Productivity (P) = Output Produced / Input Consumed
P is always measured in units (mpg, cars per day, hours per day etc..)
Efficiency (E) = Output produced/Output maximum
It is a ratio of percent and always Less than 1, not measured in any units
Productivity Change(PC) = Productivity at t+1 / Productivity at t (measured in index, can be <=> 1)
Efficiency Change (EC) = Efficiency at t+1/Efficiency at t (measured in index, can be <=> 1)
Technical Change (TC) = Slope of Production Frontier at t+1 / Slope of Production Frontier at t (measured in index, can be <or > or = 1)
Production Frontier (PF) = Maximum Limit of Production
Productivity Growth (PG) = Efficiency Change (EC) * Technical Change (TC)
Examples:
at a time T (x= 20 ppl, y= 10 cars) and Effeciency (X=20 ppl ,y=15cars)
Productivity at T= 10/20 = 0.5 cars per worker,
Effeciency at T = 10/15 = 0.667 (<1)
at a time T+1 (x=30 ppl, y=30 cars), Effeciency (X=30 ppl ,y=40cars)
Productivity of T+1 =30/30 =1 car per worker,
Effeciency of T+1= 30/40=0.75 (<1)
ProductivitGrowth = 1/0.5 = 2 (>1),
Effeciency change = 0.75/0.667=1.125 (>1)
Technical Change = SlopeofProductionFrontier at T+1/Slope of Production Frontier at T
= ( 40/30) / (15/20)
= 1.33/0.75 = 1.777 ( GreaterThan 1)
Verify Productivity Growth (PG) = EC*TC = 1.125 * 1.777 = 2
