The Production Function (l3a, l3b)

8/11/2019 The Production Function (l3a, l3b)

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THEPRODUCTIONFUNCTION

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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

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Plant size is

fixed, labor

is variable

Both Plant

size and labor

are variable


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SHORTRUNVS. LONGRUN

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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

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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)

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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.

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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

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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.

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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

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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

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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

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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.

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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

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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

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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

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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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The Production Function (l3a, l3b)

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