production function

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

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Production Function

Inputs Process Output

Land

Labour

Capital

Product or service

generated– value added

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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

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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

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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.

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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.

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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.

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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?

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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

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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

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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?

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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

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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

production function

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