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THE PRODUCTION FUNCTIONProduction and Cost Analysis I
9/19/2013
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A PLANT
Is the factory (space) whereproduction takes place and
All the equipment necessary toproduce
The plant includes everything neededto produce, except workers and raw
materials.
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SHORT RUNVS. LONG RUN
The short run is defined asthe period of time when theplant size is fixed.
The long run is defined asthe time period necessary tochange the plant size.
Duration of the long/shortrun depends on theproduction process
3
Plant size is
fixed, labor
is variable
Both Plant
size and labor
are variable
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SHORT RUNVS. LONG RUN
4
Plant size is
fixed, labor
is variable
Short Run
To increase
production firms
increase Labor
but cant expandtheir plant
Short Run
Firms produce in the short run
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SHORT RUNVS. LONG RUN
5
Plant size is
variable, labor is
variable
Long Run
To increase
production firms
increase Labor
and expand theirplant.
Long Run
Firms plan in the long run
How can
the plant
size be
variable?
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THEREARETHREEIMPORTANTWAYSTO
MEASURETHEPRODUCTIVITYOFLABOR:
Total product (TP)
Average product (AP)Marginal product (MP)
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TOTAL PRODUCT FUNCTION (TP)
Represents the relationship between
the number of workers (L) and the
TOTAL number of units ofoutput
produced (Q) holding all other factorsof 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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BUILDINGA TOTAL PRODUCT GRAPH
The Total Product Curve must show that:
1. The more workers are hired the more
output would be produced.
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INCREASING FUNCTION.
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Constant Slope
1 2 3 4 5
5
10
15
20
25
5
5
5
5
5
Constant
Number of Workers hired
Number of units of
output produced
0
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Increasing Slope
1 2 3 4 5
5
15
30
50
75
10
15
20
25
Increasing
ALL workers become
more productive asthey concentrate on
doing only one task
5
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Decreasing Slope
1 2 3 4 5
25
75
60
45
705
1015
20
Decreasing
25
ALL workers become
LESS productive as
the plant getscrowded and
equipment breaks
down often
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1 3 5 7 9
5
15
30
50
75
5
10
15
20
25
2 4 6 8 10
95
120125
110
510
15
20
Positive Increasing and Positive Decreasing SlopeIncreasing Decreasing
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1 3 5 7 9
5
15
30
50
75
5
10
15
20
25
2 4 6 8 10
95
120125
110
510
15
20
Positive Increasing, Positive Decreasing and Negative
Slope
-5-10
-15
11 12
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ALL THREE FUNCTIONS ARE INCREASING.Q
As L increases, Q increases by
the same amount
Constant Slope
L
Increasing Slope
As L increases, Q increases by
increasing amounts
L
Q
Decreasing Slope
As L increases, Q increases by
decreasing amounts
L
Q
Larger steps
Smaller steps
Same size steps
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WHICHOFTHESETHREESHAPES
BESTDESCRIBESWHATISCOMMONTOMOSTPRODUCTION
PROCESSES?
In other words: Does each additional worker add the
SAME? MORE? Or LESS to output that the previous
worker?
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FORMOSTPRODUCTIONPROCESSES
In the short run, the plant size is fixed.
Adding more workers is favorable toproduction at first, as specialization
increases productivity.Eventually, adding more and more workers
to a FIXED PLANTsize results indecreasesin productivity due to crowded
conditions: Workers will have to SHARE EXISTING
EQUIPMENT
Equipment will break down more often.
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THE LAWOFDIMINISHING MARGINAL
PRODUCT.
As more of a variable input (labor) isadded to a fixed input (plant), additionsto output eventually slow down.
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NEGATIVE MARGINAL PRODUCT
If more of the variable input (labor)continues to be added to a fixedinput (plant), additions to outputcontinue to decline until eventually
output decreases
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CHOOSINGTHESLOPE:
2. For most productions processes as we addmore workers, additions to output increase
at the beginning but eventually decrease
(could become negative).
For this, we combine the graph with increasingsteps (slope) and the graph with decreasing
steps
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The most common productionfunction has an increasing slope
at the beginning, and eventually
decreasing slope which may
become negative
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MARGINAL PRODUCT (MP)The additional output that can be
produced by adding one more
worker while holding plant sizeconstant.
MP = DQ/DLIs the slope of the Total Product
Function
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MP: SLOPEOFTHE PRODUCTION FUNCTION
Q (unitsproduced)
L (Workers hired)10
160 units TP(Q)
Slope = 30/1 = 30MP = 30
Rise DQ
Run DL
9
130 units
30 units
1
The 10th
workeradds
30 units to
production
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MP: SLOPEOFTHE PRODUCTION
FUNCTION
Q
L12
160 units TP
Slope = 30/3 = 10MP = 10
Rise
Run
9
130 units
30
3
Each one of
these three
workers adds 10
units to
production
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MP INCREASES AND DECREASES WHILE
TOTAL PRODUCT STILL RISING
1 2 3 4
8
20
2527
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
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TOTAL PRODUCTVS. MARGINAL PRODUCT
MP = 8
MP = 12
MP = 5
MP = 2
MP = -4 1 2 3 45
MP
1 2 3 4
8
20
2527
23
5
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TOTAL PRODUCTVS. MARGINAL PRODUCT
MP = 8
MP = 12
MP = 5
MP = 2
MP = -4 1 2 3 45
MP
1 2 3 4
8
20
2527
23
5
TP rises up to
4th worker
MP fallsafter to
2ndworker
MP becomes
negative after
4th worker
TP falls after4thworker
MP rises up
to 2ndworker
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L MP Q01 52 103 154 205 256 307 358 409 4510 5011 5512 60
L MP Q0 01 602 1153 1654 2105 2506 2857 3158 3409 36010 37511 38512 390
In this table: youre given
the Marginal Product and
you must use it to calculate
the Total Product.
In this table: youre given
the Total Product and you
must use it to calculate the
Marginal Product.
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AVERAGE PRODUCT (AP)
Represents the amount of
output produced by eachworker on average.
Or Output per worker.
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Q
L10
150 units
TP
AP = 150/10 = 15
When 10 workersproduce 150 units,
Rise
Run
Output per
worker = 15units
Q
L
AP = Q/L
OUTPUTPERWORKER
Slope of that
ray= Q/L =AP
If we draw a
line (a ray)
from the
origin to apoint on the
production
function
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AP = Q/L
AP = SLOPEOFRAYFROMORIGIN
Q L AP5 5 1.0020102.0030122.5070164.3880
20
4.00
82233.57
29
Q
L
70
TP
What happens
to the slope as
L increases?
8280
30
20
5
5 10 12 16 20 23
What happens
to the AP as L
increases?
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AP: INCREASES, REACHESAMAXIMUMAND
DECREASES.
30
AP
L16
AP Increases up
to 16 workers
AP Decreases
after L=16
70/16=4.38
L
Q L AP5 5 1.0020102.0030122.5070164.3880
20
4.00
82233.57
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THE RELATIONSHIPBETWEENAPANDMP
If MP (70) > AP (60), then the AverageProduct 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.
31
If your next grade is say 70 > your testaverage 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 testaverage 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) 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.
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THE AP AND MP
32
Slope of ray is max
Changes concavity
MPAP
TP
MP,AP
L
L
AP is max
MP is max
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MPAND AP
33
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
So when the 9th worker is hired 9 workers produce a total of 45 units
9 AP of 9 workers = 45/9=5
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MPAND AP
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MP
AP
MP AP
5.9
AP of 12 workers = 71/12 = 5.9
5.9
Suppose that MP = AP: Marginal product of 13th worker = 5.9
13
Suppose that 12 workers produce a total of 71 units
So when the 13th worker is hired 13 workers produce a total of 76.9 units
AP of 13 workers = 76.9/13 = 5.9
AP remains same
12
MP=5.95.9
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RELATIONSHIPBETWEEN MPAND AP9/19/2013
35
MP
APMP below AP
MP above AP
MP AP MP = AP, AP doesntchange and
AP is max
70
6060
70
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CONSIDER A SMALL SANDWICH SHOP
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L Q MP AP0 01 10 10 10.02 25 15 12.5
2.5 31.3 12.5 12.53 35 10 11.74 40 5 10.05 42 2 8.4
6 42 0 7.07 35 -7 5.08 25 -10 3.19 10 -15 1.1
# sandwiches# workers
MP= previous AP
AP doesnt
change
L MP Q AP
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In this table: youre given
the Marginal Product and
you must use it to calculate
the Total Product.
L MP Q AP0
1 5
2 10
3 15
4 205 25
6 30
7 35
8 40
9 45
10 50
11 55
12 60
L MP Q AP0 0
1 60
2 115
3 165
4 210
5 2506 285
7 315
8 340
9 360
10 375
11 385
12 390
Q i i f h
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Table 1 Table 2
L Q MP AP0
10 520 2530
70
40 11050 13560
153
70 11880 38
L MP Q AP0
10 520 2030
45
40 4050 2560
18
70 -3580 -80
Questions to practice for the test
Here you
have the Total
Product Q and
you mustcalculate the
MP and AP Here you have
the Marginal
Product MP and
you must
calculate the TotalProduct and AP
Q ti t ti f th t t
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Table 1 Table 2
L Q MP AP010 520 2530 7040 11050 13560
153
70 11880 38
L MP Q AP010 520 2030 4540 4050 2560
18
70 -3580 -80
Questions to practice for the test
Q ti t ti f th t t
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Table 1 Table 2
L Q MP AP01 52 253 704 1105 1356
153
7 1188 38
L MP Q AP01 52 203 454 405 256
18
7 -358 -80
Questions to practice for the test
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L Q DQ DL MP0 010 5 5 10 0.520 25 20 10 230 70 45 10 4.540 110 40 10 450 135 25 10 2.560 153 18 10 1.870 118 -35 10 -3.580 38 -80 10 -8
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L Q DQ DL MP MP *10 Q0 0 010 5 5 10 0.5 5 520 25 20 10 2 20 2530 70 45 10 4.5 45 7040 110 40 10 4 40 11050 135 25 10 2.5 25 13560 153 18 10 1.8 18 15370 118 -35 10 -3.5 -35 11880 38 -80 10 -8 -80 38
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For each table in the next slides answer the following
questions:
1. What is the shape of the Total Product Curve? Should beable 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 beable 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
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FILLINTHE TPAND AP SHOULDBEABLE
TODRAWTHESEGRAPHS.
L MP TP(Q) AP01 52 53 54 55 56 57 58 59 510 511 512 5
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FILLINTHE TPAND AP SHOULDBEABLE
TODRAWTHESEGRAPHS.
L MP TP (Q) AP01 52 103 154 205 256 307 358 409 4510 5011 5512 60
9/
19/2013
45
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FILLINTHE TPAND AP SHOULDBEABLE
TODRAWTHESEGRAPHS.
L MP TP (Q) AP01 602 553 504 455 406 357 308 259 2010 1511 1012 5
9/
19/2013
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FILLINTHE TPAND AP SHOULDBEABLE
TODRAWTHESEGRAPHS.
L MP TP(Q) AP01 52 103 154 205 176 157 138 129 1010 811 612 5
9/
19/2013
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A B C
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A B
D E
C
F
MP=AP
APAP
AP
AP
AP
G
AP
MP
MP
MPMP
MP
MP
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A B
D E
C
I II IIIMP
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I II
IV
III
MPMP
MP MPMP
V
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