Timber production Efficiency Analysis
Timber Production Efficiency Analysis
Content A e Defining the production technology and technical efficiency e The measurement and decomposition of cost efficiency ● Empirical methods e Technical efficiency in southern U. s pulpwood harvesting
Defining the production technology and technical efficiency The measurement and decomposition of cost efficiency Empirical methods Technical efficiency in southern U. S. pulpwood harvesting
Summary f(X) f(x) X Standard production economics analysis begins with the production function y=f(x) where y is output and x is input
Summary Standard production economics analysis begins with the production function y =f (x) where y is output and x is input
1. Defining the production technology and technical efficiency All feasible input-output vector relationships are described by the graph of the production technology or production possibilities set, PT such that PT=i(y, x): x can produce y j
1.Defining the production technology and technical efficiency All feasible input-output vector relationships are described by the graph of the production technology or production possibilities set , PT, such that PT=｛(y, x) : x can produce y｝ 7.1
Input and output sets 只能能共影与 The input(output)sets of the production technology which describe the sets of all input(output) vectors that are feasible for each output(input) vector y(x), are defined as y)={x:(y,x)∈PT} 72 P(x)={y:(y,x)∈PT 73
Input and output sets The input (output) sets of the production technology, which describe the sets of all input (output) vectors that are feasible for each output (input) vector y (x), are defined as L(y)=｛x: (y, x) ∈PT｝ 7.2 P(x)=｛y: (y, x) ∈PT｝ 7.3
Input and output isoquants 只能能共影与 An input isoquant Isoq l(y)={x:(y,x)∈PT,x∈(Y),1}7.5
Input and output isoquants An input isoquant Isoq L(y)=｛x: (y, x) ∈PT, λx ∈ L(Y), λ＜1｝ 7.4 An output isoquant Isoq P(x)=｛y: (y, x) ∈PT, θy ∈ P(x), θ＞1｝ 7.5
Definiting the technical dfficiency The definition for input-oriented technical efficiency is given by the function TEn(y,x)=minx:y≤f(x)}0<TE1(y,x)≤1 7.6 The definition for input-oriented technical efficiency is given by the function TEo(y,x)=[max{0:0y≤f(x)}10<TE0(y,x)≤1
Definiting the technical dfficiency The definition for input-oriented technical efficiency is given by the function TE1 (y, x) = min{λ:y ≤ f (λx)} 0＜ TE1 (y, x) ≤1 7.6 The definition for input-oriented technical efficiency is given by the function TE0 (y, x) = [max{θ:θy ≤ f (λx)}]-1 0＜ TE0 (y, x) ≤1 7.7
2. The measurement and ecomposition Of cost effIcIency For a single output, the cost frontier is a function c(y,1)= min w'x:y≤f(x)} Inputprice w=(n…0)∈R 7.8 The ratio of minimum to observed cost is termed cost efficiency and given by the function CE,x,w=c(, w)/wX, OCCE( Jyx,)≤1 7.9
2. The measurement and ecomposition of cost efficiency For a single output, the cost frontier is a function 7.8 The ratio of minimum to observed cost is termed cost efficiency and given by the function 7.9 N c y w f x w w wN ∈R++ ( , ) min {w x : y ≤ ( )} inputprice ( ,...., ) 1 T ＝ x ＝ CE(y, x,w) c(y,w)/w X, 0 CE(y, x,w) ≤1 ＝ T ＜
Two components 静能值给坐 )修 The overall level of cost inefficiency can be decomposed into two components The input-oriented technical component, i TEn(y,x)=min{:y≤f(x)}0<TE1(y,x)≤1 7.10 The allocative component, 0 AE, x, w=CE(,x, w)/TE ( x) CAE(,x,w)1 7.11
Two components The overall level of cost inefficiency can be decomposed into two components The input-oriented technical component , λ TE1 (y, x) = min{λ:y ≤ f (λx)} 0＜ TE1 (y, x) ≤1 7.10 The allocative component ,θ 7.11 AE1(y, x,w)＝CE(y, x,w)/TE1(y, x) 0＜AE1(y, x,w)≤1
3. Empirical methods 给能坐的影 SFA model DEA model CCR model
3. Empirical methods SFA model DEA model CCR model