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Production Function
Single FactorTwo Factors
Returns to Scale
Managerial EconomicsMicroeconomics
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Production Function
All inputs for production are referred as Factors of Production and classified
as Land Rent
Labour Wages
Kapital Interest
Entrepreneur skill Profits
Production function functional relationship between quantities of factors of
production and the resultant quantity of output. Thus the quantity of Output (Q) from the process of Production can thus be
expressed as a functional relationshipQ =f(L, Lb, K, E)
Implying that
A change in the proportion of factors may vary the level of output
Same level of output can be achieved using different proportions of factors For the sake of simplicity we further assume that there are only 2 factors of
production i.e. Kapital and Labour
The Production Function can thus be written asQ =f(K, L)
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Single Factor Model
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Single Factor Model
Production can further be thought of as a function of a single factor eg. Labour
by keeping the other factors constant.
Eg. Say a certain amount of investment is done in Plant & machinery which
remains fixed over a period i.e. Does not change with additions to Labour.
Then
Total Product can be defined as the total quantity of output produced on employing
certain units of Labour Marginal Product of Labour (MPL) can be defined as addition to total product due to an
addition of one unit of labour
Thus MPL = dTP/dL
In such situation
Marginal Product will
Increase initially
Then decrease after certain level
Will reach Zero
Then becomes negative
Total Product will
Increase at increasing rate
Increase at decreasing rate
Reach a maximum
Start declining
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Total and Marginal Product
Marginal Product will
Increase initially (OA)
Then decrease after certain level (AB)
Will reach Zero (B)
Then becomes negative (BC)
Total Product will
Increase at increasing rate (OD)
Increase at decreasing rate (DE)
Reach a maximum (E)
Start declining (EF)
Kapital Labour MP TP AP
100 1 10 10 10
100 2 20 30 15
100 3 30 60 20
100 4 20 80 20
100 5 15 95 19
100 6 7 102 17
100 7 0 102 15
100 8 -10 92 12
Output
O
utput
Labour Units
Labour Units
A
B
E
F
D
O
O
30
102
C
3 7
3 7
Marginal Product
Total Product
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Average and Marginal Product
When Marginal Product (MP) increases Average Product (AP) also increases MP
curve is above AP (OA OF)
When MP starts to decline AP keeps increasing MP curve is above AP (AD FD)
Till such point where AP is equal to MP MP and AP intersect (D)
Thereafter, AP also starts declining AP curve is above MP (DB DC)
Kapital Labour MP TP AP
100 1 10 10 10
100 2 20 30 15
100 3 30 60 20
100 4 20 80 20
100 5 15 95 19
100 6 7 102 17
100 7 0 102 15
100 8 -10 92 12
Output
Labour Units
A
BO
30
C
3 7
20
4
D
EF
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Total Product, Marginal Product and Average Product
MP = dTP/dL = Slope of TP curve
AP = TP/L = Slope of line joining point on TPcurve and Origin
At point H on the TP curve
AP is the slope of line OH
MP is the slope of line PQ
PQ is steeper than OH thus MP is higherthan AP
At point G on the TP curve
Slope of OG = AP = MP
Point G corresponds to Point D where MPintersects AP
Beyond point G on the TP curve
Slope of TP Curve < Slope of Line from Originto point on Curve
MP < AP
Output
O
utput
Labour Units
Labour Units
A
B
E
F
O
O
30
102
C
3 7
3 7
D
G
H
P
Q
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Two Factor Model
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Two Factor Model
Given Production Function Q =f(K,L) let us now
assume that both factors are variable. Thus
Increasing quantity of K or L or both K and L will increaseOutput
Decreasing quantity of K or L or both K and L will decreaseOutput
ALSO, Increasing K and decreasing L in some proportion will
keep the Output constant
The last proposition above gives us iso-output curve i.e.A curve joining different combinations of K and L suchthat Output remains constant referred to as ISOQUANTcurves.
Properties similar to indifference curves
Negative sloping Convex to origin
Higher Isoquant represent higher levels of Output
Slope of the curve here referred to as Marginal Rate ofTechnical Substitution (MRTS) gives the MRS betweenKapital and Labour = dK/dL for a given level of Output.
Labour
Kapital
IQ1IQ2
IQ3
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Properties of Isoquants
Substitution
The 2 inputs K and L are substitutable
A rate of substitution exists between K and L such that
the resultant Output remains constant
Diminishing MRTS
The convexity of the curve implies a diminishing MRTS
Thus every additional units of K can be substituted bylesser and lesser units of L
Implying Law of Diminishing Marginal Returns
L K K/Y
A 1 4 -
B 2 1.75 2.25/1
C 3 1.25 0.5/1
D 4 1 0.25/1
Labour
Kapital
1
2
3
4
1 2 3 4 5
A
B
DC
Marginal Rate of Technical Substitution
Q =f(K, L)
dQ = dL . (Q/L) + dK . (Q/K) . . . Total differentiation
[Marginal addition to total Output] = [additional units if L] x
[MPL] + [additional units of K] + [MPK]
dQ = dL . (MPL) + dK . (MPK)
But along an Isoquant Curve marginal addition to Output is 0.
So, dQ = dL . (MPL) + dK . (MPK) = 0
- dK/dL = MPL/MPK = MRTSKL
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Special Cases
Perfect Substitutes
In fig 1 the Isoquant is linear
Constant MRTS
Constant MP of factors (not diminishing)
Factors perfectly substitutable at all stagesof production
Entire production possible only by K
Entire Production possible only by L
Fixed Factor Proportions
In fig 2 Isoquants are rt. angled
A certain level of Output possible onlywith a unique combination of K and L
Quantity of K and L along line OP For any IQ increase in K or L more than the
combination given by OP results in ZeroMP of factors
Typically modular expansion of production
IQ1
IQ2
IQ3
IQ1
IQ2
IQ3
Labour
Kapital
Labour
Kapital
O
O
P
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Choice of Inputs
The Choice of optimum combination of Factors is
determined by the Relative Prices of Factors The logic is similar to that used in the Indifference
Curve analysis
In fig, - IQ1, IQ2 and IQ3 are various Output levels possible by
combinations of K and L
AB is the Iso-cost Line (similar to the Budget line)
If all resources are used in buying K OA is themaximum K that can be employed
OA i.e. Total units of K affordable is determined bycost of K i.e interest rate (r)
If all resources are used in buying L OB is themaximum L that can be employed
OB i.e. Total units of L affordable is determined bycost of L i.e. Wages (w)
Slope of AB = w/r
Optimum Choice of Inputs would be point whereIsocost line is tangential to the Isoquant
At equilibrium
Slope of Isoquant = Slope of Isocost
MRTS = w/r
MPL/MPK = w/r
Labour
Kapital
IQ1IQ2
IQ3
RS
Q
P
T
B
A
O
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Returns To Scale
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Returns to Scale
A unit increase in inputs how much change in output will it result in ?
Double the InputsMore than double change in Output Increasing Returns
Double the Inputs Less than double change in Output Decreasing Returns
Double the Inputs Double the Output Constant returns
Labour
Kapital
1
2
3
4
1 2 3 4 5
55
50
30
10O
A
B
D
C
In the fig.
From OA to AB Inputs have doubled but
output has more than doubled Increasing
returns
From AB to BC Inputs have grown by 50% -
Output has grown by more than 50% -
Increasing returns
From BC to CD Inputs have grown by 33% -Output has increased by 10% - Decreasing
returns
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Returns to Scale
Managerial Efficiency
Benefits of specialization
Benefits of R&D
Technology
Business too big to manage
Specialised Units Common Infrastructure
Emergence of Market Place
Over utilisation of infrastructure Competition takes business
share
Internal Factors Resulting from Expansion of the Firm
External Factors Resulting from Expansion of the Industry
Dis-economies
Dis-economiesEconomies
Economies
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