2. Short Run vs. Long Run
The short run is defined as
the period of time when
the plant size is fixed.
The long run is defined as
the time period necessary
to change the plant size.
Duration of the long/short
run depends on the
production process…
2
Plant size is
fixed, labor
is variable
Both Plant
size and labor
are variable
3. Short Run vs. Long Run
3
Plant size is
fixed, labor
is variable
Short Run
To increase
production firms
increase Labor
but can’t expand
their plant
Short Run
Firms produce in the short run
4. Short Run vs. Long Run
4
Plant size is
variable, labor is
variable
Long Run
To increase
production firms
increase Labor
and expand their
plant.
Long Run
Firms plan in the
long run
How can
the plant
size be
variable?
Plant size is
variable in the
‘planning’
stage
5. There are three important ways to
measure the productivity of labor:
Total product (TP)
Average product (AP)
Marginal product
(MP)
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5
6. Total Product (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”
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6
7. Building a Total Product Graph
The Total Product Curve must show
that:
1. With more workers more output can
be produced.
12/22/14
INCREASING FUNCTION.
Labor
TotalProduct
Labor
TotalProduct
Labor
TotalProduct
8. Marginal Product
Marginal = additional
Marginal Product is the additional output
produced by the last worker hired.
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8
9. If TP has a Constant Slope
1 2 3 4 5
5
10
15
20
25
+5
+5
+5
+5
+5
Constant
Number of Workers hired
Units
produced
0
Output
increases by the
same amount
for each worker
hired
Output
increases by the
same amount
for each worker
hired
This
is
an
increasing
function
w
ith
a
constant slope
10. If TP has a Constant Slope
1 2 3 4 5
Constant
Worker #
Marginal
Product
Output
increases by the
same amount
for each worker
hired
Output
increases by the
same amount
for each worker
hired
5
+5 +5 +5 +5 +5
Marginal
Product
11. Increasing Slope
1 2 3 4 5
5
15
30
50
75
10
15
20
25
Increasing
ALL workers
become more
productive as they
concentrate on
doing only one task
ALL workers
become more
productive as they
concentrate on
doing only one task
5
Output increases
by increasing
amounts for each
worker hired
Output increases
by increasing
amounts for each
worker hired
Thisisan
increasing
function
with
an
increasing
slope
12. Increasing Slope
1 2 3 4 5
5
10
15
20
25
10
15
20
25
Increasing
5
Output increases
by increasing
amounts for each
worker hired
Output increases
by increasing
amounts for each
worker hired
Marginal
Product
Marginal
Product
Worker #
13. Decreasing Slope
1 2 3 4 5
25
75
60
45
70
5
10
15
20
Decreasing
25
ALL workers
become LESS
productive as the
plant gets crowded
and equipment
breaks down often
ALL workers
become LESS
productive as the
plant gets crowded
and equipment
breaks down often
Output increases by
decreasing
amounts for each
worker hired
Output increases by
decreasing
amounts for each
worker hired
This
is
an
increasing
function
w
ith
an
D
ecreasing
slope
14. 1 2 3 4 5
5
10
15
20
25
10
15
20
25
Decreasing
5
Output increases
by decreasing
amounts for each
worker hired
Output increases
by decreasing
amounts for each
worker hired
Marginal
Product
Marginal
Product
Worker #
15. ALL THREE FUNCTIONS ARE INCREASING….Q
As L increases, Q increase by the
same amount
Constant Slope
L
Increasing Slope
As L increases, Q increase by
increasing amounts
L
Q
Decreasing Slope
As L increases, Q increase by
decreasing amounts
L
Q
Larger steps
Smaller steps
Same size steps
16. Which of these three
shapes best describes
what is common to most
production processes?
In other words: Does the Marginal Product
increase, decrease or remains the same as
workers are hired?
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16
17. 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.
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17
18. The Law of Diminishing
Marginal Product.
As more of a variable input (labor) is
added to a fixed input (plant),
additions to output eventually slow
down.
18
19. Negative Marginal Product
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
decrease
12/22/14
19
20. Choosing the best shape for the
production function:
2. 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 (eventually
negative) MP
12/22/14
20
The most common production
function has increasing slope at
the beginning. Eventually,
slope decrease and slope may
become negative
23. Marginal Product (MP)
The additional output that can
be produced by adding more
workers to a constant size plant.
MP = ∆Q/∆L
Is the slope of the Total Product
Function
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23
24. MP: Slope of the Production Function
Q (units
produced)
L (Workers hired)
10
160 units TP(Q)
Slope = 30/1 = 30MP = 30
Rise ∆Q
Run ∆L
9
130 units
30 units
1
The 10th
worker adds
30 units to
production
MP
25. MP: Slope of the Production Function
Q
L
12
160 units TP
Slope = 30/3 = 10
MP = 10
Rise
Run
9
130 units
30
3
Each one of
these three
workers adds 10
units to
production
MP
26. MP INCREASES AND DECREASES WHILE
TOTAL PRODUCT STILL RISING
1 2 3 4
8
20
25
27
Q
1st 4th3rd2nd
MP = 8
MP = 12
MP = 5
MP = 2
23
5th
MP = -4
If more workers are added, MP turns NEGATIVE
8
12
5
2 -4
1 2 3 4
5
MP
5
27. Total Product vs. Marginal Product
MP = 8
MP = 12
MP = 5
MP = 2
MP = -4 1 2 3 4
5
MP
1 2 3 4
8
20
25
27
Q
23
5
TP rises up to
4th worker
MP falls
after to
2nd
worker
MP becomes
negative after
4th worker
TP falls after 4th
worker
MP rises up
to 2nd
worker
Diminishing Returns to Labor set in after
worker 2
28. L MP Q
0
1 5
2 10
3 15
4 20
5 25
6 30
7 35
8 40
9 45
10 50
11 55
12 60
L MP Q
0 0
1 60
2 115
3 165
4 210
5 250
6 285
7 315
8 340
9 360
10 375
11 385
12 390
In this table: you’re given
the Marginal Product and
you must use it to calculate
the Total Product.
In this table: you’re given
the Total Product and you
must use it to calculate the
Marginal Product.
32. Average Product (AP)
Output per worker
12/22/14
32
AP = Total Product / LaborAP = Total Product / Labor
AP = Q/LAP = Q/L
33. Output per
worker = 15
unitsQ
L
10
150 units
TP
AP = 150/10 = 15
Output per worker
Draw a line
(a ray) from
the origin to
any point on
the
production
function
Draw a line
(a ray) from
the origin to
any point on
the
production
function
Output per worker: Average Product (AP)
Slope of that
ray= Q/L = AP
If 10 workers
produce 150 units,
34. AP = Q/L
AP = Slope of ray from origin
Q L AP
5 5 1.00
20 10 2.00
30 12 2.50
70 16 4.38
80 20 4.00
82 23 3.57
34
Q
L
70
TP
What happens
to the slope as
L increases?
What happens
to the slope as
L increases?
82
80
30
20
5
5 10 12 16 20 23
What happens
to the AP as L
increases?
What happens
to the AP as L
increases?
35. AP: Increases, reaches a maximum
and decreases.
35
AP
L
16
AP Increases up
to 16 workers
AP Decreases
after L=16
70/16
=4.38
L
Q L AP
5 5 1.00
20 10 2.00
30 12 2.50
70 16 4.38
80 20 4.00
82 23 3.57
36. The Relationship between AP and MP
If MP (70) > AP (60), then the
Average Product increases.
If MP (50) < AP (60), then the AP will
decrease.
If MP = AP, then the AP is not
increasing or decreasing: it is at the
maximum point.
36
If your next grade is say 70 > your test
average so far say 60, then your test
Average increases.
If your next grade is say 50 < your test
average so far say 60, then your test
Average decreases.
If your next grade is 60 = your test
average so far 60, then your test Average
stays the same .
If the MP of the next worker is say 50 <
per worker average so far say 60, then
the per worker average (AP) decreases.
If the MP of the next worker is say 70 >
per worker average so far say 60, then
the per worker average (AP) increases.
If the MP of the next worker is say 60 = per
worker average so far say 60, then the per
worker average (AP) stays the same.
37. THE AP AND MP…
37
Slope of
ray is
max
Changes
concavity
MP
AP
TP
MP, AP
L
L
AP is max
MP is
max
DRT set
in
DRT set in
TP is
max
MP is
zero
38. MP and AP
38
MP
AP
MP AP 10
5
8
AP of 8 workers = 35/8 = 4.4
4.4
Marginal product of 9th
worker = 10
9
Suppose that 8 workers produce a total of 35 units
9 workers produce a total of 45 units
9
AP of 9 workers = 45/9=5
AP
increases
M
P
>
AP
39. MP and AP
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39
MP
AP
MP AP
5.9
AP of 12 workers = 71/12 = 5.9
5.9
13
Suppose that 12 workers produce a total of 71 units
13 workers produce a total of 76.9 units
AP of 13 workers = 76.9/13 = 5.9
AP remains same
12
AP = MP=5.9
5.9
MP = 5.9
40. Relationship between MP and AP
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40
MP
AP
AP
increases
MP below AP
MP above AP AP
decreases
MP AP
MP = AP, AP doesn’t
change and
AP is max
70
60
41. MARGINAL REVENUE PRODUCT
MRP = Revenue generated by last worker hired
MP = Units added to total product by last worker
hired.
MRP = MP * Price
The firm should hire all workers for whom the
revenue each generate exceeds his wage.
The firm should hire all workers for whom the
MRP > wage.
41
42. HOW MANY WORKERS SHOULD BE
HIRED?
42
L TP
0 0
1 15
2 27
3 37
4 44
5 47
6 49
7 48
8 45
L TP MP
0 0
1 15 15
2 27 12
3 37 10
4 44 7
5 47 3
6 49 2
7 48 -1
8 45 -3
L TP MP MRP
0 0 MP*Price
1 15 15 450
2 27 12 360
3 37 10 300
4 44 7 210
5 47 3 90
6 49 2 60
7 48 -1 -30
8 45 -3 -90
Worker one adds 15
units to output which
bring $450 dollars in
additional revenue.
This additional revenue
is larger than his salary
($200) so the firm
should hire this worker
Worker two adds 12
units to output which
bring $360 dollars in
additional revenue.
This additional revenue
is larger than his salary
($200) so the firm
should hire this worker
Worker three adds 10
units to output which
bring $300 dollars in
additional revenue.
This additional revenue
is larger than his salary
($200) so the firm
should hire this worker
Worker four adds 7 units
to output which bring
$210 dollars in
additional revenue.
This additional revenue
is larger than his salary
($200) so the firm
should hire this worker
Worker 5 adds 3 units
to output which bring
$90 dollars in
additional revenue.
This additional revenue
is smaller than his
salary ($200) so the firm
should NOT hire this
worker
When the wage is $200:
Demand for workers is 4
Wage per worker per day = $200 Price per unit = $30
43. BUILDING LABOR DEMAND LINE
43
L TP MP MRP
0 0 MP*Price
1 15 15 450
2 27 12 360
3 37 10 300
4 44 7 210
5 47 3 90
6 49 2 60
7 48 -1 -30
8 45 -3 -90
If wage is:
The firm will
hire _ workers
450 1
360 2
300 3
210 4
90 5
60 6
50 ?
40 ?
The firm should hire all workers for whom the MRP
greater than or equal to the wage.
44. THE OPTIMAL USE OF
AN INPUT
44
L TP MP MRP
0 0 MP*Price
1 15 15 450
2 27 12 360
3 37 10 300
4 44 7 210
5 47 3 90
6 49 2 60
7 48 -1 -30
8 45 -3 -90
Once diminishing
returns to labor set in
the MP decreases
When the MP
decreases, the MRP
also decreases
The firm should hire
more workers as long as
the MRP > wage
We know the firm has
hired the optimum
number of workers when
the MRP = wage
Rule: Increase use of an
input until
MPR of that input =
Price of the input
46. CONSIDER A SMALL SANDWICH
SHOP…
12/22/14
46
L Q M
P
AP
0 0
1 10 10 10.0
2 25 15 12.5
2.5 31.3 12.5 12.5
3 35 10 11.7
4 40 5 10.0
5 42 2 8.4
6 42 0 7.0
7 35 -7 5.0
8 25 -10 3.1
9 10 -15 1.1
# sandwiches# workers
MP= previous AP
AP doesn’t
change
47. In this table: you’re given
the Marginal Product and
you must use it to calculate
the Total Product.
L MP Q AP
0
1 5
2 10
3 15
4 20
5 25
6 30
7 35
8 40
9 45
10 50
11 55
12 60
L MP Q AP
0 0
1 60
2 115
3 165
4 210
5 250
6 285
7 315
8 340
9 360
10 375
11 385
12 390
48. Table 1 Table 2
L Q MP AP
0
10 5
20 25
30 70
40 110
50 135
60 153
70 118
80 38
L MP Q AP
0
10 5
20 20
30 45
40 40
50 25
60 18
70 -35
80 -80
Questions to practice for the test
Here you
have the Total
Product Q and
you must
calculate the
MP and AP Here you have
the Marginal
Product MP and
you must
calculate the Total
Product and AP
49. Table 1 Table 2
L Q MP AP
0
10 5
20 25
30 70
40 110
50 135
60 153
70 118
80 38
L MP Q AP
0
10 5
20 20
30 45
40 40
50 25
60 18
70 -35
80 -80
Questions to practice for the test
50. Table 1 Table 2
L Q MP AP
0
1 5
2 25
3 70
4 110
5 135
6 153
7 118
8 38
L MP Q AP
0
1 5
2 20
3 45
4 40
5 25
6 18
7 -35
8 -80
Questions to practice for the test
53. For each table in the next slides answer the following questions:
1. What is the shape of the Total Product Curve? Should be
able to draw the total product curve.
2. What is the shape of the Marginal Product Curve? Should
be able to draw the Marginal Product Curve.
3. What is the shape of the Average Product Curve? Should be
able to draw the Average Product Curve.
4. With which worker(s) do we realize
increasing/decreasing/negative marginal productivity? How
do you know?
5. Would you employ the 6th worker? Why yes/why not?
6. How are the marginal product and the average product
related?
Questions to practice for the test
54. Fill in the TP and AP Should be able
to draw these graphs.
L MP TP(Q) AP
0
1 5
2 5
3 5
4 5
5 5
6 5
7 5
8 5
9 5
10 5
11 5
12 5
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54
55. Fill in the TP and AP Should be able
to draw these graphs.
L MP TP (Q) AP
0
1 5
2 10
3 15
4 20
5 25
6 30
7 35
8 40
9 45
10 50
11 55
12 60
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55
56. Fill in the TP and AP Should be able
to draw these graphs.
L MP TP (Q) AP
0
1 60
2 55
3 50
4 45
5 40
6 35
7 30
8 25
9 20
10 15
11 10
12 5
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56
57. Fill in the TP and AP Should be able
to draw these graphs.
L MP TP(Q) AP
0
1 5
2 10
3 15
4 20
5 17
6 15
7 13
8 12
9 10
10 8
11 6
12 5
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Generalize the concepts of total, average and marginal. Regardless of the particular application, average is a “per unit” concept. Regardless of the application, marginal is a “change in” concept.
