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LONG RUN PRODUCTION FUNCTION
MBA (PM) IInd SEM
What Is Production FunctionProduction function deals with
the maximum output that can be produced with a limited and given quantity of inputs.
PRODUCTION FUNCTION
1. The tool of analysis used to explain the input-output relationship
2. Describes the technological relationship between inputs and outputs in physical terms
3. It tells that the production of a commodity depends on specific inputs
4. It represents quantitative relationship between inputs and output
5. It represents the technology of a firm, of an industry, or of the economy as a whole
Production FunctionMathematical representation
of the relationship:Q = f (K, L, La)
Output (Q) is dependent upon the amount of capital (K), Land (L) and Labour (La) used
ASSUMPTIONS
THE PRODUCTION FUNCTIONS ARE BASED ON CERTAIN ASSUMPTIONS
1. Perfect divisibility of both inputs and outputs
2. Limited substitution of one factor for another
3. Constant technology
4. Inelastic supply of fixed factors in the short run
THE LAWS OF PRODUCTION
LAWS OF VARIABLEPROPORTIONS
LAWS OF RETURNSTO SCALE
Relates to the study of input output relationship in the short run with one variable input while other inputs are held constant
Relates to the study of input output relationship in the long run assuming all inputs to be variable
What is long run production function ?
Long run refers to that time in the future when all inputs are variable inputs.
In the long run both capital and labour are included
Output can be varied by changing the levels of both L & K and the long run production function is expressed as:
Q = f (L, K)
THE LAW OF RETURNS TO SCALE
EXPLAINED BY
ISOQUANT CURVE
TECHNIQUE
PRODUCTIONFUNCTION
LONG RUN TOTAL PRODUCTION-Returns to scale
During the short period, some factors of production are relatively scarce, therefore , the proportion of the factors may be changed but not their scale. But in the long run, all factors are variable, therefore, the scale of production can be changed in the long run
Returns to scale is a factor that is studied in the long run.
Returns to scale show the responsiveness of total product when all the inputs are increased proportionately.
Returns to ScaleWhen all inputs are changed in
the same proportion (or scale of production is changed),the total product may respond in three possible ways:
1) Increasing returns to scale2) Constant returns to scale, and 3) Diminishing returns to scale
INCREASING RETURNS TO SCALEThe law of increasing
returns to scale operates when the percentage increase in the total product is more than the percentage increase in all the factor inputs employed in the same proportion.
Many economies set in and increase in return is more than increase in factors.
For e.g 10 percent increase in labour and capital causes 20 percent increase in total output. Similarly, 20 percent increase in labour and capital causes 45 percent increase in total output.
CONSTANT RETURNS TO SCALE
Law of constant returns to scale operates when a given percentage increase in the factor inputs in the same proportion causes equal percentage increase in total output.
Economies of scale are counter balanced by diseconomies of scale.
DIMINISHING RETURNS TO SCALE The law of diminishing
returns to scale occurs when a given percentage increase in all factor inputs in equal proportion causes less than percentage increase in output.
Output increases in a smaller proportion.
Diseconomies outweigh economies of scale
Q
X,Y
IRTS Q
X,Y
DRTSQ
X,Y
CRTS
Graphically, the returns to scale concept can be illustrated using the following graphs
ADVANTAGES AND DISADVANTAGES OF LARGE SCALE PRODUCTION
Specialization
Economy of labour
Economics of buying and
selling
Overhead charges
Rent
ECONOMIES OF SCALE
INTERNAL ECONOMIES
EXTERNAL ECONOMIES
Reduction in costs when the scale of production increases
is called
INTERNAL ECONOMIES
Economies in Production
Economies in
Marketing
Technological Advantages
Advantages of divisions of labour & Specialization
Large scale production provides opportunities for technological advances
Large scale production workers of varying skills & qualifications are employed which facilitates division of labour as per specialization
.. Large scale selling of firms own products
.. Advertising cost .. Large scale distribution
.. Large scale purchase of raw materials & other inputs
Improves the overall performance of the firm
Managerial Economies
Transport & Storage Economies
.. Specialization in managerial activities
.. Mechanization of managerial functions
.. Improves managerial efficiency
.. Efficient management of the transport function
.. Proper utilization of storage facilities
.. Helps in reducing transportation and storage costs
CAUSES OF INTERNAL ECONOMIES
SIZE Big Machine
Bigger capacity lower Energy less labour
LIMITING PROCESS
MergersSpreading of
costs
TECHNIQUE
Superior Technique
Shorter period of time
SPECIALI - ZATION
Division of Labour
Increase in efficiency
MANAGERIAL ECONOMICS
COMMERCIAL ECONOMIES
Aggregation
Financial economies
Wide Market
Credit facilities
Encourages investment
Managerial economies
RISK BEARING ECONOMIES Spreading
RisksDiversification
CAUSES OF EXTERNAL ECONOMIES
CONCENTRATION
Advantages of locality
Common Pool of Knowledge of localityReduced transportation cost
INFORMATION
DISINTEGRATION
Breaking up processes
The benefits which companies derive from trade publications and technical journalsBy virtue of location, common pool of research can be created and benefits can be shared
Knowledge sharing
Breaking up of processes which can be handled by specialist firms
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Production Isoquants/ isoquant curve/iso-product
curve• In the long run, all inputs are
variable & isoquants are used to study production decisions– An isoquant or iso-product curve is a
curve showing all possible input combinations capable of producing a given level of output
– Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output
ASSUMPTIONS
1. THERE ARE ONLY TWO FACTORS OF PRODUCTION…CAPITAL (K) AND LABOUR (L) TO PRODUCE A COMMODITY X
2. THE TWO FACTORS CAN SUBSTITUTE EACH OTHER UP TO A CERTAIN LIMIT
3. THE TECHNOLOGY IS GIVEN OVER A PERIOD
Example Isoquant Curve
01
2345
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0 2 4 6 8 10
Units of X
Units
of Y
Isoquant; TP = 100 units
The following combinations of inputs X and Y produce 100 units of output:
º 2,6º 3,4º 4,3º 6,2º 8,2 Units of Labour
Unit
s of
cap
ital
Iq1 = 100
A
B
C
D
K4
K3
K2
K1
0L1
Units of L
Unit
s of
K
L2
L3
L4
Isoquant curve for 100 units of output PROPERTIES:-
1. Slopes downward towards right
2. Convex to the origin point because of diminishing
marginal rate of technical substitution (MRTS)
3. Two iso-product curves do not cut each other
labourin change
capitalin changeMRTS
Iq4
Iq3
Iq2
Iq1 = 100
A
B
C
D
K4
K3
K2
K1
0L1 L2 L3 L4
Units of L
Unit
s of
K
= 200
= 300
= 400
ISOQUANT MAP- A family or a group of isoquants is called an ISOQUANT MAP
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The Isocost Line
0 1 2 3 4 5 6 7 8 9 10 Labor, L (worker-hours employed)
Cap
ital,
K (
mac
hine
s re
nted
)
Cost = Rs50Per unit price of labor input = Rs10/hourPer unit price of capital input = Rs5/machine
2
4
8
10
a
b
c
d
e
f
6
A
B
M=PL.QL+PK.QK
Where, M=total outlay PL= price per unit of labor QK= price per unit of capital QL= units of labor QK= units of capital
Slope of isocost line= OA/OF
Slope of isocost line can be change in two ways:1) Change in the factor price, and2) Change in total outlay or total cost
Slope of isocost line
input capital ofunit per price
inputlabour ofunit per price
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Changes in One factor Price
Decrease in the factor price causes rightward shift and increase in factor price causes leftward
shift in iso-cost line.
0 1 2 3 4 5 6 7 8 9 10
Cap
ital,
K (
mac
hine
s re
nted
)
2
4
6
8
10
Labor, L (worker-hours employed)
a
f
Cost = 500; labor,R = 16.5 or 10or 1/ hourThe money wage, W = Rs5/machine
…Rs10
…Rs1
A Change in unit price of labor
hRs16.5
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L
K
Units of labour(w)
Slope = -w/r
Direction of increasein total cost
Change in total outlay or total cost
Un
its o
f
cap
ital (r
)
TC=Rs. 50
TC= Rs. 75
TC= Rs. 100
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L
K
Units of Labour
•
Isoquants and Cost Minimization
•
Q=200
Q=300
Q=100
IQ
1IQ 2
IQ 3
TC=Rs50
•
•
0 2 4 6 8 10 12 14 16 18 20
Unit
s of
Cap[i
tal
0
2
4
6
8
10
TC=Rs=75
TC=Rs100
P
P”
P’
•N
M
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Optimization & Cost• Expansion path gives the efficient
(least-cost) input combinations of labor and capital needed foe every levels of output.Derived for a specific set of input pricesAlong expansion path, input-price ratio
is constant & equal to the marginal rate of technical substitution
• It is defined as the locus of tangency points between iso-cost lines and isoquants.
•It implies to Long run because: No input is fixed.Path starts from origin indicating that if output is zero costs are zero.•Expansion path gives us thelevel of output & one leastcombination that canproduce this level of output.•Movement along the line givesthe costs at which output canbe expanded•So called Expansion Path.
EXPANSION PATH
Labor input
Capita
l input
ISOQUANTS AND RETURNS TOSCALE
INCREASING RETURNS TO SCALE
0E>EE1>EE2
CONSTANT RETURNS TO SCALE
EE1=EE2=EE3
DIMINISHNING RETURNS TO SCALE
0E<EE1<EE2
The LR Relationship Between Production and Cost
In the long run, all inputs are variable.◦ What makes up LRAC?
Long run average cost
•LRAC refers to minimum possible per unit costof producing different quantities of output ofa good in the long period.
•SRAC curves represent various plant sizes
•Once a plant size is chosen, per-unit production costs are found by moving along that particular SRAC curve
• LRAC is made up of SRACs. Since LRAC envelopes all short run curves, hence Called ENVELOPE CURVE
Envelope curve
• LRAC can never cut SRAC but it will be tangential to each SRAC at some point.
• Average cost can not be higher in the long run than in the short run;
•Explanation;1.Any adjustment which will reduce costs
possible to be made in the short run must also be possible in the long run
2.It is not always possible in the short run to produce a given output in the cheapest possible way as all the factors are not variable.
properties U-shaped curve.Based on assumption of unchanging technology.LRAC is flatter curve than the SRAC. In economics ,we define long period as that during which size of the organization can be altered to meet changed conditions.Normally; Output increases and average costs also increases But in long run, size of the firm Can be increased therefore Variable costs are likely to rise less sharply. Hence a flatter curve.
Long run average cost curve Minimum
efficient scale is the lowest output level for which LRAC is minimized
The Long-Run Cost Function
• Reasons for Economies of Scale…Increasing returns to scaleSpecialization in the use of labor and
capital• Economies in maintaining inventory• Discounts from bulk purchases• Lower cost of raising capital funds• Spreading promotional and R&D costs
Management efficiencies
The Long-Run Cost Function
• Reasons for Diseconomies of Scale…Decreasing returns to scaleInput market imperfections e.g. wage rate driven
upManagement coordination and controlproblemsDisproportionate rise in transportation costsDisproportionate rise in staff and indirect labour
Application of the conceptIn the long run, a firm exercises its choicewith regard to the size of the plant andscale of production, on the basis of long runaverage cost.Selection of the optimal plant size
accordingto the expected demand.Avoid unnecessary costs due to
inappropriateplant size.