production function
TRANSCRIPT
Tanu Kathuria 1
Production Function
Tanu Kathuria 2
Tanu Kathuria 3
Production Function
Tanu Kathuria 4
Production Function States the relationship between inputs and outputs Inputs – the factors of production classified as:
Land – all natural resources of the earth – not just ‘terra firma’!
Price paid to acquire land = Rent Labour – all physical and mental human effort involved
in production Price paid to labour = Wages
Capital – buildings, machinery and equipment not used for its own sake but for the contribution it makes to production
Price paid for capital = Interest
Tanu Kathuria 5
Production Function
Inputs Process Output
Land
Labour
Capital
Product or service
generated– value added
Tanu Kathuria 6
Production Function
Mathematical 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
Tanu Kathuria 7
Analysis of Production Function:Short Run
In the short run at least one factor fixed in supply but all other factors capable of being changed
Reflects ways in which firms respond to changes in output (demand)
Can increase or decrease output using more or less of some factors but some likely to be easier to change than others
Increase in total capacity only possible in the long run
Tanu Kathuria 8
Analysis of Production Function:Short Run
In times of rising sales (demand) firms can increase labour and capital but only up to a certain level – they will be limited by the amount of space. In this example, land is the fixed factor which cannot be altered in the short run.
Tanu Kathuria 9
Analysis of Production Function:Short Run
If demand slows down, the firm can reduce its variable factors – in this example it reduces its labour and capital but again, land is the factor which stays fixed.
Tanu Kathuria 10
Analysis of Production Function:Short Run
If demand slows down, the firm can reduce its variable factors – in this example, it reduces its labour and capital but again, land is the factor which stays fixed.
Tanu Kathuria 11
Short-Run Changes in ProductionFactor Productivity
Units of KEmployed Output Quantity (Q)
8 37 60 83 96 107 117 127 1287 42 64 78 90 101 110 119 1206 37 52 64 73 82 90 97 1045 31 47 58 67 75 82 89 954 24 39 52 60 67 73 79 853 17 29 41 52 58 64 69 732 8 18 29 39 47 52 56 521 4 8 14 20 27 24 21 17
1 2 3 4 5 6 7 8Units of L Employed
How much does the quantity of Q change, when the quantity of L is increased?
Tanu Kathuria 12
The Marginal Product of Labour The marginal product of labour is the
increase in output obtained by adding 1 unit of labor but holding constant the inputs of all other factors
Marginal Product of L:
MPL= Q/L (holding K constant)
= Q/L
Average Product of L:
APL= Q/L (holding K constant)
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Relationship Between Total, Average, and Marginal Product: Short-Run Analysis Total Product (TP) = total quantity of
output
Average Product (AP) = total product per total input
Marginal Product (MP) = change in quantity when one additional unit of input used
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Short-Run Analysis of Total,Average, and Marginal Product
If MP > AP then AP is rising
If MP < AP then AP is falling
MP = AP when AP is maximized
TP maximized when MP = 0
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Three Stages of Production in Short Run
AP,MP
X
Stage I Stage II Stage III
APX
MPXFixed input grossly underutilized; specialization and teamwork cause AP to increase when additional X is used
Specialization and teamwork continue to result in greater output when additional X is used; fixed input being properly utilized
Fixed input capacity is reached; additional X causes output to fall
Tanu Kathuria 16
Law of Diminishing Returns(Diminishing Marginal Product)
Holding all factors constant except one, the law of diminishing returns says that: As additional units of a variable input are
combined with a fixed input, at some point the additional output (i.e., marginal product) starts to diminish
e.g. trying to increase labor input without also increasing capital will bring diminishing returns
Nothing says when diminishing returns will start to take effect, only that it will happen at some point
All inputs added to the production process are exactly the same in individual productivity
Tanu Kathuria 17
Analysing the Production Function: Long Run
The long run is defined as the period of time taken to vary all factors of production By doing this, the firm is able to increase its total capacity – not
just short term capacity Associated with a change in the scale of production The period of time varies according to the firm
and the industry In electricity supply, the time taken to build new capacity could be
many years; for a market stall holder, the ‘long run’ could be as little as a few weeks or months!
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Analysis of Production Function:Long Run
In the long run, the firm can change all its factors of production thus increasing its total capacity. In this example it has doubled its capacity.
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Long-Run Changes in ProductionReturns to Scale
Units of KEmployed Output Quantity (Q)
8 37 60 83 96 107 117 127 1287 42 64 78 90 101 110 119 1206 37 52 64 73 82 90 97 1045 31 47 58 67 75 82 89 954 24 39 52 60 67 73 79 853 17 29 41 52 58 64 69 732 8 18 29 39 47 52 56 521 4 8 14 20 27 24 21 17
1 2 3 4 5 6 7 8Units of L Employed
How much does the quantity of Q change, when the quantity of both L and K is increased?
Tanu Kathuria 20
Optimal Combination of Inputs Now we are ready to answer the question
stated earlier, namely, how to determine the optimal combination of inputs
As was said this optimal combination depends on the relative prices of inputs and on the degree to which they can be substituted for one another
This relationship can be stated as follows:
MPL/MPK = PL/PK
(or MPL/PL= MPK/PK)
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An IsoquantGraph of Isoquant
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 X
Y
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Law of Diminishing Marginal Rate of Technical Substitution:
Table 7.8 Input Combinationsfor Isoquant Q = 52Combination L K
A 6 2B 4 3C 3 4D 2 6E 2 8
L K MRTS
-2 1 2 -1 1 1 -1 2 1/2 0 2
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Law of Diminishing Marginal Rate of Technical Substitution continued
0
1
2
3
4
5
6
7
2 3 4 6 8 X
Y
X = 2Y = -1
X = 1
Y = -1
X = 1
Y =- 2
A
BC
D E
Tanu Kathuria 24
Isocost Curves
Assume PL =$100 and PK =$200Input Combinations Rs.1000 BudgetCombination L K
A 0 5B 2 4C 4 3D 6 2E 8 1G 10 0
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Isocost Curve and Optimal Combination of L and K
Isocost and isoquant curve for inputs L and K
5
10 L
K
“Q52”
100L + 200K = 1000
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Un
its
of
cap
ita
l (K
)
OUnits of labor (L)
100
200
300
Expansion path
TC =£20 000
TC =£40 000
TC =£60 000
The long-run situation:both factors variable
Expansion Path: the locus of points which presents the optimal input combinations for different isocost curves
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Returns to Scale
Let us now consider the effect of proportional increase in all inputs on the level of output produced
To explain how much the output will increase we will use the concept of returns to scale
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Returns to Scale continued
If all inputs into the production process are doubled, three things can happen: output can more than double
increasing returns to scale (IRTS)
output can exactly double constant returns to scale (CRTS)
output can less than double decreasing returns to scale (DRTS)
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Graphically, the returns to scale concept can be illustrated using the following graphs
Q
X,Y
IRTSQ
X,Y
CRTSQ
X,Y
DRTS