Assignment 1: Problem 1
A company that makes shopping carts for supermarkets recently purchased some new
equipment that reduced the labor content of the jobs needed to produce shopping
carts.
The information regarding the old system (before adding the new equipment) and after
adding the new equipment are given below.
Current System
Output/hr
80
Workers
5
Wage/hr
$10
Machine/hr
$40
New Equipment Added
84
4
$10
$50
a) Compute labor productivity for both the Old System and the New System
b) Compute AFP productivity for both the Old System and the New System
c) Suppose production with old equipment was 30 units of cart A at price of $100 per
cart, and 50 units of cart B at price of $120. Also suppose that production with new
equipment is 50 units of cart A, at price of $100 per cart, and 30 units of cart B at
price of $120. Compare all factor productivity for old and new systems.
Assignment 1: Problem 1
Output/hr
Workers
Wage/hr
Machine/hr
Current Situation
80
5
$10
$40
New Machine Added
84
4
$10
$50
(a) Compute labor productivity
Old System : 80/5 = 16 units/worker
New System : 84/4 = 21units/worker
(b) Compute all factor productivity
Old System : 80 / (5×10 + 40) = 0 .89 units/$
New System : 84 / (4×10 + 50) = 0.93 units/$
Assignment 1: Problem 1
(c) Now suppose:
Production with old equipment was 30 units of cart A at price of
$100 per cart, and 50 units of cart B at price of $120.
Production with new equipment is 50 units of cart A, at price of
$100 per cart, and 30 units of cart B at price of $120.
Compare all factor productivity for old and new systems.
AFP of the Old System =
[(30)(100)+(50)(120)] / [5×10 + 40] = 9000/90 = 100
AFP of the New System =
[(50)(100)+(30)(120)] / [4×10+50] = 8600/90 = 95.6
Assignment 1: Problem 2
A company has introduced a process improvement that reduces processing
time for each unit so that output is increased by 25% with less material
but one additional worker required.
Under the old process, five workers could produce 60 units per hour.
Labor costs are $12/hour, and material input was $16/unit.
For the new process, material is now $10/unit. Overhead is charged at
1.6 times direct labor cost.
Finished units sell for $31 each.
a)
b)
Compute single factor productivity of labor in the old system.
(Compute it in four possible ways.)
Compute all factor productivity for both old and new systems.
Factor
Output
Old System
60
New System
60(1.25) = 75
# of workers
Worker cost
Material
Overhead
Price
5
$12/hr
$16/unit
1.6(labor cost)
31
6
$12/hr
$10/unit
1.6(labor cost)
31
Problem 2; An additional computation
Factor
Output
# of workers
Worker cost
Material
Overhead
Price
Old System
60
5
$12/hr
$16/unit
1.6(labor cost)
31
New System
75
6
$12/hr
$10/unit
1.6(labor cost)
31
a) Compute labor productivity for the old system
Labor Productivity = 60/5 = 12 units per worker
Labor Productivity = [(60)(31)]/5 = 372 $ per worker
Labor Productivity = 60/[(5)(12)] = 1 unit per dollar
Labor Productivity = [(60)(31)]/[(5)(12)] = 31
Problem 2; AFP
Factor
Output
# of workers
Worker cost
Material
Overhead
Price
Old System
60
5
$12/hr
$16/unit
1.6(labor cost)
31
New System
75
6
$12/hr
$10/unit
1.6(labor cost)
31
b) Compute AFP
Since there is only a single output, in the numerator we can
have either # or $.
Since it is all factor productivity, in the denominator we must
have $
Problem 2; AFP
Factor
Output
# of workers
Worker cost
Material
Overhead
Price
Old System
60
5
$12/hr
$16/unit
1.6(labor cost)
31
New System
75
6
$12/hr
$10/unit
1.6(labor cost)
31
Old System
Denominator of all factor productivity is computed as
(5)(12) + (16)(60) + (1.6) (5)(12) = 1116
The numerator is (60)(31) = 1860
All factor productivity for old system = 1860/1116 = 1.67
New System
[(75)(31)]/ [(6)(12) + (10)(75) + (1.6) (6)(12)] = 2.48
1.67 in the old system, 2.48 in the new system