Mir Mohammed BelalPremier University ChittagongBBA (Hons)

Production function: The functional relationship between physical inputs and physical output of a firm is known as production function.Algebraically, production function can be written as p=f(Q),Q=f(L,K,M)Where Q stands for the quantity of factors labor, capital and raw materials respectively .

Types of production function:2 types:

(1)Short run.

(2)Long run.•Short run: The period when some input are constant and one on few in variable.•Long run: About 5 year all input are variable.

Product schedule:

Unit of labor TP AP MP

1 80 80 80

2 170 85 90

3 270 90 100

4 368 92 98

5 430 86 62

6 480 80 50

7 504 72 24

8 504 63 0

9 495 55 -9

10 480 48 -15

O X

TP

Y

1 2 3 4 5 6 7 8 9 10 Labor Figure:1

50

100

150

200

250

300

350

400

450

500

550

TP

• The total product curve is shown by TP in figure:-1. it will be seen that in the beginning total curve rises at an increasing rate. The stop of the TP curve is rising in thee beginning a point total product curve starts rising at a diminishing variable factor is increased.

1 2 3 4 5 6 7 8 9 10 X

0

-10

-20

100

90

80

70

60

50

40

30

20

10

AP

MP

• The average product are of a variable factor first rises and it declines . That is the average product are has been inverted U shape. The marginal product are first rises and the diminishing variable factor is increased and at a certain point MP is negative.

Law of variable proportion• Alfred Marshall: It refers input-output relation when

output is increased by varying the quantity of one input.• Condition:

3 conditions_

1.Technology is constant.

2.Some inputs must be kept constant.

3.The possibility of varying the proportion.

Point of in

flation

Y

O

MP

X

AP

TP

Unit of labor

TP, M

P, A

P

first

second thirdF Ox axis

represent the unit of factor, OY axis represent the TP, AP and MP.

•1st stage: Total product increase, Marginal product increase and average product also increase. Point F is point of inflation, point of inflation means rate of change, rate of change means before F TP increase, after F, TP increase – decreasing rate. At point F MP is highest.

•2nd stage: TP increase, AP decrease, MP decrease, At the end of 2nd stage TP highest, MP is zero.

•3rd stage: TP decrease, AP decrease, MP decrease, but MP is negative.

Expansion path/Scale line:

Expansion path

IQ1(200)

IQ2(300)

IQ3(400)

O M1 M2 M3 IC1 IC2 IC3 X

Y

N1

N2

N3

AB

C

capi

tal

labor

Ox represent the labor & and OY represent the capital. There are thee ISO Quant ISO1. ISO2, ISO3, they represent 200, 300, 400, unit. Three ISO cost IC1, IC2, IC3. When OM labor & ON capital produce the output level denoted by IQ1(200) unit & we get point A. The OM1 & OM2 labor ON1 & ON2 capital produce the high output level denoted by IQ2& IQ3 (300 & 400 unit) & we get point B&C. The joining point A, B, C is called expansion path.

ISO quant• ISO quant indicates various combination of two factors of production which

give the same level of output per unit of time.

Schedule:

12 A

capital

8 B

5 C

3 D

2 E

O 1 2 3 4 5 X

labor

combination

Factor labor

Factor capital

production

A 1 12 40

B 2 8 40

C 3 5 40

D 4 3 40

E 5 2 40IQ

OX axes represent the labor and OY represent the capital. IQ is an ISO quant curve. A consisting of one unit of labor and 12 units of capital produce the given 40 unit of output. Similarly B, C, D, E consisting of 2, 3, 4 ,5 labor and 8, 5, 3, 2 unit of capital produce the given 40 unit of output. The every combination represented on it can produce 40 unit of output.

ISO quant map an ISO quant map can be define the set of ISO quant curves that show technically efficient combination inputs that can produce different levels of output.

IQ1(40)IQ2(60) IQ3(80)

IQ4(100)

Y

O

capital

Xlabor

ISO cost line

30

capital 25

20 ISO cost line

15

10

5

O 10 20 30 40 50 60 X Labor

Y

ISO cost line:

Properties of ISO quantThere are three properties they are:-

a)ISO-quant is convex to the origin

b)Two ISO-quant can’t intersect.

c) ISO-quant slopes down word to the right.

(1) ISO-quant is convex to the origin: due to diminishing MRTS this curve opposite to the origin.

capital

Y

K

O labour X

IQ

Figure:1

MRTS>increasing

Y

IQ

K

O labor X figure:2

MRTS>constant

IQ

XlaborO

Y

capital

Figure:3

OX represent the labor & OY represent the capital in fig:1, 2, 3.Fig:1 is correct. Fig:2 is constant. Fig:3 is state line. So Fig 2&3 is not correct.

(2) Two ISO quant can’t intersect each other at any point:

C

B A

IQ2(60unit)

IQ1 (40 unit)

O Labor X

capital

Y

OX represent the labor & OY represent the capital. There is ISO quant there IQ 1 it represent 40 units another IQ 2 represent 60 units. In IQ1 there is A two point A and C. In IQ2 there is two point B & C . There are same production in IC1 , B=C=60 units. C is the different product in level in the two productions.

(3)ISO quant slop down ward to the right:This implies that the ISO quant is a negatively sloped curve. This is because when the quantity of factors C is increased , the quantity of labor must be reduced so as to keep the same level of output.

a

b

ISO (40)

Ycapital

O X1 X2 labor X Figure:1

From the figure we find that as the producer moves a to b, the producer employed more labor and less capital and its represents 40 units of production. It is show that an IQ curves downward to the right.

Marginal rate of technical substitution(MRTS)

combination

Factorlabor

Factorcapital

product MRTS

A 1 12 40

B 2 8 40 4

C 3 5 40 3

D 4 3 40 2

E 5 2 40 1

O 1 2 3 4 5 x Labor

12

8

5

321

Y

IQ

a

b

c

d

e

Factorcapital

OX represent the labor & OY represent the capital. A, B, C, D & E is an IQ curve. The slope of labor will increase. The slope of labor will decrease in capital.

Return of scale• Return of scale refers

different level of production at different factors of production..

There are three types of returns to scale:-

a) Increasing returns to scale: output increase in greater than increase in input.

b) Constant returns to scale: output increase in less same proportion as input increase.

c) Decreasing return to scale :output increase in less proportion than increase in input.

combination

labor capital Total return

Marginal return

1 1 3 2 2

2 2 6 5 3

3 3 9 9 4

4 4 12 14 5

5 5 15 19 5

6 6 18 24 5

7 7 21 28 4

8 8 24 31 3

9 9 27 33 2

constant

Combination of factor

X

decreasingincreasing

Marginal return

Y

5

4

3

21

O

1 2 3 4 5 6 7 8 9

• OX represent the combination of factor. OY represent the marginal return. When the combination of factor 1, 2, 3 then marginal return is increasing the combination of factor 4, 5, 6 the marginal return is constant. When the combination of factor 7, 8, 9 the marginal return is decreasing.

Efficiency of production/producers equilibrium.The ability produced a good using the fewest resources possible.Two kinds of efficiency of production.

(1)Cost minimization.

(2)Output minimization.

Least cost of combination/Cost minimization:

The producer is said to be in equilibrium when the chooses that combination of factors that represent minimum cost & no tendency to rearrange.

Condition:

(1)Slope of ISO quant is equal to slope of ISO cost line.

(2) ISO quant is tangent to ISO cost.

(3)ISO quant is convex to origin.

(4)The production is fixed.

Equilibrium point

A

C

EBD

N

O

M IC1 IC2 IC3 X (100) (200) (300) labor

Y

Output maximization:

• Output maximization said to be in equilibrium when B produces maximum output with given cost.

• There are four conditions:

1) Slope of ISO-quant is equal to slope of ISO cost line.

2) ISO-quant is tangent to cost line.

3) ISO-quant is convex to origin.

4) The total cost is fixed, I,E. suppose taka 300.

Y

X

A

C

B

N

O M ISO cost (300)

IQ3 (700)

IQ2 (600)

IQ1 (500)

Equilibrium point

Capital

Labor