หลักสูตรอบรม การวัดประสิทธิภาพและผลิตภาพของการผลิตสินค้าเกษตรด้วยแบบจำลอง

DEA. .

Lecture 1:

(production function)

(production technology)

M N

M

K

(production technology)

(input-output vectors)

S = {(x,y): x can produce y}

(input sets)

L(y) = {x: x can produce y} = {x:(x,y)S}

2 1 : L(y) = {x=(x1, x2) : x can produce y} = {x=(x1, x2) :(x,y)S} L(yA) L(yA) (isoquant) 2

(output sets)

P(x) = {y: x can produce y} = {y :(x, y)S}

1 2 P(x) = {y =(y1, y2) : x can produce y} = {y =(y1, y2) :(x, y)S} P(xB) P(xB) (production possibilities curve, PPC) 2

(distance function)

Shephard (1953, 1970) (distance function) 1 (multiple inputs and outputs)

2 1. (input distance function, DI) L(y)

2. (output distance function, Do) P(x)

(DI) (isoquant) (radially contracted)

DI (y, x) DI(y, x) = max {: (x/) L(y)} = 0B/0A 1 x y y (x/*)

DI(y, x) = * 1

DI(y, x) = 1

(i) (non-decreasing in x)DI(y, x) DI(y, x) 1

(ii) (non-increasing in y)DI(y, x) DI(y, x) 1

(iii) 1 (homogeneous degree one in x)DI(y, x) = DI(y, x) > 0

(Do) (production possibility curve, PPC)

Do(x,y) DO(x, y) = min {: (y/) P(x)} = 0B/0A 1 x x (y/*)

D0(x, y) = * 1

Do(x, y) = 1

(i) (non-decreasing in y) Do (x, y) Do (x, y) 0 1

(ii) (non-increasing in x)Do (x, y) Do (x, y) 1

(iii) 1 (homogeneous degree one in y)Do (x, y) = Do (x, y) > 0

Debreu (1951) Farrell (1957) (technical efficiency, TE) 2

1. (input-orientated technical efficiency, TEI) TEI

2. (outputorientated technical efficiency, TEo) TEo

A: Di(yA,xA) = 0A/0BTEI = 0B/0A = 1 / DI(yA,xA) TEI 0 1 TEI = 1 B C(1-TEI) TEI a) (input-orientated measures)

a) (input-orientated measures)AEI = AEI = OD/OB AEI 0 1 AEI = 1 (Allocative efficiency, AEI) (optimal)

EE = CE = TEI x AEIEE = CE = (OB/OA)x(OD/OB) = OD/OA CE (Economic efficiency, EE or cost efficiency, CE) = TEI AEIa) (input-orientated measures)

A: Do(xA,yA) = 0A/0B TEo = OA/OB = Do(xA,yA) TEo 0 1 TEo = 1 B C (1-TEo) b) (output-orientated measures)TEo =

TEo = OA/OB = Do(xA,yA) AEo = OB/OD = EE = PE = TEo x AEo = OA/OD = (Economic efficiency, EE or profit efficiency, PE) = TEo AEob) (output-orientated measures)

(variable returns to scale, VRS) (increasing returns to scale, IRS) (decreasing returns to scale, DRS) VRS technology: TEI TEo : AB/AP < CP/CD CRS technology: TEI = TEo : AB/AP = CP/CD

(increasing returns to scale) (decreasing returns to scale) (scale inefficiency) (scale efficiency)

A C B (most productive scale size, MPSS)MPSS = max {y/x | (x,y) S} A C B B (scale efficiency)

TEI (VRS) = DA/DCTEI (CRS) = DE/DCSE = DE/DA = TEI(CRS) / TEI(VRS) = (DE/DC) / (DA/DC)(1 SE) TE CRS TE VRS (scale efficiency)

2 1 = 1 = 1 =

: Free disposability The professorial contest

Y = X1 = X2 = The professorial contest

Professor yx1x2x1/yx2/y1l2525222412336622413232526231

Frontier13245154320 (Frontier)

DMU yx1x2TEIPeerTargetx1Targetx21l250.521.002.0022241.022.004.0033660.8332, 55.005.0041320.7142, 52.1431.4295262156.002.00