Efficiency and Productivity Measurement: Basic Concepts. D.S. Prasada Rao School of Economics The University of Queensland, Australia. Objectives for the Workshop. Examine the conceptual framework that underpins productivity measurement Introduce three principal methods Index Numbers - PowerPoint PPT Presentation
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Efficiency and Productivity Measurement:Basic Concepts
D.S. Prasada Rao
School of Economics
The University of Queensland, Australia
Examine these techniques, relative merits, necessary assumptions and guidelines for their applications
Main ReferenceAn Introduction to Efficiency and Productivity Analysis (2nd Ed.)Coelli, Rao, O’Donnell and BatteseSpringer, 2005Supplemented with material from other published papers
S = {(x,q): x can produce q}.
P(x) = {q: x can produce q} = {q : (x,q) S}
L(q) = {x: x can produce q} = {x: (x , q) S}
do(x,q) = min{: (q/)P(x)}
y2
B
y2A
C
A
P(x)
y1A
y1
0
PPC-P(x)
Output Distance Function
Do(x,y)
The value of the distance function is equal to the ratio =0A/0B.
Output-oriented Technical Efficiency Measure:
TE = 0A/0B = do(x,q)
di(x,q) = max{: (x/)L(q)}
Input Distance Function
Di(x,y
The value of the distance function is equal to the ratio =0A/0B.
Technical Efficiency = TE = 1/di(x,q) = OB/OA
di(x,q) 1 if and only if do(x,q) 1.
di(x,q) = 1/do(x,q), for all x and q
where p is a vector of M output prices and w is a vector of K input prices
Iso-profit line:
q = π/p + (w/p)x
q
frontier
Profit max
x
x1
Cost min
Iso-cost line:
x1 = c/w1 – (w2/w1)x2
Isoquant (q=q0)
x2
y1
Revenue max
Iso-revenue line:
y1 = r/p1 – (p2/p1)y2
PPC (x=x0)
y2
Production function
Marginal product
Production elasticity
Scale elasticity
q
DRS
CRS
IRS
x
q
Frontier
B
Output orientation: TEO=DA/DB
Input orientation: TEI=EC/EA
C
E
A
D
x
CRS Frontier
q
VRS Frontier
TEVRS=DB/DA
TECRS = DC/DA
SE=DC/DB = TECRS/TEVRS
C
D
A
B
x
AE=360/420=0.86
TE=400/560=0.71
AE=360/400=0.9
CE=360/560=0.64
shirts
C
·
·
B
D
·
iso-revenue line
·
A
PPC
TEO=0A/0B
AEO=0B/0C
RE=0A/0C
=TEO×AEO
0
trousers