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THEPRODUCTIONFUNCTION
10/8/2014
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PRODUCTION
An entrepreneur must put together resources --
land, labour, capital -- and produce a product people
will be willing and able to purchase
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PRODUCTION FUNCTION
THE RELATIONSHIP BETWEEN THE AMOUNT
OF INPUT REQUIRED AND THE AMOUNT OF
OUTPUT THAT CAN BE OBTAINED IS CALLED
THE PRODUCTION FUNCTION
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MARGINALPRODUCT
As the quantity of a variable input (labor, in
the example) increases while all other inputs
are fixed, output rises. Initially, output will
rise more and more rapidly, but eventually itwill slow down and perhaps even decline.
MP = change in QTY / change in INPUT
This is called the LAW OF DIMINISHINGMARGINAL RETURNS
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LAW OF DIMINISHING
RETURNSIT HOLDS THAT WE WILL GET LESS & LESS
EXTRA OUTPUT WHEN WE ADD
ADDITIONAL DOSES OF AN INPUT WHILE
HOLDING OTHER INPUTS FIXED. IT IS
ALSO KNOWN AS LAW OF VARIABLE
PROPORTIONS.
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THESHORT RUN IS A PERIOD JUST SHORT
ENOUGH THAT AT LEAST ONE RESOURCE
(INPUT-INDUSTRIAL PLANT,MACHINES)
CANNOT BE CHANGED -- IS FIXED ORINELASTIC. THUS IN THE SHORT RUN
PROUDCTION OF A COMMODITY CAN BE
INCREASED BY INCREASING THE USE OF
ONLY VARIABLE INPUTS LIKE LABOUR
AND RAW MATERIALS.
PRODUCTION IN THE SHORT RUN
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LONG RUN
THE LONG RUN IS A PERIOD SUFFIECIENTLYLONG THAT ALL FACTORS INCLUDINGCAPITAL CAN BE ADJUSTED OR AREVARIABLE.
THIS MEANS THAT THE FIRM CAN CHOOSEANY COMBINATION ON THE MANUFACTURING
TABLE -- NOT JUST THOSE ALONG COLUMNLABELLED 10
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SHORTRUNVS. LONGRUN
The short runis 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/short rundepends on the productionprocess
8
Plant size is
fixed, labor
is variable
Both Plant
size and labor
are variable
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SHORTRUNVS. LONGRUN
9
Plant size is
fixed, labor
is variable
Short Run
To increase
production firms
increase Labor
but cant expandtheir plant
Short Run
Firms producein the short run
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SHORTRUNVS. LONGRUN
10
Plant size is
variable, labor is
variable
Long Run
To increase
production firmsincrease Labor
and expand their
plant.
Long Run
Firms planin the
long run
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THEREARETHREEIMPORTANTWAYSTO
MEASURETHEPRODUCTIVITYOFLABOR:
Total product (TP)
Average product (AP)Marginal product (MP)
1
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TOTALPRODUCT(TP)
Represents the relationship between
the number of workers (L) and the
TOTALnumber of units of output
produced(Q) holding all other factorsof production (the plant size) constant. For a coffee shop, outputwould be measured in
number of coffee cups a day For a steel mill, outputwould be measured in
tons of steel produced a day
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BUILDINGATOTALPRODUCTGRAPH
The Total Product Curve must show that:
1. With moreworkers moreoutput can
be produced.
1
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INCREASING FUNCTION.
Labor
TotalProduct
LaborT
otalProduct
Labor
TotalProduct
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MARGINALPRODUCTMarginal = additional
Marginal Product is the additional output produced by
the last worker hired.
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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 sameamount for each
worker hired
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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 as
they concentrate ondoing only one task
5
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Increasing Slope
1 2 3 4 5
51015
20
25
1015
20 25
Increasing
5
Output increases
by increasing
amounts for eachworker hired
MarginalProduct
MarginalProduct
Worker #
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Decreasing Slope
1 2 3 4 5
25
75
60
45
705
1015
20
25
ALL workers becomeLESS productive as
the plant gets
crowded and
equipment breaksdown often
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51015
20
25
1015
2025
Decreasing
5
Output increases
by decreasing
amounts for eachworker hired
MarginalProduct
MarginalProduct
Worker #
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ALL THREE FUNCTIONS ARE INCREASING.Q
As Lincreases, Qincreaseby the
sameamount
Constant Slope
L
Increasing Slope
As Lincreases, Qincreaseby
increasingamounts
L
Q
Decreasing Slope
As L increases, Q increaseby
decreasingamounts
L
Q
Larger steps
Smaller steps
Same size steps
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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 SHAREEXISTING
EQUIPMENT
Equipment will break down more often.
1
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THELAWOFDIMINISHINGMARGINAL
PRODUCT.
As more of a variableinput (labor) isadded to a fixedinput (plant), additionsto output eventually slow down.
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NEGATIVEMARGINALPRODUCT
If more of the variableinput (labor)continues to be added to a fixedinput (plant), additionsto outputcontinue to decline until eventually
output decrease
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CHOOSINGTHEBESTSHAPEFORTHE
PRODUCTIONFUNCTION:
2. For most productions processes as we addmore workers, additionsto output increase
at the beginning but eventually decrease
(could become negative).
For this, we use a function with both increasingand decreasing(eventually negative) MP
1
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The most common production
function has increasing slopeat
the beginning. Eventually, slope
decrease and slope may become
negative
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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
P iti I i P iti D i d N ti
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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 Decreasingand Negative
Slope
-5-10
-15
11 12
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MARGINALPRODUCT(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
1
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MP: SLOPEOFTHEPRODUCTIONFUNCTION
Q (unitsproduced)
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
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MP: SLOPEOFTHEPRODUCTION
FUNCTION
Q
L12
160 units TP
Slope= 30/3 = 10MP= 10
Rise
Run
9
130 units
30
3
Each one of
these three
workers adds10
units to
production
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MP INCREASESAND DECREASESWHILE
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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TOTALPRODUCTVS. MARGINALPRODUCT
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 after 4thworker
MP rises up
to 2ndworker
Diminishing Returns to Labor set in after
worker 2
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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: 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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L MP Q L MP Q
0 0 01 5 5 1 60 60
2 10 15 2 55 115
3 15 30 3 50 165
4 20 50 4 45 210
5 25 75 5 40 250
6 30 105 6 35 285
7 35 140 7 30 315
8 40 180 8 25 340
9 45 225 9 20 36010 50 275 10 15 375
11 55 330 11 10 385
12 60 390 12 5 390
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AVERAGEPRODUCT(AP)
Output per worker
1
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AP = Total Product / Labor
AP = Q/L
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Output per
worker = 15unitsQ
L10
150 units
TP
AP= 150/10 = 15Rise
Run
Q
L
OUTPUTPERWORKER
Draw a line
(a ray) from
the origin to
any point on
theproduction
function
OUTPUTPERWORKER: AVERAGEPRODUCT(AP)
Slope of that
ray= Q/L = APIf 10 workers
produce 150 units,
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AP: INCREASES, REACHESAMAXIMUMAND
DECREASES.
36
AP
L16
AP Increases up
to 16 workers
AP Decreases
after L=16
70/16=4.38
L
Q L AP
5 5 1.00
20102.00
30
12
2.50
70164.38
80
20
4.00
82
23
3.57
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MPANDAP
37
MP
AP
MP AP 10
5
8
AP of 8 workers = 35/8= 4.44.4
Marginal product of 9thworker= 10
9
Suppose that 8 workers produce a total of 35 units9 workers produce a total of 45units
9
AP of 9 workers = 45/9=5
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MPANDAP
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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 71units
13 workers produce a total of76.9 units
AP of 13 workers =76.9/13= 5.9
AP remains same
12
AP= MP=5.95.9
MP = 5.9
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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 exceedshis wage.
The firm should hire all workers for whom the MRP >
wage.
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