A successful person is the one who

had the chance and took it

Lecture7:

Covers: Factor- Factor Relationships: meaning-

isoquant-definition and types- isoquant map- marginal rate
of technical substitution- factor intensity-isoclines-ridge line

Out line :
1. Isoquant or iso product curve
2. Linear isoquant
3. Fixed proportion combination of inputs
4. Varying (decreasing) rate of substitution
5. MRTS
6. Least cost combination
7. Isoclines, expansion path & profit maximization
Factor-Factor Relationship
When two or more inputs are variables, a given amount of
output may be produced in more than one way, i.e., there
is a possibility of substituting one factor (X1) for another
(X2) as product level (Y) is held constant.
objectives of factor-factor relationship;
i) minimization of cost at a given level of output and
ii) optimization of output to the fixed factors through
alternative resource-use combinations
A. ISOQUANT (OR) ISO PRODUCT CURVE
An isoquant is defined as the locus of all combinations
of inputs, X1 and X2, for obtaining a given level of
output, say, Y(0).
X1 = f (X2, Y(0)) or X2= f (X1, Y(0)).
Types of isoquants
i) Linear Isoquant: If two inputs substitute at constant rates. The rate at
which one factor (X1) is substituted for one unit increase in another factor
(X2) at a given level of output is called Marginal Rate of Substitution (MRS).
The marginal rate of substitution of X2 for X1 is denoted by:
MRSX2X1=

In linear isoquant, the rate at which these two inputs can be substituted at a
given level of output is constant regardless of the level of the two inputs used

MRSX2X1=
X1 X1

. X1 = f (X2, Y (0) )
X1 = f (X2, Y (0))
.
.
X2
X2
Fig.10.1 Linear Isoquant Fig.10.2 Inputs Combine in Fixed Proportion
ii) Fixed Proportion Combination of Inputs (Perfect
Complements): Only one exact combination of inputs will
produce the specified output, eg., A tractor and a driver ,
Here, there is no economic problem in decision-making
because there exists no alternative choice

iii) Varying (Decreasing) Rate of Substitution: : The

amount of one input (X1) required to be substituted for
by one unit of another input (X2) at a given level of
production decreases every subsequent increase in the
use of one factor replaces less and less of the other
Characteristics of isoquant:
1. Each point on the isoquant is the maximum output that can be
achieved with the corresponding input combination
2. Isoquants are convex to the origin
3. Two isoquants do not intersect each other
4. Isoquant map indicates the shape of the production surface,
which again indicates the nature of output response to the inputs
5. An isoquant which is far away from the origin represents higher
level of output
Marginal Rate of Input (Factor) substitutions (or) Rate of Technical
Substitution (RTS): Marginal Rate of Substitution of X2 for X1 (MRS X1X2) is
defined as the amount by which X1 must be decreased to maintain output
at a constant level when X2 is increased by one unit. Between the two points.
Eg.: Suppose two combinations (X2 =2, X1 =10) and X2 =3, X1 = 5),
MRS of X2 for X1 is

Decreasing Rate of Substitution

Variable Variable
input(X1) input (X2)
23 0 - - -
16 1 7 1 -7
10 2 6 1 -6
5 3 5 1 -5
1 4 4 1 -4
0 5 1 1 -1
 X1
X1 = f (X2, Y (0)) X1 Isocost Line

X2

X2
Fig.10.3 Convex Isoquant. Fig.10.4 Isocost Line
Isocost line
1. Isocost line determines all combinations of the two inputs that cost the
same amount
2. a combination of inputs that can be purchased with the same outlay of funds
3. As total outlay increases, isocost line moves higher and higher and moves
farther away from the origin.
4. Changes in the input prices will change the slope of isocost line
5. A decrease in the input price means that more of that input can be
purchased with the same total variable cost
6. isocost line can be found by solving the TVC equation for X1
7. TVS=Px1X1+Px2X2; Px1X1 = TVC – Px2X2 ;
Least cost combination
The tangency of isocost and isoquant would indicate the least cost combination of X 1 and
X2, i.e., slope of isoquant = slope of isocost

Isoquant
Iso Cost Line
Least Cost
Combination

Fig.10.5 Least Cost Combination

Isoclines are lines or curves that pass through points of equal
marginal rates of substitution on an isoquant map
There are as many different isoclines as there are different
slopes or marginal rates of substitution on an isoquant
The expansion path is also an isocline that connects the least
cost combinations of inputs for all yield levels
On expansion path, the marginal rate of substitution must equal
the input price ratio: Expansion Path (MRS X2X1)=

Ridge lines: the boundaries beyond which the isocline and isoquant maps
have no economic meaning
 Isoclines and Expansion path
Ridge line for X1=
X1 Irrational Zone Y=140
9
Expansion path

Y=130 Isoclines
Y=120

Ridge line for X2=

Y=108 X2
Y=100

Irrational Zone
Y= 45
 Expansion Path and Profit Maximization
Which output level is profitable?
value of the product added by increasing the two inputs along the expansion path is
equal to the combined cost of the added amount of two inputs

Profit = Py Y - Px1 X1 - Px2 X2 – TFC

The above two equations can be written as:

VMPx1 = Px1 (or) VMPx2 = Px2.

Y = 18X1 - X12 + 14X2 - X22 Equating VMP’s with the input prices
VMPx1 = (18 - 2X1) 0.65 (18 – 2X1) 0.65 = 9
VMPx2 = (14 - 2X2) 0.65 (14 – 2X2) 0.65 = 7
solutions are 2.08 for X1 and 1.6 for X2 Y equal to 53 units

Profit = 0.65 (53) - 9 (2.08) - 7 (1.60) - TFC= Rs. 4.53 - TFC

 optimum criterion

All variable inputs must be earning as much as they cost on the margin

The above expression is the same as MR = MC under perfect competition