Production Function In Long RunProduction Function In Long Run

Concept of Production

• In General Terms– Production means transforming inputs (labour, machines, raw materials, time, etc.) into an output. This concept of production is however limited to only ‘manufacturing’.

• In Managerial Terms – Creation of utility in a commodity is production.

• In Economical Terms – Production means a process by which resources (men, material, time, etc.) are transformed into a different and more useful commodity or service.

Where;Input – It is a good or service that goes into the process of production.Output – It is any good or service that comes out production process.

The Production FunctionThe Production Function

• A Production Function is a tool of analysis used to explain the input-

output relationship. It expresses physical relationship between production

inputs and the resultant output. It tells us that how much maximum output

can be obtained in the specified set of inputs and in the given state of

technology.

• Mathematically, the production function can be expressed as

Q=f(K, L) Q is the level of output K = units of capital L = units of labour

• f= represents the production technology

The Production Function(cont’d…)

• When discussing production function, it is important to distinguish between two time frames.

The short-run production function which may also be termed as ‘single variable production

function’ describes the maximum quantity of good or service that can be produced by a set of

inputs, assuming that at least one of the inputs is fixed at some level which means that the

production can be increased by increasing the variable inputs only. It can be expressed as;

Q = f(L)

The long-run production function which may also be termed as ‘returns to scale’ describes the

maximum quantity of good or service that can be produced by a set of inputs, assuming that

the firm is free to adjust the level of all inputs. It can be expressed as;

Q = f(K, L)

Production Function in the Long Run

• Long run production function shows relationship between inputs and

outputs under the condition that both the inputs, capital and labour, are

variable factors.

• In the long run, supply of both the inputs is supposed to be elastic and

firms can hire larger quantities of both labour and capital. With large

employment of capital and labour, the scale of production increases.

Isoquant Curve

• The term ‘isoquant’ has been derived from the Greek word iso meaning ‘equal’ and

Latin word quantus meaning ‘quantity’. The ‘isoquant curve’ is, therefore, also

known as ‘Equal Product Curve’.

• An isoquant curve is locus of points representing various combinations of two

inputs - capital and labour - yielding the same output ,i.e., the factors combinations

are so formed that the substitution of one factor for the other leaves the output

unaffected.

• It is drawn on the basis of the assumption that there are only two inputs, i.e.,

labour(L) and capital(K), to produce a commodity X.

Isoquant Schedule

A schedule showing various combinations of two inputs (say labour and

capital) at which a producer gets equal output is known as isoquant

schedule. The table depicts that all combinations A,B,C,D and E of

labour and capital give 2000 units of output to a producer. Hence, the

producer remains neutral.

Combination Labour (L)

Capital(K)

Output(Q,Units)

A 1 15 2000

B 2 10 2000

C 3 6 2000

D 4 3 2000

E 5 1 2000

Isoquant Curve -Diagrammatic Presentation

Labour

Capital

0

K1

K2

L1 L2

A

BIP(2000 units)

X

Y

Characteristics of Isoquant Curve• They slope downward to the right : They slope downward to the right because if one of the inputs

is reduced, the other input has to be so increased that the total output remains unaffected.

• They are convex to the origin : They are convex to the origin because of Marginal Rate of

Technical Substitution of labour for capital. (MRTSLK) is diminishing. MRTSLK is the slope of an

isoquant curve. Isoquant curves are negatively sloped.

• Two isoquant curves do not intersect each other : Two isoquant curves do not intersect each

other as it is against the fundamental condition that a producer gets equal output along an isoquant

curve.

• Higher the isoquant curve higher the output : A producer gets equal output along an isoquant

curve but he does not get equal output among the isoquant curves. A higher isoquant curve yields

higher level of output.

Marginal Rate of Technical Substitution (MRTS)The MRTSlk is the amount of capital forgone for employing an additional amount of labour. Hence, it is a rate of change in factor K in relation to one unit change in factor L. This rate of change is diminishing. So the slope of iso-product curve is diminishing.

Slope = -dK/dL = change in capital/change in labour = MRTSlk

Combination Labour(L)

Capital(K)

MRTSlk(-dk/dl)

A 1 15 -

B 2 10 5/1

C 3 6 4/1

D 4 3 3/1

E 5 1 2/1

Marginal rate of technical substitution (MRTS)

LK MRTS

0 1 2 3 4 5 6 7

7

6

5

4

3

2

1

0

K

L

ΔK=3

ΔL=1

ΔK=1ΔL=1

ΔK=1/3ΔL=1

Labour

Isoquant Curve

X

1

2

3

4

1 2 3 4 5

5

Q1 =55

A

D

B

Q2 =75

Q3 =90

C

EY

Capital

Iso-cost CurvesAn Iso-cost curve on the one hand shows the resources of producer and on the other hand it

shows relative factor price ratio. It shows various combinations of two factors (say labour

and capital) that can be employed by the producer in the given producer’s resources.

Its slope is given by relative factor prices i.e. w/r where w is wage rate (price of labour) and r is

rate of interest (price of capital). The area under an iso-cost line is known as cost region. In order

to obtain least cost combination, cost region is super imposed over production region.

Y

X0 Labour

Capital

K

L

Cost Region

Slope = w/r

Increasingreturns to scale

Constantreturns to scale

Diminishing returns to scale

Total output may increasemore than proportionately

Total output may Increase proportionately

Total output may increase Less than proportionately

Increasing Returns to Scale

When a certain proportionate change in both the inputs, K and L, leads to a more

than proportionate change in output, it exhibits increasing returns to scale. For

example, if quantities of both the inputs, K and L, are successively doubled and

the corresponding output is more than doubled, the returns to scale is said to be

increasing.

ScheduleLabour and Capital

Output(TP)

Proportional change in

labour and capital

Proportional change in

output

1+1 10 - -

2+2 22 100 120

4+4 50 100 127.2

8+8 125 100 150

Increasing Returns to Scale-Diagrammatic Presentation

Y

X0Labour

Capital

Scale LineA

P

Q

R

S

IP1 (100)

IP2 (200)

IP3 (300)

IP4 (400)

OP>PQ>QR>RS

Constant Returns to Scale

When the change in output is proportional to the change in inputs, it exhibits

constant returns to scale. For example, if quantities of both the inputs, K and L,

are doubled and output is also doubled, then returns to scale are said to be

constant.

Schedule

Labour and Capital

Output(TP)

Proportional change in

labour and capital

Proportional change in

output

1+1 10 - -

2+2 20 100 100

4+4 40 100 100

8+8 80 100 100

Constant Returns to Scale-Diagrammatic Presentation

0 X

Y

Labour

Capital

P

Q

R

S

Scale LineA

IP1 (100)

IP2 (200)

IP3 (300)

IP4 (400)

OP=PQ=QR=RS

Diminishing Returns to Scale

When a certain proportionate change in inputs, K and L, leads to a less than

proportionate change in output. For example, when inputs are doubled and output is

less than doubled, then decreasing returns to scale is in operation.

Schedule

Labour and Capital

Output(TP)

Proportional change in

labour and capital

Proportional change in

output

1+1 10 - -

2+2 18 100 80

4+4 30 100 66.6

8+8 45 100 50

Diminishing Returns to Scale-Diagrammatic Presentation

0X

Y

P

Q

R

S

IP1 (100)

IP2 (200)

IP3 (300)

IP4 (400)

Scale LineAOP<PQ<QR<RS

Labour

Capital

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