# PRODUCTION FUNCTIONS - Weebly

PRODUCTIO N AND COSTS: THE SHORT RUN Production An entrepreneur must put together resources -- land, labour, capital -and produce a product people will be willing and able to purchase PRODUCTION FUNCTION THE RELATIONSHIP BETWEEN THE AMOUNT OF INPUT REQUIRED AND THE AMOUNT OF OUTPUT THAT CAN BE OBTAINED IS CALLED THE PRODUCTION FUNCTION What can you say about Marginal Product ? As the quantity of a variable input (labour, in the example) increases while all other inputs are fixed, output rises. Initially, output will

rise more and more rapidly, but eventually it will slow down and perhaps even decline. This is called the LAW OF DIMINISHING MARGINAL RETURNS LAW OF DIMINISHING RETURNS IT HOLDS THAT WE WILL GET LESS & LESS EXTRA OUTPUT WHEN DOSES WE OF ADD ADDITIONAL AN INPUT WHILE HOLDING OTHER INPUTS FIXED. IT IS ALSO KNOWN AS LAW OF VARIABLE PROPORTIONS. COMBINING RESOURCES THERE ARE MANY COMBINATIONS OF RESOURCES THAT COULD BE USED CONSIDER THE FOLLOWING TABLE

SHOWING DIFFERENT NUMBER OF MECHANICS AND AMOUNT OF CAPITAL THAT THE HYPOTHETICAL FIRM, INDIA INC., MIGHT USE ALTERNATIVE QUANTITIES OF OUTPUT THAT CAN BE PRODUCED BY DIFFERENT COMBINATIONS OF RESOURCES Number of Mechanics CAPITAL 0 1 2 3 4 5 6 7 5

0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 30 60 100 130 130 110

100 100 250 360 440 500 540 550 250 360 480 580 650 700 720 340 450 570 640 710 760 790 410 520 610

690 760 800 820 400 530 620 700 770 820 850 400 520 620 700 780 830 870 390 500 610 690 770 840 890

PRODUCTION IN THE SHORT RUN THE SHORT RUN IS A PERIOD JUST SHORT ENOUGH THAT AT LEAST ONE RESOURCE (INPUT-INDUSTRIAL PLANT,MACHINES) CANNOT BE CHANGED -- IS FIXED OR INELASTIC. 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. Quantities of Output that Can Be Produced When One Resource is Fixed Number of Mechanics 0 1 2 3 4 5 6

7 CAPITAL 5 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 30 60

100 130 130 110 100 100 250 360 440 500 540 550 250 360 480 580 650 700 720 340 450 570 640 710 760 790

410 520 610 690 760 800 820 400 530 620 700 770 820 850 400 520 620 700 780 830 870 390 500 610 690

770 840 890 LONG RUN THE LONG RUN IS A PERIOD SUFFIECIENTLY LONG THAT ALL FACTORS INCLUDING CAPITAL CAN BE ADJUSTED OR ARE VARIABLE. THIS MEANS THAT THE FIRM CAN CHOOSE ANY COMBINATION ON THE MANUFACTURING TABLE -NOT JUST THOSE ALONG COLUMN LABELLED 10 The Long Run or Planning Period: As we double both resources, what happens to output? Number of Mechanics 0 1 2 3 4 5 6 7

CAPITAL 5 0 30 60 100 130 130 110 100 10 0 100 250 360 440 500 540 550 15 0 250 360 480 580 650 700

720 No. of workers (N) THREE STAGES OF PRODUCTION Total product Marginal TPL (tonnes) Product (MPL) Average Product (APL) Stage of production (5) (1) (2) (3) (4) 1 24

24 24 2 72 48 36 3 138 66 46 4 216 78 54

5 300 84 60 6 384 84 64 7 462 78 66 8 528 66

66 9 576 48 64 10 600 24 60 11 594 -6 54 12

552 -42 46 I INCREASING AND CONSTANT RETURNS II DIMINISHING RETURNS III -VE RETURNS BEHAVIOUR OF TPP,MPP AND APP DURING THE THREE STAGES OF PRODUCTION TOTAL PHYSICAL PRODUCT STAGE I INCREASES AT AN INCREASING RATE STAGE II

INCREASES AT A DIMINISHING RATE TILL IT REACHES MAXIMUM STAGE III STARTS MARGINAL PHYSICAL PRODUCT AVERAGE PHYSICAL PRODUCT INCREASES, REACHES ITS MAXIMUM & THEN DECLINES TILL MR = AP INCREASES & REACHES ITS MAXIMUM IS DIMINISHING AND BECOMES EQUAL TO ZERO STARTS

DIMINISHING BECOMES NEGATIVE CONTINUES FROM THE ABOVE TABLE ONLY STAGE II IS RATIONAL WHICH MEANS RELEVANT RANGE FOR A RATIONAL FIRM TO OPERATE. IN STAGE I IT IS PROFITABLE FOR THE FIRM TO KEEP ON INCREASING THE USE OF LABOUR. IN STAGE III, MP IS NEGATIVE AND HENCE IT IS INADVISABLE TO USE ADDITIONAL LABOUR. i.e ONLY STAGE I AND III ARE IRRATIONAL ISOQUANT AN ISOQUANT OR ISO PRODUCT CURVE OR EQUAL PRODUCT CURVE OR A PRODUCTION INDIFFERENCE CURVE SHOW THE VARIOUS COMBINATIONS OF TWO VARIABLE INPUTS RESULTING IN THE SAME LEVEL OF OUTPUT. IT IS DEFINED AS A CURVE PASSING THROUGH THE PLOTTED POINTS REPRESENTING ALL THE COMBINATIONS OF

THE TWO FACTORS OF PRODUCTION WHICH WILL PRODUCE A GIVEN OUTPUT. For example from the following table we can see that different pairs of labour and capital result in the same output. Labour (Units) Capital (Units) Output (Units) 1 5 10 2 3 10 3

2 10 4 1 10 5 0 10 FOR EACH LEVEL OF OUTPUT THERE WILL BE A DIFFERENT ISOQUANT. WHEN THE WHOLE ARRAY OF ISOQUANTS ARE REPRESENTED ON A GRAPH, IT IS CALLED AN ISOQUANT MAP. IMPORTANT ASSUMPTIONS THE TWO INPUTS CAN BE SUBSTITUTED

FOR EACH OTHER. FOR EXAMPLE IF LABOUR IS REDUCED IN A COMPANY IT WOULD HAVE TO BE COMPENSATED BY ADDITIONAL MACHINERY TO GET THE SAME OUTPUT. SLOPE OF ISOQUANT THE SLOPE OF AN ISOQUANT HAS A TECHNICAL NAME CALLED THE MARGINAL RATE OF TECHNICAL SUBSTITUTION (MRTS) OR THE MARGINAL RATE OF SUBSTITUTION IN PRODUCTION. THUS IN TERMS OF CAPITAL SERVICES K AND LABOUR L MRTS = Dk/DL TYPES OF ISOQUANTS 1. LINEAR ISOQUANT 2. RIGHT-ANGLE ISOQUANT 3. CONVEX ISOQUANT LINEAR ISOQUANT IN LINEAR ISOQUANTS THERE IS PERFECT SUBSTIUTABILTY OF INPUTS. FOR EXAMPLE IN A POWER PLANT

EQUIPED TO BURN OIL OR GAS. VARIOUS AMOUNTS OF ELECTRICITY COULD BE PRODUCED BY BURNING GAS, OIL OR A COMBINATION. i.e OIL AND GAS ARE PERFECT SUBSITUTES. HENCE THE ISOQUANT WOULD BE A STRAIGHT LINE. RIGHT-ANGLE ISOQUANT IN RIGHT-ANGLE ISOQUANTS THERE IS COMPLETE NON-SUBSTIUTABILTY BETWEEN INPUTS. FOR EXAMPLE TWO WHEELS AND A FRAME ARE REQUIRED TO PRODUCE A BYCYCLE THESE CANNOT BE INTERCHANGED. THIS IS ALSO KNOWN AS LEONTIEF ISOQUANT OR INPUT-OUTPUT ISOQUANT. CONVEX ISOQUANT IN CONVEX ISOQUANTS THERE

IS SUBSTIUTABILTY BETWEEN INPUTS BUT IT IS NOT PERFECT. FOR EXAMPLE (1) A SHIRT CAN BE MADE WITH LARGE AMOUNT OF LABOUR AND A SMALL AMOUNT MACHINERY. (2) THE SAME SHIRT CAN BE WITH LESS LABOURERS, BY INCREASING MACHINERY. (3) THE SAME SHIRT CAN BE MADE WITH STILL LESS LABOURERS BUT WITH A LARGER INCREASE IN MACHINERY. WHILE A RELATIVELY SMALL ADDITION OF MACHINERY FROM M1(MANUAL EMBROIDERY) TO M2(TAILORING MACHINE EMBROIDERY) ALLOWS THE INPUT OF LABOURERS TO BE REDUCED FROM L1 TO L2. A VERY LARGE INCREASE IN MACHINERY TO M3 (COMPUTERISED EMBROIDERY) IS REQUIRED TO FURTHER DECREASE LABOUR FROM L2 TO L3. THUS SUBSTIUTABILITY OF

LABOURERS FOR MACHINERY DIMINISHES FROM M1 TO M2 TO M3. PROPERTIES OF ISOQUANTS 1. AN ISOQUANT IS DOWNWARD SLOPING TO THE RIGHT. i.e NEGATIVELY INCLINED. THIS IMPLIES THAT FOR THE SAME LEVEL OF OUTPUT, THE QUANTITY OF ONE VARIABLE WILL HAVE TO BE REDUCED IN ORDER TO INCREASE THE QUANTITY OF OTHER VARIABLE. PROPERTIES OF ISOQUANTS 2. A HIGHER ISOQUANT REPRESENTS LARGER OUTPUT. THAT IS WITH

THE SAME QUANTITY OF 0NE INPUT AND LARGER QUANTITY OF THE OTHER INPUT, LARGER OUTPUT WILL BE PRODUCED. PROPERTIES OF ISOQUANTS 3. NO TWO ISOQUANTS INTERSECT OR TOUCH EACH OTHER. IF THE TWO ISOQUANTS DO TOUCH OR INTERSECT THAT MEANS THAT A SAME AMOUNT OF TWO INPUTS CAN PRODUCE TWO DIFFERENT LEVELS OF OUTPUT WHICH IS ABSURD. PROPERTIES OF ISOQUANTS 4. ISOQUANT IS CONVEX TO THE ORIGIN. THIS MEANS THAT THE SLOPE DECLINES FROM LEFT TO RIGHT ALONG THE CURVE. THAT IS WHEN WE GO ON INCREASING THE QUANTITY OF ONE INPUT SAY

LABOUR BY REDUCING THE QUANTITY OF OTHER INPUT SAY CAPITAL, WE SEE LESS UNITS OF CAPITAL ARE SACRIFICED FOR THE ADDITIONAL UNITS OF LABOUR. Now, lets just consider the column under 10 capital Number Total Mechanics Output 0 0 1 100 2 250 3 360 4 440

5 500 6 540 7 550 8 540 The Total Product Curve Total 60 0 TPP 50 Output 0 , TPP 40 0 30 0 20

0 10 0 1 2 3 4 Number of Mechanics 5 6 7 8 Average Product = Total Output # of mechanics 0 0

1 100 250 360 440 500 540 550 540 2 3 4 5 6 7 8 0 100 125 120 110 100 90 78.6 67.5

Number Total Mechanics Output Average Product, APP 15 0 12 5 10 0 AP P 75 50 1 2 3 Number 7 8 of Mechanics 4

5 6 0 1 2 3 4 5 6 7 8 0 100 250 360 440 500 540 550 540 Average Product 0

100 125 120 110 100 90 78.6 67.5 Marginal Product = Mechanics Change in Total Output Change in Number of MechanicsOutput Product Product 0 0 0 0 100 1 100 100 150 2 250 125

110 3 360 120 80 4 440 110 60 5 500 100 40 6 540 90 10 7 550 78.6 -10 8 540 67.5 Lets Plot the MPP Schedule Well place it on top of the APP schedule so we can compare the two

Average and Marginal Marginal Product MPP>APP 150 |----------| and Average MPP

3 4 5 6 Number of Mechanics 7 8 MPP RETURNS TO SCALE DIMINISHING RETURNS REFER TO RESPONSE OF OUTPUT TO AN INCREASE OF A SINGLE INPUT WHILE OTHER INPUTS ARE HELD CONSTANT. WE HAVE TO SEE THE EFFECT BY INCREASING ALL INPUTS. WHAT WOULD HAPPEN IF WHEAT IF LAND, LABOUR, ETC,. ARE ALL DOUBLED. RETURNS TO SCALE OR INCREASES OF INPURTS

PRODUCED. THE PRODUCTION OF FERTILISERS, WATER THIS REFERS TO THE EFFECT OF SCALE ON THE QUANTITY CONSTANT RETURNS TO SCALE THIS DENOTES A CASE WHERE A CHANGE IN ALL INPUTS LEADS TO A PROPORTIONAL CHANGE IN OUTPUT. FOR EXAMPLE IF LABOUR, LAND CAPITAL AND OTHER INPUTS DOUBLED, THEN UNDER CONSTANT RETURNS TO SCALE OUTPUT WOULD ALSO DOUBLE. INCREASING RETURNS TO SCALE THIS IS ALSO CALLED ECONOMIES OF SCALE. THIS ARISES WHEN AN INCREASE IN ALL INPUTS

LEADS TO A MORE-THANPROPORTIONAL INCREASE IN THE LEVEL OF OUTPUT. FOR EXAMPLE AN ENGINEER PLANNING A SMALL SCALE CHEMICAL PLANT WILL GENERALLY FIND THAT BY INCREASING INPUTS OF LABOUR, CAPITAL AND MATERIALS BY 10% WILL INCREASE THE TOTAL OUTPUT BY MORE THAN 10%. DECREASING RETURNS TO SCALE THIS OCCURS WHEN A BALANCED INCREASE OF ALL INPUTS LEADS TO A LESS THAN PORPORTIONAL INCREASE IN TOTAL OUTPUT.

IN MANY PROCESS, SCALING UP MAY EVENTUALLY REACH A POINT BEYOND WHIH INEFFICIENCIES SET IN. THESE MIGHT ARISE BECAUSE THE COSTS OF MANAGEMENT OR CONTROL BECOME LARGE. THIS WAS VERY EVIDENT IN ELECTRICITY GENERATION WHEN PLANTS GREW TOO LARGE, RISK OF PLANT FAILURE INCREASED. IMPORTANCE OF RETURNS TO SCALE CONCEPT IF AN INDUSTRY IS CHARACTERIZED BY INCREASING RETURNS TO SCALE, THERE WILL BE A TENDENCY FOR EXPANDING THE SIZE OF THE FIRM AND THUS THE INDUSTRY WILL BE DOMINATED BY LARGE FIRMS. THE OPPOSITE WILL BE TRUE IN INDUSTRIES WHERE DECREASING RETURNS TO SCALE PREVAIL. IN CASE OF INDUSTRIES WITH CONSTANT RETURNS TO SCALE, FIRMS OF ALL SIZES WOULD SURVIVE EQUALLY WELL. FROM PRODUCTION TO COST TO GET TO WHERE WE REALLY WANT TO BE, WE MUST TRANSLATE THE PRODUCT SCHEDULES AND CURVES TO

COSTS. LETS ASSUME THE COST PER VARIABLE RESOURCE -- PER WORK -- IS \$1000 PER WEEK. ASSUME THIS IS THE ONLY COST. Production and Costs T o ta l O u tp u t # o f m e c h a n ic s 0 1 2 3 4 5 6 7 T o ta l C os t 0 100 250 360 440

500 540 550 0 1000 2000 3000 4000 5000 6000 7000 Total Costs (thousands) Total Costs 6 5 4 3 2 1 0 100 2 00 300

400 Total Output 500 600 Average and Marginal Economists find it useful to talk about three dimensions of something: Total Average = per unit Marginal = incremental Production and Costs Total Total # of mechanics Output Cost 0 0 0 1 100 1000

2 250 2000 3 360 3000 4 440 4000 5 500 5000 6 540 6000 7 550 7000 Quantity of Output Total Cost 100 250 360 440 500

540 550 Average Cost Marginal Cost 1,000 10 2,000 3,000 4,000 5,000 6,000 7,000 8 8.33 9 10 11.1 12.7 10 6.7

9.1 12.5 16.7 25 100 Plot the Average Cost and the Marginal Cost Schedules Average Cost is the per unit cost: total cost divided by quantity of output Marginal Cost is the change in total cost divided by the change in total output.

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