cannot increase when increasing the residuals; this goes against the material balance Desirable and undesirable outputs 12

13 Frisch multioutput production A system of equations Degree of assortment : m μ Factor bands F b ( x,.., x ) 0, bb 1 Product couplings 1 n F c ( y,.., y ) 0, cc m Desirable and undesirable outputs 13

14 Factorially determined multioutput production Product separation i y f ( x,.., x ), i 1,.., m i 1 n No substitution for fixed inputs, but change in input mix changes the mix of outputs Desirable and undesirable outputs 14

15 Factorially determined multi-output production with pollutants The Frisch pollution model y f ( x, x ), f, f 0 x x z g( x, x ), g 0, g 0 ax by cz, a 0, b 0, c 0 x x aterial inputs x, service inputs x, residuals z Explaining a positive marginal productivity of x in f(.) Explaining a negative marginal productivity of x in g(.) The materials balance is an accounting identity Desirable and undesirable outputs 15

16 Isoquant map in input space Good output y and bad output z Input x B z, pollutant C y, output A Input x Desirable and undesirable outputs 16

17 Technical change t t 2 1 f x x f x x t (, ) (, ) t 2 1 g ( x, x ) g ( x, x ), t t 2 1 The new technologies ft2(.) and gt2(.) yield more good output and less bads for given inputs The new frontier technology is input-saving especially in material inputs and thus get more output from given inputs with less bads Desirable and undesirable outputs 17

18 cale properties y f ( x, x) y ( fx fx ), 1, y ( fx fx ) y, y y z g( x, x) z ( gx gx ), z 1, ( gx gx ) z, z z Essentiality of material inputs y f (0, x ) 0, z g(0, x ) 0 Desirable and undesirable outputs 18

19 Abatement a a a a z z za( x, x ), A x, A 0, [0,1] x z D a z z z 0 ax cz bz cz a a D Harmless residual za Primary residual z econdary residual zd Desirable and undesirable outputs 19

20 Optimal solution with abatement f ( x, x ) w0 ax p( w) dw q x q x D( z ) st.. y w0 y f ( x, x ) z g( x, x ) a a a z za( x, x ) D a a a z z z z(1 A( x, x )) a a D j j j j j, j, ax p( w) dw q x q x D( g( x, x )(1 A( x, x )) a a a a j j j j j, j, Desirable and undesirable outputs 20

21 First-order conditions f p q Dg (1 A) 0, j, x j x j a q DzA 0, j, j Economic interpretations Rate of substitution x a j arginal Unit factor arginaldamage of revenue cost increase in a factor j f p q Dg (1 A), j, x j x j f x q (1 ) Dgx A f q Dg (1 A) x x j Optimal abatement: a DzA q, j, x a j j Desirable and undesirable outputs 21

22 Implementing a Pigou tax The optimisation problem of the firm ax st.. py q x q x tz y f ( x, x ) z g( x, x ) a a a z za( x, x ) a a D j j j j j, j, D a z z z ax pf ( x, x ) q x q x tg( x, x )(1 A( x, x )) a a a a j j j j j, j, Desirable and undesirable outputs 22

23 First-order conditions, interior solutions f p q tg (1 A) 0, j, x j x j a q tza 0, j, j Value of marginal product equal to factor price plus tax cost at the margin arginal rate of substitution: x a j j f x q (1 ) tgx A f q tg (1 A) x x Cost of abatement resource equal to saved tax on secondary residuals at the margin Implementation of social solution: tax set equal to marginal damage of the secondary pollutant Desirable and undesirable outputs 23

24 The production-set representation Introducing inefficient combinations explicitly The production possibility set, T T = {( y,z,x ):( y,z ) can be produced by x } Weak disposability to block z=0 for y>0 Does weak disposability have any sound economic interpretation? If ( y, z, x) T,and 0,1 then ( y, z, x) T Desirable and undesirable outputs 24

25 Weak disposability hephard 1970 Desirable and undesirable outputs 25

26 Färe et al. (1986), (1989); problems Good E B A. P W C O D Bad Desirable and undesirable outputs 26

27 Inefficiency The potential engineering or blue-print technology, the frontier, is not achieved For given inputs the frontier can be achieved by reducing pollutants and increasing output The material balance holds for both inefficient and efficient points Can inefficient units have optimised? Problems studying effects of policy instruments Desirable and undesirable outputs 27

28 Estimation of the model using DEA y f ( x, x ) z g( x, x ) a a a z / z A( x, x ) ax by cz ax cz bz cz a a D Desirable and undesirable outputs 28

29 Efficiency measures (0,1]: Using observed outputs and potential ones Desirable output efficiency, E y E y / f ( x, x ) y Primary residual efficiency, E z E g( x, x ) / z z Abatement efficiency, E A a a a E z / za( x, x ) A Desirable and undesirable outputs 29

30 Conclusions The use of weak disposability as a reduced form: Violates the materials balance principle and general logic of residuals generation Cannot be used to study abatement without extensions Not convenient studying policy instruments Recommended: Use of Frisch factorially determined multioutput production as a multi-equation system Desirable and undesirable outputs 30