1. A production function defines the relationship between inputs used in production and the maximum output that can be produced. It takes the form Q = f(X1, X2, ..., Xk), where Q is output and X1, X2, ..., Xk are inputs. 2. In the short run, at least one input is fixed, while in the long run all inputs can be varied as the firm has time to adjust plant size. The short run is when plant size is fixed, while the long run allows changing plant size. 3. For most production processes, adding more labor initially increases total product but eventually marginal product decreases and can become negative due to crowded conditions in a fixed plant

1. THE THEORY AND
ESTIMATION OF
PRODUCTION
1

2. PRODUCTION FUNCTION
10/14/13

Production function: defines the relationship
between inputs and the maximum amount that
can be produced within a given period of time
with a given level of technology
Q
= f(X1, X2, ..., Xk)
Q
= level of output
X1, X2, ..., Xk
= inputs used in production
2

3. PRODUCTION FUNCTION
10/14/13

Short-run production function: the maximum
quantity of output that can be produced by a set
of inputs
 Assumption:
the amount of at least one of the inputs
used remains unchanged

Long-run production function: the maximum
quantity of output that can be produced by a set
of inputs
 Assumption:
the firm is free to vary the amount of all
the inputs being used
3

4. SHORT RUN VS. LONG RUN

The short run is defined as
the period of time when
the plant size is fixed.
Plant size is
fixed, labor
is variable

The long run is defined as
the time period necessary
to change the plant size.
Both Plant
size and labor
are variable
Duration of the long/short
run depends on the
production process…
4

5. SHORT RUN VS. LONG RUN
Plant size is
Short Run
fixed, labor
is variable
To increase
Short Run
production firms
increase Labor
but can’t expand
their plant
5
Firms produce in the short run

6. SHORT RUN VS. LONG RUN
Long Run
How can
the plant
Long Run
size be
variable?
Firms plan in the
long run
Plant size is
variable, labor is
variable
To increase
production firms
increase Labor
and expand
Plant size is their
plant. in the
variable
‘planning’
stage
6

7. SHORT-RUN ANALYSIS OF TOTAL,
AVERAGE, AND MARGINAL
PRODUCT

Alternative terms in reference to inputs
 ‘inputs’
 ‘factors’
 ‘factors
of production’
 ‘resources’

Alternative terms in reference to outputs
 ‘output’
 ‘quantity’
(Q)
 ‘total product’ (TP)
 ‘product’
7

8. THERE ARE THREE IMPORTANT
WAYS TO MEASURE THE
PRODUCTIVITY OF LABOR:
Total
product (TP)
Average product (AP)
Marginal product
(MP)
8

9. TOTAL PRODUCT FUNCTION (TP)
 Represents
the relationship between
the number of workers (L) and the
TOTAL number of units of output
produced (Q) holding all other
factors of production (the plant size)
constant.
 For
a coffee shop, output would be measured
in “number of coffee cups a day”
 For a steel mill, output would be measured in
“tons of steel produced a day”
9

10. BUILDING A TOTAL PRODUCT GRAPH
The Total Product Curve must show
that:
1. With more workers more output can
be produced.
Total Product
Total Product
Total Product
INCREASING FUNCTION.
Labor
Labor
Labor

11. Number of units of
output produced
Constant Slope
25
20
5
5
Output
Output
increases by the
increases by the
same amount
same amount
for each worker
for each worker
hired
hired
15
10
5
5
5
0
5
1
Number of Workers hired
2
3
4
5

12. Increasing Slope
75
25
ALL workers
ALL workers
become more
become more
productiveincreases
productive as they
Output as they
Output increases
concentrate on
concentrate on
by increasing
by increasing
doing only one task
doing only one task
amounts for each
amounts for each
worker hired
worker hired
50
20
30
15
15
5
10
5
1
2
3
4
5

13. 75
70
60
Decreasing Slope
5
10
15
ALL workers
ALL workers
become LESS
become LESS
productive as the
productive as the
Output increases by
Output increases by
plant gets crowded
plant gets crowded
decreasing
and equipment
decreasing
and equipment
amounts for each
breaks down often
amounts for each
breaks down often
worker hired
worker hired
45
20
25
25
1
2
3
4
5

14. Positive Increasing and Positive Decreasing Slope
Increasing
125
120
110
Decreasing
5
10
15
95
20
75
25
50
20
30
15
15
5
10
5
1
2
3
4
5
6
7
8
9
10

15. Positive Increasing, Positive Decreasing and Negative
Slope
125
120
110
-5
5
10
15
95
-10
-15
20
75
25
50
20
30
15
5
15
10
1
5
2
3
4
5
6
7
8
9
10 11 12

16. Q
ALL THREE FUNCTIONS ARE INCREASING….
Q
Same size steps
Larger steps
Constant Slope
Increasing Slope
L
As L increases, Q increase by the
same amount
Q
L
As L increases, Q increase by
increasing amounts
Smaller steps
Decreasing Slope
As L increases, Q increase by
decreasing amounts
L

17. THREE SHAPES BEST
DESCRIBES WHAT IS
COMMON TO MOST
PRODUCTION
PROCESSES?
17
In other words: Does each additional worker add
the SAME? MORE? Or LESS to output that the
previous worker?

18. FOR MOST PRODUCTION PROCESSES
 In
the short run, the plant size is fixed.
 Adding more workers is favorable to
production at first, as specialization
increases productivity.
 Eventually, adding more and more
workers to a FIXED PLANT size results
in decreases in productivity due to
“crowded conditions”:
 Workers
will have to SHARE EXISTING
EQUIPMENT
 Equipment will break down more often.
18

19. As more of a variable input (labor) is
added to a fixed input (plant),
additions to output eventually slow
down.
THE LAW OF DIMINISHING
MARGINAL PRODUCT.
19

20. If more of the variable input
(labor) continues to be added to
a fixed input (plant), additions
to output continue to decline
until eventually output
decreases
NEGATIVE MARGINAL
PRODUCT
20

21. CHOOSING THE SLOPE:
For most productions processes as we add
more workers, additions to output
increase at the beginning but eventually
decrease (could become negative).
For this, we use a function with both
increasing and decreasing steps.
2.
The most common production
function has increasing slope at
the beginning. Eventually,
slope decrease and slope may
become negative
21

22. MARGINAL PRODUCT
(MP)
The additional output that can
be produced by adding one more
worker while holding plant size
constant.
MP = ∆Q/∆L
Is the slope of the Total Product
Function
22

23. MP: SLOPE OF THE PRODUCTION
FUNCTION
Q (units
MP
produced)
Slope = 30/1 = 30
MP = 30
TP(Q)
160 units
30 units Rise ∆Q
130 units
The 10th
worker adds
30 units to
production
Run ∆L
1
9
10
L
(Workers hired)

24. MP: SLOPE OF THE PRODUCTION
FUNCTION
MP
Slope = 30/3 = 10
Q
MP = 10
TP
160 units
30
Each one of
these three
workers adds 10
units to
production
Rise
130 units
Run
3
9
12
L

25. MP INCREASES AND DECREASES WHILE
TOTAL PRODUCT STILL RISING
If more workers are added, MP turns NEGATIVE
Q
25
MP
27
2
23
MP = 12
-4
5
20
MP = 8
MP = 5
12
8
MP = 2
8
1st
5
1
2nd
2
3rd
3
4th
4
5th
5
1
2
3
4
MP = -4

26. TOTAL PRODUCT VS. MARGINAL
PRODUCT
Q
TP rises up to
4th worker
TP falls after 4th
worker
27
25
23
MP rises up
to 2nd
worker
MP
MP falls
after to
2nd
worker
MP = 12
20
MP becomes
negative after
4th worker
MP = 8
MP = 5
8
MP = 2
1
2
3
4
5
MP = -4
1
2
3
4
5

27. L
MP
Q
L
MP
Q
0
0
0
1
5
1
60
2
10
2
115
3
15
3
165
4
20
4
210
5
25
5
250
6
30
6
285
7
35
7
315
8
40
8
340
9
45
9
360
10this table: 50 given
In
you’re
10In this table: you’re given
375
the Marginal Product and
11 must use 55 calculate
you
it to
the
Product and
11 Total it to calculateyou
385
must use
the
Product.
12 the Total 60
12
Marginal Product.
390

28. L
MP
Q
L
MP
Q
0
1
2
3
4
5
6
7
8
9
10
11
12
5
10
15
20
25
30
35
40
45
50
55
60
5
15
30
50
75
105
140
180
225
275
330
390
0
1
2
3
4
5
6
7
8
9
10
11
12
60
55
50
45
40
35
30
25
20
15
10
5
0
60
115
165
210
250
285
315
340
360
375
385
390
28

29. AVERAGE PRODUCT
(AP)
Represents the amount of
output produced by each
worker on average.
Or
 Output per worker.

29

30. OUTPUT PER WORKER: AVERAGE
OUTPUT PER WORKER
PRODUCT (AP)
Slope of that
ray= Q/L = AP
Q
When 10 workers
produce 150 units,
TP
150 units
If we draw a
line (a ray)
from the
origin to a
point on the
production
function
Output per
worker = 15
units
AP = Q/L
AP = 150/10 = 15
Q
Rise
Run
L
10
L

31. AP = Q/L
AP = SLOPEWhat happens FROM
OF RAY
What happens
to the AP as L
to the AP as L
ORIGIN
What happens
What happens
increases?
increases?
Q
to the slope as
to the slope as
L increases?
L increases?
Q L AP
5 5 1.00
82
80
70
TP
20 10 2.00
30 12 2.50
70 16 4.38
30
80 20 4.00
20
5
5
10 12 16 20 23
82 23 3.57
L
31

32. AP: INCREASES, REACHES A
MAXIMUM AND DECREASES.
AP AP Increases up
to 16 workers
AP Decreases
after L=16
Q L AP
5 5 1.00
20 10 2.00
70/16
=4.38
30 12 2.50
70 16 4.38
80 20 4.00
16
82 23 3.57
L
L
32

33. THE RELATIONSHIP BETWEEN AP
AND MP
IfIfthe MP of the next worker is say 70 >
your next grade is say 70 > your test
 If MP (70) > AP (60), then the
per worker average so far say 60, test
average so far say 60, then your then
Average Product increases.
the per worker average (AP) increases.
Average increases.
 If MP (50) < AP (60), then the AP will
Ifdecrease. the next worker is your50 <
Ifthe MP of grade is say 50 < say test
your next
 If MP = AP, then the far saynot then
per worker average 60, AP isyour test
average so far say so then 60,
increasing or decreasing: it is at the
the per worker average (AP) decreases.
Average decreases.
maximum point.
your next grade is 60 = your test
IfIfthe MP of the next worker is say 60 = per
average so far so then your then the per
worker average 60,far say 60, test Average
33
stays the same(AP) stays the same.
.
worker average

34. MP AND AP
P
>
AP
Suppose that 8 workers produce a total of 35 units
9 workers produce a total of 45 units
MP AP
10 Marginal product of 9th worker = 10
M
5 AP of 9 workers = 45/9=5
4.4
AP
i
cr
n
aAP of 8 workers = 35/8 = 4.4 AP
e
9
8
es
s
MP
34

35. MP AND AP
Suppose that 12 workers produce a total of 71 units
13 workers produce a total of 76.9 units
MP = 5.9
MP AP
5.9
AP = MP=5.9
5.9 5.9
AP remains same
AP
MP
AP of 13 workers = 76.9/13 = 5.9 1213
AP of 12 workers = 71/12 = 5.9
35

36. RELATIONSHIP BETWEEN MP AND AP
MP AP
MP = AP, AP doesn’t
change and
AP is max
70
MP above AP
60
AP
i
cr
n
ea
es
s
AP
de
cr
e
as
es
MP below AP
AP
MP
36

37. LONG-RUN PRODUCTION FUNCTION
In the long run, a firm has enough time to change the amount of all
its inputs
The long run production process is described by the concept of
returns to scale
Returns to scale = the resulting increase
in total output as all inputs increase
37

38. LONG-RUN PRODUCTION FUNCTION
If all inputs into the production process are doubled, three
things can happen:
output can more than double
‘increasing returns to scale’ (IRTS)
output can exactly double
‘constant returns to scale’ (CRTS)
output can less than double
‘decreasing returns to scale’ (DRTS)
38

39. LONG-RUN PRODUCTION FUNCTION
One way to measure returns to scale is to use a coefficient of
output elasticity:
Percentage change in Q
EQ =
Percentage change in all inputs
if EQ > 1 then IRTS
if EQ = 1 then CRTS
if EQ < 1 then DRTS
39

40. LONG-RUN PRODUCTION FUNCTION
Graphically, the returns to scale concept can be illustrated using
the following graphs
Q
IRTS
Q
X,Y
DRTS
CRTS
Q
X,Y
X,Y
40

41. ESTIMATION OF PRODUCTION
FUNCTIONS
Production function examples
•short run: one fixed factor, one variable factor
Q = f(L)K
•cubic: increasing marginal returns followed by decreasing
marginal returns
Q = a + bL + cL2 – dL3
•quadratic: diminishing marginal returns but no Stage I
Q = a + bL - cL2
41

42. ESTIMATION OF PRODUCTION
FUNCTIONS
Production function examples
•Cobb-Douglas function: exponential for two inputs
Q = aLbKc
if b + c > 1, IRTS
if b + c = 1, CRTS
if b + c < 1, DRTS
42

43. ESTIMATION OF PRODUCTION
FUNCTIONS
Statistical estimation of production functions
• inputs should be measured as ‘flow’ rather than
‘stock’ variables, which is not always possible
• usually, the most important input is labor
• most difficult input variable is capital
• must choose between time series and cross-sectional
analysis
43

44. IMPORTANCE OF PRODUCTION
FUNCTIONS IN MANAGERIAL
DECISION MAKING
Careful planning can help a firm to use its resources in a
rational manner.
• Production levels do not depend on how much a
company wants to produce, but on how much its
customers want to buy.
• There must be careful planning regarding the
amount of fixed inputs that will be used along with
the variable ones.
44

45. IMPORTANCE OF PRODUCTION
FUNCTIONS IN MANAGERIAL
DECISION MAKING
Capacity planning: planning the amount of fixed inputs
that will be used along with the variable inputs
Good capacity planning requires:
• accurate forecasts of demand
• effective communication between the production
and marketing functions
45

46. IMPORTANCE OF PRODUCTION
FUNCTIONS IN MANAGERIAL
DECISION MAKING
•
The intensity of current global competition often
requires managers to go beyond these simple
production function curves.
•
Being competitive in production today mandates that
today’s managers also understand the importance of
speed, flexibility, and what is commonly called “lean
manufacturing”.
46

47. THANK YOU
47